From 1fb669ccbeed6b66465cc2bbec3e7726787b04d6 Mon Sep 17 00:00:00 2001 From: EscapedGibbon Date: Fri, 27 Jun 2025 18:45:51 +0200 Subject: [PATCH 01/16] docs: wip add documentation on the new version of transform function --- docs/Features/Geometry/Transform.md | 24 +- .../Applying transform function on images.md | 348 ++++++++++++++++++ .../transformations/affine-transform.gif | Bin 0 -> 181970 bytes .../images/transformations/image.png | Bin 0 -> 19796 bytes 4 files changed, 364 insertions(+), 8 deletions(-) create mode 100644 docs/Tutorials/Applying transform function on images.md create mode 100644 docs/Tutorials/images/transformations/affine-transform.gif create mode 100644 docs/Tutorials/images/transformations/image.png diff --git a/docs/Features/Geometry/Transform.md b/docs/Features/Geometry/Transform.md index 05c30644..67afb6ac 100644 --- a/docs/Features/Geometry/Transform.md +++ b/docs/Features/Geometry/Transform.md @@ -10,20 +10,28 @@ _Applies linear transformations to an image, such as scaling, rotation, skewing, [🖼️ Image options and parameters of `transform` method](https://image-js.github.io/image-js-typescript/classes/Image.html#transform 'github.io link') -`transform` method uses transformation matrix to rotate, translate, and/or scale the image. User needs to pass on the matrix that will be applied to the image. Matrix must have 2 rows and 3 columns: +`transform` method uses transformation matrix to rotate, translate, and/or scale the image. +User needs to pass on the matrix that will be applied to the image. Matrix must have 2 rows and 3 columns: $$ \begin{bmatrix} -1 & 2 & 3\\ -a & b & c +a & b & c\\ +d & e & f \\ +g & h & i \end{bmatrix} $$ -Where the first two columns are responsible for image [rotation](https://en.wikipedia.org/wiki/Rotation 'wikipedia link on rotation') and [shear](https://en.wikipedia.org/wiki/Shear_mapping 'wikipedia link on image shearing'), while last column is responsible for image [translation]( 'wikipedia link on translation'). - -:::caution -Matrix cannot be singular. Otherwise it cannot be inverted. Click [here](https://en.wikipedia.org/wiki/Invertible_matrix 'wikipedia link on invertible matrices') to learn more. -::: +Where + +- the first `a` and `e` are responsible for image scaling +- `b` and `d` are responsible for [shear](https://en.wikipedia.org/wiki/Shear_mapping 'wikipedia link on image shearing'). Combination of these 4 variables allows [rotating](https://en.wikipedia.org/wiki/Rotations_and_reflections_in_two_dimensions 'wikipedia link on rotation'). `c` and `f` are responsible for image [translation]( 'wikipedia link on translation'). +- `g` and `h` are used for an operation called projection. + :::note + `transform()` function can accept 2x3 as well as 3x3 matrix. If matrix's size is 2x3 that it becomes an affine transformation. This means that transformation happens on the same + ::: + :::caution + Matrix cannot be singular. Otherwise it cannot be inverted. Click [here](https://en.wikipedia.org/wiki/Invertible_matrix 'wikipedia link on invertible matrices') to learn more. + ::: diff --git a/docs/Tutorials/Applying transform function on images.md b/docs/Tutorials/Applying transform function on images.md new file mode 100644 index 00000000..75f58a25 --- /dev/null +++ b/docs/Tutorials/Applying transform function on images.md @@ -0,0 +1,348 @@ +## Synopsis + +Image transformations are fundamental operations in computer graphics and image processing that allow you to manipulate the position, size, shape, and perspective of images. This tutorial covers both affine and projective transformations, providing practical examples and clear explanations of how each parameter affects your image. + +![Affine transformations](./images/transformations/affine-transform.gif); + +## Understanding Transformation Types + +In this tutorial, we distinguish between two primary types of transformations: + +### Affine Transformations + +- **Preserve**: Collinearity and ratios of distances +- **Properties**: Parallel lines remain parallel, straight lines remain straight +- **Use cases**: Scaling, rotation, translation, shearing +- **Matrix size**: 2×3 (the bottom row [0, 0, 1] is implied) + +### Projective Transformations + +- **Preserve**: Only collinearity (straight lines remain straight) +- **Properties**: Parallel lines may converge, creates perspective effects +- **Use cases**: Perspective correction, 3D projections, keystone correction +- **Matrix size**: 3×3 (full matrix required) +- **The key difference**: affine transformations might stretch, rotate, or shift a rectangle, but parallel lines remain parallel. Projective transformations can make a rectangle appear tilted or receding into the distance, with parallel lines converging to vanishing points. + +## The Transformation Matrix + +We use this 3×3 matrix throughout the tutorial: + +$$ +\begin{bmatrix} +a & b & c\\ +d & e & f \\ +g & h & i +\end{bmatrix} +$$ + +Each parameter controls specific aspects of the transformation: + +`a`, `e`: Scaling (horizontal and vertical) +`b`, `d`: Shearing and rotation +`c`, `f`: Translation (horizontal and vertical) +`g`, `h`: Perspective distortion +`i`: Normalization factor (usually 1) + +## Getting Started + +First, let's load an image: + +```ts +import { readSync } from 'image-processing-library'; + +const image = readSync('/path/to/image.png'); +``` + +## Affine Transformations + +1. Scaling + Scaling changes the size of your image. Parameters a and e control horizontal and vertical scaling respectively. + +Uniform Scaling (Maintaining Aspect Ratio) + +```ts +// Scale image by factor of 2 (double the size) +const transformationMatrix = [ + [2, 0, 0], // a=2 (horizontal scale), b=0, c=0 + [0, 2, 0], // d=0, e=2 (vertical scale), f=0 +]; + +const scaledImage = image.transform(transformationMatrix); +``` + +### Non-uniform Scaling + +```ts +// Stretch horizontally by 3x, compress vertically by 0.5x +const transformationMatrix = [ + [3, 0, 0], // Horizontal stretch + [0, 0.5, 0], // Vertical compression +]; + +const stretchedImage = image.transform(transformationMatrix); +``` + +#### Common Scaling Examples + +```ts +// Shrink to half size +const shrinkMatrix = [ + [0.5, 0, 0], + [0, 0.5, 0], +]; + +// Mirror horizontally (flip left-right) +const mirrorMatrix = [ + [-1, 0, 0], + [0, 1, 0], +]; + +// Mirror vertically (flip up-down) +const flipMatrix = [ + [1, 0, 0], + [0, -1, 0], +]; +``` + +### Translation + +Translation moves your image to a different position. Parameters `c` and `f` control horizontal and vertical movement. + +```ts +// Move image 50 pixels right and 30 pixels down +const translationMatrix = [ + [1, 0, 50], // c=50 (move right) + [0, 1, 30], // f=30 (move down) +]; + +const translatedImage = image.transform(translationMatrix); + +// Move image 100 pixels left and 50 pixels up +const moveMatrix = [ + [1, 0, -100], // Negative values move left + [0, 1, -50], // Negative values move up +]; +``` + +### Rotation + +Rotation transforms your image around a point (typically the origin). It uses a combination of parameters a, b, d, and e. + +For rotation by angle θ (in radians): + +`a` = cos(θ) +`b` = -sin(θ) +`d` = sin(θ) +`e` = cos(θ) + +```ts +// Rotate 45 degrees clockwise +const angle = Math.PI / 4; // 45 degrees in radians +const rotationMatrix = [ + [Math.cos(angle), -Math.sin(angle), 0], + [Math.sin(angle), Math.cos(angle), 0], +]; + +const rotatedImage = image.transform(rotationMatrix); + +// Rotate 90 degrees counter-clockwise +const rotation90Matrix = [ + [0, 1, 0], // cos(90°)=0, -sin(90°)=-(-1)=1 + [-1, 0, 0], // sin(90°)=1, cos(90°)=0 +]; +``` + +### Rotation Around Image Center + +To rotate around the image center instead of the origin, combine translation with rotation: + +```ts +function rotateAroundCenter(image, angle) { + const centerX = image.width / 2; + const centerY = image.height / 2; + + const cos = Math.cos(angle); + const sin = Math.sin(angle); + + // Translate to origin, rotate, translate back + const matrix = [ + [cos, -sin, centerX * (1 - cos) + centerY * sin], + [sin, cos, centerY * (1 - cos) - centerX * sin], + ]; + + return image.transform(matrix); +} + +const centeredRotation = rotateAroundCenter(image, Math.PI / 6); // 30 degrees +``` + +### Shearing + +Shearing skews the image, making rectangles appear as parallelograms. Parameters b and d control shearing. + +```ts +// Horizontal shear - lean the image to the right +const horizontalShearMatrix = [ + [1, 0.5, 0], // b=0.5 creates horizontal shear + [0, 1, 0], +]; + +// Vertical shear - lean the image upward +const verticalShearMatrix = [ + [1, 0, 0], + [0.3, 1, 0], // d=0.3 creates vertical shear +]; + +// Combined shearing +const combinedShearMatrix = [ + [1, 0.5, 0], // Horizontal shear + [0.3, 1, 0], // Vertical shear +]; +``` + +### Complex Affine Transformations + +You can combine multiple transformations by multiplying matrices or applying them sequentially: + +```ts +// Scale, rotate, and translate in one transformation +const angle = Math.PI / 4; +const scale = 1.5; +const translateX = 100; +const translateY = 50; + +const complexMatrix = [ + [scale * Math.cos(angle), -scale * Math.sin(angle), translateX], + [scale * Math.sin(angle), scale * Math.cos(angle), translateY], +]; + +const complexTransform = image.transform(complexMatrix); +``` + +## Projective Transformations + +Projective transformations use the full 3×3 matrix, including the bottom row parameters `g`, `h`, and `i`. These create perspective effects and can map rectangular images onto quadrilaterals. + +### Understanding Perspective Parameters + +`g`, `h`: Control perspective distortion +`i`: Normalization factor (typically 1) + +```ts +// Simple perspective transformation +const perspectiveMatrix = [ + [1, 0, 0], // Standard scaling and translation + [0, 1, 0], + [0.001, 0, 1], // g=0.001 creates horizontal perspective +]; + +const perspectiveImage = image.transform(perspectiveMatrix); +``` + +### Four-Point Mapping + +The most common use of projective transformation is mapping an image to fit within four corner points: + +```ts +// Define source corners (original image corners) +const sourcePoints = [ + [0, 0], // Top-left + [image.width, 0], // Top-right + [image.width, image.height], // Bottom-right + [0, image.height], // Bottom-left +]; + +// Define destination corners (where you want them to appear) +const destPoints = [ + [50, 100], // Top-left moved + [300, 80], // Top-right + [320, 250], // Bottom-right + [30, 280], // Bottom-left +]; + +// Calculate transformation matrix (implementation depends on library) +const projectionMatrix = calculateProjectionMatrix(sourcePoints, destPoints); +const projectedImage = image.transform(projectionMatrix); +``` + +### Keystone Correction + +Correcting perspective distortion (like photographing a screen at an angle): + +```ts +// Correct keystone effect - make trapezoid into rectangle +const keystoneMatrix = [ + [1.2, 0.1, -50], + [0.05, 1.1, -20], + [0.0002, 0.0001, 1], +]; + +const correctedImage = image.transform(keystoneMatrix); +``` + +## Practical Examples and Use Cases + +### Creating Thumbnails with Proper Aspect Ratio + +```ts +function createThumbnail(image, maxWidth, maxHeight) { + const scaleX = maxWidth / image.width; + const scaleY = maxHeight / image.height; + const scale = Math.min(scaleX, scaleY); // Maintain aspect ratio + + const thumbnailMatrix = [ + [scale, 0, 0], + [0, scale, 0], + ]; + + return image.transform(thumbnailMatrix); +} +``` + +### Photo Straightening + +```ts +function straightenPhoto(image, angleDegrees) { +const angle = (angleDegrees \* Math.PI) / 180; +const centerX = image.width / 2; +const centerY = image.height / 2; + +const cos = Math.cos(-angle); // Negative for correction +const sin = Math.sin(-angle); + +const matrix = [ +[cos, -sin, centerX * (1 - cos) + centerY * sin], +[sin, cos, centerY * (1 - cos) - centerX * sin], +]; + +return image.transform(matrix); +} +``` + +### Document Scanning Perspective Correction + +```ts +function correctDocumentPerspective(image, corners) { + // corners should be [topLeft, topRight, bottomRight, bottomLeft] + const [tl, tr, br, bl] = corners; + + // Calculate document dimensions + const width = Math.max(distance(tl, tr), distance(bl, br)); + const height = Math.max(distance(tl, bl), distance(tr, br)); + + // Target rectangle corners + const targetCorners = [ + [0, 0], + [width, 0], + [width, height], + [0, height], + 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121 +++++++++--------- .../transformations/lennaCombinedShear.png | Bin 0 -> 240162 bytes .../images/transformations/lennaFlipped.png | Bin 0 -> 279851 bytes .../transformations/lennaHorizontalShear.png | Bin 0 -> 256659 bytes .../images/transformations/lennaMirrorred.png | Bin 0 -> 279113 bytes .../images/transformations/lennaRotated.png | Bin 0 -> 205655 bytes .../transformations/lennaRotatedCenter.png | Bin 0 -> 264320 bytes .../images/transformations/lennaScaled.png | Bin 0 -> 596603 bytes .../images/transformations/lennaShrunk.png | Bin 0 -> 184401 bytes .../images/transformations/lennaStretched.png | Bin 0 -> 318242 bytes .../transformations/lennaTranslated.png | Bin 0 -> 259639 bytes .../transformations/lennaVerticalShear.png | Bin 0 -> 263637 bytes 12 files changed, 62 insertions(+), 59 deletions(-) create mode 100644 docs/Tutorials/images/transformations/lennaCombinedShear.png create mode 100644 docs/Tutorials/images/transformations/lennaFlipped.png create mode 100644 docs/Tutorials/images/transformations/lennaHorizontalShear.png create mode 100644 docs/Tutorials/images/transformations/lennaMirrorred.png create mode 100644 docs/Tutorials/images/transformations/lennaRotated.png create mode 100644 docs/Tutorials/images/transformations/lennaRotatedCenter.png create mode 100644 docs/Tutorials/images/transformations/lennaScaled.png create mode 100644 docs/Tutorials/images/transformations/lennaShrunk.png create mode 100644 docs/Tutorials/images/transformations/lennaStretched.png create mode 100644 docs/Tutorials/images/transformations/lennaTranslated.png create mode 100644 docs/Tutorials/images/transformations/lennaVerticalShear.png diff --git a/docs/Tutorials/Applying transform function on images.md b/docs/Tutorials/Applying transform function on images.md index 75f58a25..836d5f9f 100644 --- a/docs/Tutorials/Applying transform function on images.md +++ b/docs/Tutorials/Applying transform function on images.md @@ -37,11 +37,11 @@ $$ Each parameter controls specific aspects of the transformation: -`a`, `e`: Scaling (horizontal and vertical) -`b`, `d`: Shearing and rotation -`c`, `f`: Translation (horizontal and vertical) -`g`, `h`: Perspective distortion -`i`: Normalization factor (usually 1) +- `a`, `e`: Scaling (horizontal and vertical) +- `b`, `d`: Shearing and rotation +- `c`, `f`: Translation (horizontal and vertical) +- `g`, `h`: Perspective distortion +- `i`: Normalization factor (usually 1) ## Getting Started @@ -55,13 +55,12 @@ const image = readSync('/path/to/image.png'); ## Affine Transformations -1. Scaling - Scaling changes the size of your image. Parameters a and e control horizontal and vertical scaling respectively. +### Scaling -Uniform Scaling (Maintaining Aspect Ratio) +Scaling changes the size of your image. Parameters a and e control horizontal and vertical scaling respectively. ```ts -// Scale image by factor of 2 (double the size) +// Scale image by factor of 2 (Maintaining Aspect Ratio) const transformationMatrix = [ [2, 0, 0], // a=2 (horizontal scale), b=0, c=0 [0, 2, 0], // d=0, e=2 (vertical scale), f=0 @@ -70,6 +69,8 @@ const transformationMatrix = [ const scaledImage = image.transform(transformationMatrix); ``` +![Scaled image](./images/transformations/lennaScaled.png) + ### Non-uniform Scaling ```ts @@ -82,6 +83,8 @@ const transformationMatrix = [ const stretchedImage = image.transform(transformationMatrix); ``` +![Stretched image](./images/transformations/lennaStretched.png) + #### Common Scaling Examples ```ts @@ -90,13 +93,21 @@ const shrinkMatrix = [ [0.5, 0, 0], [0, 0.5, 0], ]; +``` +![Shrunk image](./images/transformations/lennaShrunk.png) + +```ts // Mirror horizontally (flip left-right) const mirrorMatrix = [ [-1, 0, 0], [0, 1, 0], ]; +``` + +![Mirrored image](./images/transformations/lennaMirrorred.png) +```ts // Mirror vertically (flip up-down) const flipMatrix = [ [1, 0, 0], @@ -104,6 +115,8 @@ const flipMatrix = [ ]; ``` +![Flipped image](./images/transformations/lennaFlipped.png) + ### Translation Translation moves your image to a different position. Parameters `c` and `f` control horizontal and vertical movement. @@ -116,24 +129,20 @@ const translationMatrix = [ ]; const translatedImage = image.transform(translationMatrix); - -// Move image 100 pixels left and 50 pixels up -const moveMatrix = [ - [1, 0, -100], // Negative values move left - [0, 1, -50], // Negative values move up -]; ``` +![Translated image](./images/transformations/lennaTranslated.png) + ### Rotation -Rotation transforms your image around a point (typically the origin). It uses a combination of parameters a, b, d, and e. +Rotation transforms your image around a point (typically the origin). It uses a combination of parameters `a`, `b`, `d`, and `e`. For rotation by angle θ (in radians): -`a` = cos(θ) -`b` = -sin(θ) -`d` = sin(θ) -`e` = cos(θ) +- `a` = cos(θ) +- `b` = -sin(θ) +- `d` = sin(θ) +- `e` = cos(θ) ```ts // Rotate 45 degrees clockwise @@ -144,38 +153,38 @@ const rotationMatrix = [ ]; const rotatedImage = image.transform(rotationMatrix); - -// Rotate 90 degrees counter-clockwise -const rotation90Matrix = [ - [0, 1, 0], // cos(90°)=0, -sin(90°)=-(-1)=1 - [-1, 0, 0], // sin(90°)=1, cos(90°)=0 -]; ``` +![Rotated image](./images/transformations/lennaRotated.png) + ### Rotation Around Image Center To rotate around the image center instead of the origin, combine translation with rotation: ```ts -function rotateAroundCenter(image, angle) { - const centerX = image.width / 2; - const centerY = image.height / 2; - - const cos = Math.cos(angle); - const sin = Math.sin(angle); +const angle = Math.PI / 4; //45 degrees +const [centerX, centerY] = image.getCoordinates('center'); - // Translate to origin, rotate, translate back - const matrix = [ - [cos, -sin, centerX * (1 - cos) + centerY * sin], - [sin, cos, centerY * (1 - cos) - centerX * sin], - ]; +const cos = Math.cos(angle); +const sin = Math.sin(angle); - return image.transform(matrix); -} +// Translate to origin, rotate, translate back +const matrix = [ + [cos, -sin, centerX * (1 - cos) + centerY * sin], + [sin, cos, centerY * (1 - cos) - centerX * sin], +]; -const centeredRotation = rotateAroundCenter(image, Math.PI / 6); // 30 degrees +return image.transform(matrix); ``` +:::note +Image-js has functions `rotate()` and `transformRotate()`. `rotate()` function allows rotating an image by multiple of 90 degrees. +`transformRotate()` allows rotating an image by any degree. It also allows choosing the axe of rotation. So, for rotation, you have other functions that allow you to perform it. +Current tutorial just demonstrates the basic principle behind transformation of such kind. +::: + +![Rotated by center image](./images/transformations/lennaRotatedCenter.png) + ### Shearing Shearing skews the image, making rectangles appear as parallelograms. Parameters b and d control shearing. @@ -186,13 +195,21 @@ const horizontalShearMatrix = [ [1, 0.5, 0], // b=0.5 creates horizontal shear [0, 1, 0], ]; +``` +![Horizontally sheared image](./images/transformations/lennaHorizontalShear.png) + +```ts // Vertical shear - lean the image upward const verticalShearMatrix = [ [1, 0, 0], [0.3, 1, 0], // d=0.3 creates vertical shear ]; +``` + +![Vertically sheared image](./images/transformations/lennaVerticalShear.png) +```ts // Combined shearing const combinedShearMatrix = [ [1, 0.5, 0], // Horizontal shear @@ -200,6 +217,8 @@ const combinedShearMatrix = [ ]; ``` +![Combined shearing](./images/transformations/lennaCombinedShear.png) + ### Complex Affine Transformations You can combine multiple transformations by multiplying matrices or applying them sequentially: @@ -260,8 +279,8 @@ const destPoints = [ [30, 280], // Bottom-left ]; -// Calculate transformation matrix (implementation depends on library) -const projectionMatrix = calculateProjectionMatrix(sourcePoints, destPoints); +// Get transformation matrix using 4 points +const projectionMatrix = getPerspectiveWarp(sourcePoints); const projectedImage = image.transform(projectionMatrix); ``` @@ -326,23 +345,7 @@ function correctDocumentPerspective(image, corners) { // corners should be [topLeft, topRight, bottomRight, bottomLeft] const [tl, tr, br, bl] = corners; - // Calculate document dimensions - const width = Math.max(distance(tl, tr), distance(bl, br)); - const height = Math.max(distance(tl, bl), distance(tr, br)); - - // Target rectangle corners - const targetCorners = [ - [0, 0], - [width, 0], - [width, height], - [0, height], - ]; - - const matrix = calculateProjectionMatrix(corners, targetCorners); + const matrix = getPerspectiveWarp(corners{}); return image.transform(matrix); } - -function distance(p1, p2) { - return Math.sqrt((p1[0] - p2[0]) ** 2 + (p1[1] - p2[1]) ** 2); -} ``` diff --git 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+++++------------- .../images/transformations/buildings.jpg | Bin 0 -> 59478 bytes .../transformations/card-perspectiveWarp.png | Bin 0 -> 748316 bytes .../Tutorials/images/transformations/card.png | Bin 0 -> 677215 bytes 4 files changed, 29 insertions(+), 70 deletions(-) create mode 100644 docs/Tutorials/images/transformations/buildings.jpg create mode 100644 docs/Tutorials/images/transformations/card-perspectiveWarp.png create mode 100644 docs/Tutorials/images/transformations/card.png diff --git a/docs/Tutorials/Applying transform function on images.md b/docs/Tutorials/Applying transform function on images.md index 836d5f9f..d6c02330 100644 --- a/docs/Tutorials/Applying transform function on images.md +++ b/docs/Tutorials/Applying transform function on images.md @@ -163,15 +163,15 @@ To rotate around the image center instead of the origin, combine translation wit ```ts const angle = Math.PI / 4; //45 degrees -const [centerX, centerY] = image.getCoordinates('center'); +const center = image.getCoordinates('center'); const cos = Math.cos(angle); const sin = Math.sin(angle); // Translate to origin, rotate, translate back const matrix = [ - [cos, -sin, centerX * (1 - cos) + centerY * sin], - [sin, cos, centerY * (1 - cos) - centerX * sin], + [cos, -sin, center.column * (1 - cos) + center.row * sin], + [sin, cos, center.row * (1 - cos) - center.column * sin], ]; return image.transform(matrix); @@ -262,31 +262,41 @@ const perspectiveImage = image.transform(perspectiveMatrix); The most common use of projective transformation is mapping an image to fit within four corner points: +![Corrected perspective](./images/transformations/card.png); + ```ts -// Define source corners (original image corners) +const image = readSync('path/to/file.png'); +// Define source corners (original image points) and destination image width and height. +// Width and height can be omitted. In this case width and height will be calculated from points. const sourcePoints = [ - [0, 0], // Top-left - [image.width, 0], // Top-right - [image.width, image.height], // Bottom-right - [0, image.height], // Bottom-left -]; - -// Define destination corners (where you want them to appear) -const destPoints = [ - [50, 100], // Top-left moved - [300, 80], // Top-right - [320, 250], // Bottom-right - [30, 280], // Bottom-left + [ + { column: 55, row: 140 }, + { column: 680, row: 38 }, + { column: 840, row: 340 }, + { column: 145, row: 460 }, + ], + { width: 725, height: 425 }, ]; -// Get transformation matrix using 4 points +// Get transformation matrix using 4 points and `getPerspectiveWarp` function. const projectionMatrix = getPerspectiveWarp(sourcePoints); -const projectedImage = image.transform(projectionMatrix); +const projectedImage = image.transform(matrix.matrix, { + width: matrix.width, + height: matrix.height, + inverse: true, +}); ``` +![Corrected perspective](./images/transformations/card-perspectiveWarp.png); + ### Keystone Correction -Correcting perspective distortion (like photographing a screen at an angle): +Correcting perspective distortion (like photographing a screen at an angle). Let's take this image +as an example. + +![Keystone image](./images/transformations/buildings.jpg) + +A common problem when taking photos of tall buildings is that they can look as if they're leaning backwards. This is known as the "keystone effect" (or the "tombstone effect"), and it can be a very distracting form of distortion in your images. ```ts // Correct keystone effect - make trapezoid into rectangle @@ -298,54 +308,3 @@ const keystoneMatrix = [ const correctedImage = image.transform(keystoneMatrix); ``` - -## Practical Examples and Use Cases - -### Creating Thumbnails with Proper Aspect Ratio - -```ts -function createThumbnail(image, maxWidth, maxHeight) { - const scaleX = maxWidth / image.width; - const scaleY = maxHeight / image.height; - const scale = Math.min(scaleX, scaleY); // Maintain aspect ratio - - const thumbnailMatrix = [ - [scale, 0, 0], - [0, scale, 0], - ]; - - return image.transform(thumbnailMatrix); -} -``` - -### Photo Straightening - -```ts -function straightenPhoto(image, angleDegrees) { -const angle = (angleDegrees \* Math.PI) / 180; -const centerX = image.width / 2; -const centerY = image.height / 2; - -const cos = Math.cos(-angle); // Negative for correction -const sin = Math.sin(-angle); - -const matrix = [ -[cos, -sin, centerX * (1 - cos) + centerY * sin], -[sin, cos, centerY * (1 - cos) - centerX * sin], -]; - -return image.transform(matrix); -} -``` - -### Document Scanning Perspective Correction - -```ts -function correctDocumentPerspective(image, corners) { - // corners should be [topLeft, topRight, bottomRight, bottomLeft] - const [tl, tr, br, bl] = corners; - - const matrix = getPerspectiveWarp(corners{}); - return image.transform(matrix); -} -``` diff --git a/docs/Tutorials/images/transformations/buildings.jpg b/docs/Tutorials/images/transformations/buildings.jpg new file mode 100644 index 0000000000000000000000000000000000000000..a0726b6cfdab78d1ef88602572b1876b74317283 GIT binary patch literal 59478 zcmb4qRa9I}ul1SBNHPsrFP$e%wW<6~l>VG|ROk`NOR5s^`` z(2`LwQ4$f+@zOJ~v2$^8k<#)D^Kl5VaB^|{w+Ivx5)$%fWIPlUJPvXqa*qFRdjAc; zK!nPHwugbD06=3v!C*kW{{avJ0MIZ{P*8yXM^Ml(uyF7QA58oY#((txc!2+5zOMj~ 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zhpq>bk_#)wtZRGZ7ig}6MV#=(YUYba%6)Gh#y;a%N1SD`ai6BP?u;6FTU1Kw!{%S8 z(m%ux0sX!c#n0LluLFq}*Y$C-tY{UlRUIy?>vS&j`IkG3`N^hT(Zcm%Pmda5X4fQ6 zJJ;g!rzdXga##)-*;@2I;X|S10H=%he|PV{PQ<@M4mbntpX{{%EaNm7|1AEy@c(}) zPE-09Nyi`e_+MOm{FFD;2k*~>=^sn}mHh8~+n;#UKdOI+*Zvw4{H~+?zuJGc&LKta zzq{Q(JL3PaPyT&RKOSUKZV3A4BmVu+fb74${`br_|9SEM)&9{YcS6s?bpHZZ{6px& i^XNb88Uy?quWu$$Qk}IXEr#E~{a~uvkYZ)?;Qt4%MY!ky literal 0 HcmV?d00001 From 942a235f953ccffd450ab328e5a1881531fc9320 Mon Sep 17 00:00:00 2001 From: EscapedGibbon Date: Thu, 3 Jul 2025 10:35:41 +0200 Subject: [PATCH 04/16] docs: add explanation and examples for projective transformation --- .../Applying transform function on images.md | 160 ++++++++++-------- .../transformations/buildingsCorrected.png | Bin 0 -> 382690 bytes .../transformations/buildingsPerspective.png | Bin 0 -> 391223 bytes 3 files changed, 88 insertions(+), 72 deletions(-) create mode 100644 docs/Tutorials/images/transformations/buildingsCorrected.png create mode 100644 docs/Tutorials/images/transformations/buildingsPerspective.png diff --git a/docs/Tutorials/Applying transform function on images.md b/docs/Tutorials/Applying transform function on images.md index d6c02330..db38b2fb 100644 --- a/docs/Tutorials/Applying transform function on images.md +++ b/docs/Tutorials/Applying transform function on images.md @@ -1,11 +1,7 @@ -## Synopsis - Image transformations are fundamental operations in computer graphics and image processing that allow you to manipulate the position, size, shape, and perspective of images. This tutorial covers both affine and projective transformations, providing practical examples and clear explanations of how each parameter affects your image. ![Affine transformations](./images/transformations/affine-transform.gif); -## Understanding Transformation Types - In this tutorial, we distinguish between two primary types of transformations: ### Affine Transformations @@ -13,7 +9,7 @@ In this tutorial, we distinguish between two primary types of transformations: - **Preserve**: Collinearity and ratios of distances - **Properties**: Parallel lines remain parallel, straight lines remain straight - **Use cases**: Scaling, rotation, translation, shearing -- **Matrix size**: 2×3 (the bottom row [0, 0, 1] is implied) +- **Matrix size**: 2×3(the bottom row [0, 0, 1] is implied) ### Projective Transformations @@ -21,7 +17,8 @@ In this tutorial, we distinguish between two primary types of transformations: - **Properties**: Parallel lines may converge, creates perspective effects - **Use cases**: Perspective correction, 3D projections, keystone correction - **Matrix size**: 3×3 (full matrix required) -- **The key difference**: affine transformations might stretch, rotate, or shift a rectangle, but parallel lines remain parallel. Projective transformations can make a rectangle appear tilted or receding into the distance, with parallel lines converging to vanishing points. + +**The key difference** is that affine transformations might stretch, rotate, or shift a rectangle, but parallel lines remain parallel. Projective transformations can make a rectangle appear tilted or receding into the distance, with parallel lines converging to vanishing points. ## The Transformation Matrix @@ -43,21 +40,13 @@ Each parameter controls specific aspects of the transformation: - `g`, `h`: Perspective distortion - `i`: Normalization factor (usually 1) -## Getting Started - -First, let's load an image: - -```ts -import { readSync } from 'image-processing-library'; - -const image = readSync('/path/to/image.png'); -``` +For affine transformation 2x3 matrix will be used, because last row is not necessary for this kind of transformation. ## Affine Transformations ### Scaling -Scaling changes the size of your image. Parameters a and e control horizontal and vertical scaling respectively. +Scaling changes the size of your image. Parameters `a` and `e` control horizontal and vertical scaling respectively. ```ts // Scale image by factor of 2 (Maintaining Aspect Ratio) @@ -93,6 +82,7 @@ const shrinkMatrix = [ [0.5, 0, 0], [0, 0.5, 0], ]; +const shrunkImage = image.transform(shrinkMatrix); ``` ![Shrunk image](./images/transformations/lennaShrunk.png) @@ -103,6 +93,7 @@ const mirrorMatrix = [ [-1, 0, 0], [0, 1, 0], ]; +const mirrorredImage = image.transform(mirrorMatrix); ``` ![Mirrored image](./images/transformations/lennaMirrorred.png) @@ -113,6 +104,7 @@ const flipMatrix = [ [1, 0, 0], [0, -1, 0], ]; +const flippedImage = image.transform(flipMatrix); ``` ![Flipped image](./images/transformations/lennaFlipped.png) @@ -157,37 +149,11 @@ const rotatedImage = image.transform(rotationMatrix); ![Rotated image](./images/transformations/lennaRotated.png) -### Rotation Around Image Center - -To rotate around the image center instead of the origin, combine translation with rotation: - -```ts -const angle = Math.PI / 4; //45 degrees -const center = image.getCoordinates('center'); - -const cos = Math.cos(angle); -const sin = Math.sin(angle); - -// Translate to origin, rotate, translate back -const matrix = [ - [cos, -sin, center.column * (1 - cos) + center.row * sin], - [sin, cos, center.row * (1 - cos) - center.column * sin], -]; - -return image.transform(matrix); -``` - -:::note -Image-js has functions `rotate()` and `transformRotate()`. `rotate()` function allows rotating an image by multiple of 90 degrees. -`transformRotate()` allows rotating an image by any degree. It also allows choosing the axe of rotation. So, for rotation, you have other functions that allow you to perform it. -Current tutorial just demonstrates the basic principle behind transformation of such kind. -::: - -![Rotated by center image](./images/transformations/lennaRotatedCenter.png) - ### Shearing -Shearing skews the image, making rectangles appear as parallelograms. Parameters b and d control shearing. +Shearing skews the image, making rectangles appear as parallelograms. Parameters `b` and `d` control shearing. + +#### Horizontal shearing ```ts // Horizontal shear - lean the image to the right @@ -195,26 +161,36 @@ const horizontalShearMatrix = [ [1, 0.5, 0], // b=0.5 creates horizontal shear [0, 1, 0], ]; + +const horizontalShearImage = image.transform(horizontalShearMatrix); ``` ![Horizontally sheared image](./images/transformations/lennaHorizontalShear.png) +#### Vertical shearing + ```ts // Vertical shear - lean the image upward const verticalShearMatrix = [ [1, 0, 0], [0.3, 1, 0], // d=0.3 creates vertical shear ]; + +const verticalShearImage = image.transform(vertcialShearMatrix); ``` ![Vertically sheared image](./images/transformations/lennaVerticalShear.png) +#### Combined shearing + ```ts // Combined shearing const combinedShearMatrix = [ [1, 0.5, 0], // Horizontal shear [0.3, 1, 0], // Vertical shear ]; + +const combinedShearImage = image.transform(combinedShearMatrix); ``` ![Combined shearing](./images/transformations/lennaCombinedShear.png) @@ -222,42 +198,66 @@ const combinedShearMatrix = [ ### Complex Affine Transformations You can combine multiple transformations by multiplying matrices or applying them sequentially: +For example, to rotate around the image center instead of the origin, combine translation with rotation: ```ts -// Scale, rotate, and translate in one transformation -const angle = Math.PI / 4; -const scale = 1.5; -const translateX = 100; -const translateY = 50; - -const complexMatrix = [ - [scale * Math.cos(angle), -scale * Math.sin(angle), translateX], - [scale * Math.sin(angle), scale * Math.cos(angle), translateY], +const angle = Math.PI / 4; //45 degrees +const center = image.getCoordinates('center'); + +const cos = Math.cos(angle); +const sin = Math.sin(angle); + +// Translate to origin, rotate, translate back +const matrix = [ + [cos, -sin, center.column * (1 - cos) + center.row * sin], + [sin, cos, center.row * (1 - cos) - center.column * sin], ]; -const complexTransform = image.transform(complexMatrix); +return image.transform(matrix); ``` +![Rotated by center image](./images/transformations/lennaRotatedCenter.png) + +:::note +Image-js has functions `rotate()` and `transformRotate()`. `rotate()` function allows rotating an image by multiple of 90 degrees. +`transformRotate()` allows rotating an image by any degree. It also allows choosing the axe of rotation. So, for rotation, you have other functions that allow you to perform it. +Current tutorial just demonstrates the basic principle behind transformation of such kind. +::: + ## Projective Transformations Projective transformations use the full 3×3 matrix, including the bottom row parameters `g`, `h`, and `i`. These create perspective effects and can map rectangular images onto quadrilaterals. ### Understanding Perspective Parameters -`g`, `h`: Control perspective distortion -`i`: Normalization factor (typically 1) +- `g`, `h`: control horizontal and vertical perspective distortion. +- `i`: Normalization factor (typically 1). It simulates what happens in real vision: + +1. `i` < 1: Objects farther away appear smaller +2. `i` > 1: Objects closer appear larger +3. The division by w' mathematically recreates this effect + +The normalization factor is essentially artificial depth - it makes flat 2D coordinates behave as if they exist in 3D space with varying distances from the viewer. +The distortion allows modifying the angle under which you look at the image. ```ts -// Simple perspective transformation const perspectiveMatrix = [ - [1, 0, 0], // Standard scaling and translation + [1, 0, 0], [0, 1, 0], - [0.001, 0, 1], // g=0.001 creates horizontal perspective + [0.001, -0.0002, 1], ]; - -const perspectiveImage = image.transform(perspectiveMatrix); +const perspectiveImage = newImage.transform(perspectiveMatrix, { + //using fullImage:true to show all the pixels. + fullImage: true, + // using bicubic interpolation for a more detailed image. + interpolationType: 'bicubic', +}); ``` +![Perspective image](./images/transformations/buildingsPerspective.png) + +Now, let's take a look at practical uses of such transformation. + ### Four-Point Mapping The most common use of projective transformation is mapping an image to fit within four corner points: @@ -267,7 +267,7 @@ The most common use of projective transformation is mapping an image to fit with ```ts const image = readSync('path/to/file.png'); // Define source corners (original image points) and destination image width and height. -// Width and height can be omitted. In this case width and height will be calculated from points. +// In this case they correspond to credit card's corner points. const sourcePoints = [ [ { column: 55, row: 140 }, @@ -289,22 +289,38 @@ const projectedImage = image.transform(matrix.matrix, { ![Corrected perspective](./images/transformations/card-perspectiveWarp.png); +:::note +For calculating perspective warp matrix, width and height can be omitted as options. +In that case, they will be calculated from source points. +::: + ### Keystone Correction -Correcting perspective distortion (like photographing a screen at an angle). Let's take this image -as an example. +Let's take this image again as an example. ![Keystone image](./images/transformations/buildings.jpg) -A common problem when taking photos of tall buildings is that they can look as if they're leaning backwards. This is known as the "keystone effect" (or the "tombstone effect"), and it can be a very distracting form of distortion in your images. +A common problem when taking photos of tall buildings is that they can look as if they're leaning backwards. This is known as the "[keystone effect](https://en.wikipedia.org/wiki/Keystone_effect)" (or the "tombstone effect"), and it can be a very distracting form of distortion in your images. ```ts -// Correct keystone effect - make trapezoid into rectangle -const keystoneMatrix = [ - [1.2, 0.1, -50], - [0.05, 1.1, -20], - [0.0002, 0.0001, 1], -]; +// Correcting keystone effect - make trapezoid into rectangle. These points work for an image with +//buildings. For more automatic approach you need to use something more advanced. +const keystoneMatrix = getPerspectiveWarp([ + { column: 60, row: 0 }, + { column: newImage.width - 59, row: 0 }, + { column: newImage.width - 1, row: newImage.height - 1 }, + { column: 0, row: newImage.height - 1 }, +]); + +const correctedImage = newImage.transform(keystoneMatrix.matrix, { + inverse: true, + width: newImage.width, + height: newImage.height, + // Using bicubic interpolation for better image quality. + interpolationType: 'bicubic', +}); const correctedImage = image.transform(keystoneMatrix); ``` + +![Corrected keystone effect](./images/transformations/buildingsCorrected.png) diff --git a/docs/Tutorials/images/transformations/buildingsCorrected.png b/docs/Tutorials/images/transformations/buildingsCorrected.png new file mode 100644 index 0000000000000000000000000000000000000000..288d047f729a99cb8e5a7e9ecd52a03fe74be886 GIT binary patch literal 382690 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zOEdzg>zX{z$b>-ah=`6N%aK)%4+5<$_^{Fp*CHl+ahF{Bytf3~4~3T{XV0AB_$Ynn zRaW%FViFl+iUAKoXG8(Uq~gVNHeAWcYd84(lh25)<^1?8BR}VjS6)W$!tGo-Pgynw<5NXjh{2IHo{G=)xccJt zV*upqG5kd;$T|%wZT{6mlf#egoCpYVT_TlYT-98=y2axsjyx}T;l)eTb;qq+cOb%N zx9{U@AX6nfTjx2mwSzYuzUd%DG684HlF+tf#Rf&bLEANae&;jZz9e|_n#MkP$VYdU zi1BlL>y=lSH;OklFL3{p4|!lU%eG@49W&pt?+x{$!I|V0;GJiBI3rVIM47R*HD<9m zVllH2JTjzi+9*>j7IW~9`Et&(ofD)+=^PO?k?@~G2>)jHar>t+K3RTgCp}xw*0c3% at^W(zbsrN@OaCMQ0000 Date: Thu, 3 Jul 2025 10:42:41 +0200 Subject: [PATCH 05/16] docs: fix spelling mistakes --- docs/Tutorials/Applying transform function on images.md | 4 ++-- project-words.txt | 2 +- 2 files changed, 3 insertions(+), 3 deletions(-) diff --git a/docs/Tutorials/Applying transform function on images.md b/docs/Tutorials/Applying transform function on images.md index db38b2fb..517fb05f 100644 --- a/docs/Tutorials/Applying transform function on images.md +++ b/docs/Tutorials/Applying transform function on images.md @@ -93,7 +93,7 @@ const mirrorMatrix = [ [-1, 0, 0], [0, 1, 0], ]; -const mirrorredImage = image.transform(mirrorMatrix); +const mirroredImage = image.transform(mirrorMatrix); ``` ![Mirrored image](./images/transformations/lennaMirrorred.png) @@ -176,7 +176,7 @@ const verticalShearMatrix = [ [0.3, 1, 0], // d=0.3 creates vertical shear ]; -const verticalShearImage = image.transform(vertcialShearMatrix); +const verticalShearImage = image.transform(verticalShearMatrix); ``` ![Vertically sheared image](./images/transformations/lennaVerticalShear.png) diff --git a/project-words.txt b/project-words.txt index 9c8de749..62066311 100644 --- a/project-words.txt +++ b/project-words.txt @@ -29,4 +29,4 @@ exif electrometric Grayscaling Avgs - +Collinearity From 5f0df191ba826b77ffec4140711a7ee7ae835a34 Mon Sep 17 00:00:00 2001 From: EscapedGibbon Date: Thu, 3 Jul 2025 10:52:19 +0200 Subject: [PATCH 06/16] chore: modify exports in package.json --- package.json | 5 +++++ 1 file changed, 5 insertions(+) diff --git a/package.json b/package.json index 56ca1b78..250ea775 100644 --- a/package.json +++ b/package.json @@ -2,6 +2,11 @@ "name": "image-js-docs", "version": "0.0.0", "private": true, + "main": "docusaurus.config.js", + "exports": { + ".": "./docusaurus.config.js", + "./config": "./docusaurus.config.js" + }, "scripts": { "build": "docusaurus build", "clear": "docusaurus clear", From e23f98b74b27a5dc99124bab2ecaeb42d48b4810 Mon Sep 17 00:00:00 2001 From: EscapedGibbon Date: Thu, 3 Jul 2025 11:37:59 +0200 Subject: [PATCH 07/16] docs: add subtitle for types of transformation --- docs/Tutorials/Applying transform function on images.md | 2 ++ 1 file changed, 2 insertions(+) diff --git a/docs/Tutorials/Applying transform function on images.md b/docs/Tutorials/Applying transform function on images.md index 517fb05f..c38646ea 100644 --- a/docs/Tutorials/Applying transform function on images.md +++ b/docs/Tutorials/Applying transform function on images.md @@ -2,6 +2,8 @@ Image transformations are fundamental operations in computer graphics and image ![Affine transformations](./images/transformations/affine-transform.gif); +## Types of transformation + In this tutorial, we distinguish between two primary types of transformations: ### Affine Transformations From 86dc5b4be0c163c876930b88bdfb652d4fbf94a4 Mon Sep 17 00:00:00 2001 From: EscapedGibbon Date: Thu, 3 Jul 2025 12:34:59 +0200 Subject: [PATCH 08/16] docs: minor doc fixes --- docs/Features/Geometry/Transform.md | 22 ++++++++++------- .../Applying transform function on images.md | 24 +++++++++++-------- 2 files changed, 27 insertions(+), 19 deletions(-) diff --git a/docs/Features/Geometry/Transform.md b/docs/Features/Geometry/Transform.md index 67afb6ac..0f108eed 100644 --- a/docs/Features/Geometry/Transform.md +++ b/docs/Features/Geometry/Transform.md @@ -11,7 +11,7 @@ _Applies linear transformations to an image, such as scaling, rotation, skewing, [🖼️ Image options and parameters of `transform` method](https://image-js.github.io/image-js-typescript/classes/Image.html#transform 'github.io link') `transform` method uses transformation matrix to rotate, translate, and/or scale the image. -User needs to pass on the matrix that will be applied to the image. Matrix must have 2 rows and 3 columns: +User needs to pass on the matrix that will be applied to the image. Matrix must have either 2 rows and 3 columns or 3 rows and 3 columns: $$ \begin{bmatrix} @@ -21,17 +21,21 @@ g & h & i \end{bmatrix} $$ -Where +If 2x3 matrix is passed, the algorithm will consider it as [affine transformation](https://en.wikipedia.org/wiki/Affine_transformation) so last row will be set as `[0,0,1]`; - the first `a` and `e` are responsible for image scaling - `b` and `d` are responsible for [shear](https://en.wikipedia.org/wiki/Shear_mapping 'wikipedia link on image shearing'). Combination of these 4 variables allows [rotating](https://en.wikipedia.org/wiki/Rotations_and_reflections_in_two_dimensions 'wikipedia link on rotation'). `c` and `f` are responsible for image [translation]( 'wikipedia link on translation'). -- `g` and `h` are used for an operation called projection. - :::note - `transform()` function can accept 2x3 as well as 3x3 matrix. If matrix's size is 2x3 that it becomes an affine transformation. This means that transformation happens on the same - ::: - :::caution - Matrix cannot be singular. Otherwise it cannot be inverted. Click [here](https://en.wikipedia.org/wiki/Invertible_matrix 'wikipedia link on invertible matrices') to learn more. - ::: +- `g` and `h` are used for an operation called projection. It allows changing image perspective. +- `i` is a normalization factor. It acts like a "scaling factor" for the entire coordinate system. Think of it as a zoom lens setting. + +For more information take a look at the tutorial about [image transformations](../../Tutorials/Applying%20transform%20function%20on%20images.md) + +:::note +`transform()` function can accept 2x3 as well as 3x3 matrix. If matrix's size is 2x3 that it becomes an affine transformation. This means that transformation happens on the same +::: +:::caution +Matrix cannot be singular. Otherwise it cannot be inverted. Click [here](https://en.wikipedia.org/wiki/Invertible_matrix 'wikipedia link on invertible matrices') to learn more. +::: diff --git a/docs/Tutorials/Applying transform function on images.md b/docs/Tutorials/Applying transform function on images.md index c38646ea..ef232cc7 100644 --- a/docs/Tutorials/Applying transform function on images.md +++ b/docs/Tutorials/Applying transform function on images.md @@ -1,17 +1,21 @@ -Image transformations are fundamental operations in computer graphics and image processing that allow you to manipulate the position, size, shape, and perspective of images. This tutorial covers both affine and projective transformations, providing practical examples and clear explanations of how each parameter affects your image. +In a broader sense of the term, image transformation refers to the process of modifying or converting images from one form to another. This can involve changes to the image's appearance, format, size, or mathematical representation. Therefore converting image's color model from "RGB" format to grayscale can also be considered a transformation. -![Affine transformations](./images/transformations/affine-transform.gif); +In ImageJS, however, `transform()` function does transformations that can be accomplished through [matrix multiplication](https://en.wikipedia.org/wiki/Matrix_multiplication). + +In this tutorial we will cover and explain basic transformation techniques as well as explain how `transform()` function allows us to modify images. ## Types of transformation -In this tutorial, we distinguish between two primary types of transformations: +Here, we distinguish between two primary types of transformations: ### Affine Transformations +![Affine transformations](./images/transformations/affine-transform.gif); + - **Preserve**: Collinearity and ratios of distances - **Properties**: Parallel lines remain parallel, straight lines remain straight - **Use cases**: Scaling, rotation, translation, shearing -- **Matrix size**: 2×3(the bottom row [0, 0, 1] is implied) +- **Matrix size**: 2×3(the bottom row `[0, 0, 1]` is implied) ### Projective Transformations @@ -39,7 +43,7 @@ Each parameter controls specific aspects of the transformation: - `a`, `e`: Scaling (horizontal and vertical) - `b`, `d`: Shearing and rotation - `c`, `f`: Translation (horizontal and vertical) -- `g`, `h`: Perspective distortion +- `g`, `h`: Perspective distortion (horizontal and vertical) - `i`: Normalization factor (usually 1) For affine transformation 2x3 matrix will be used, because last row is not necessary for this kind of transformation. @@ -221,7 +225,7 @@ return image.transform(matrix); ![Rotated by center image](./images/transformations/lennaRotatedCenter.png) :::note -Image-js has functions `rotate()` and `transformRotate()`. `rotate()` function allows rotating an image by multiple of 90 degrees. +Image-js also has `rotate()` and `transformRotate()` functions. `rotate()` function allows rotating an image by multiple of 90 degrees. `transformRotate()` allows rotating an image by any degree. It also allows choosing the axe of rotation. So, for rotation, you have other functions that allow you to perform it. Current tutorial just demonstrates the basic principle behind transformation of such kind. ::: @@ -232,12 +236,12 @@ Projective transformations use the full 3×3 matrix, including the bottom row pa ### Understanding Perspective Parameters -- `g`, `h`: control horizontal and vertical perspective distortion. +- `g`, `h`: control horizontal and vertical perspective distortions. They allow - `i`: Normalization factor (typically 1). It simulates what happens in real vision: -1. `i` < 1: Objects farther away appear smaller -2. `i` > 1: Objects closer appear larger -3. The division by w' mathematically recreates this effect +1. `i` < 1: Objects appear larger +2. `i` > 1: Objects appear smaller +3. The division by `i` mathematically recreates this effect The normalization factor is essentially artificial depth - it makes flat 2D coordinates behave as if they exist in 3D space with varying distances from the viewer. The distortion allows modifying the angle under which you look at the image. From 8da604b06d55c4ddedfa4ae46a0e2972dec65258 Mon Sep 17 00:00:00 2001 From: EscapedGibbon Date: Fri, 4 Jul 2025 14:39:44 +0200 Subject: [PATCH 09/16] docs: resolve conversations --- .github/workflows/nodejs.yml | 1 + docs/Features/Geometry/Geometry.md | 15 ++-- .../Geometry/Get Perspective Warp Matrix.md | 51 +++++++++++ .../Geometry/images/cardPerspective.png | Bin 0 -> 295326 bytes .../Applying transform function on images.md | 85 ++++++++++++++++-- project-words.txt | 1 + 6 files changed, 140 insertions(+), 13 deletions(-) create mode 100644 docs/Features/Geometry/Get Perspective Warp Matrix.md create mode 100644 docs/Features/Geometry/images/cardPerspective.png diff --git a/.github/workflows/nodejs.yml b/.github/workflows/nodejs.yml index 16089e5e..d4284274 100644 --- a/.github/workflows/nodejs.yml +++ b/.github/workflows/nodejs.yml @@ -14,3 +14,4 @@ jobs: npm-test-command: npm run build node-version-matrix: '[18]' upload-coverage: false + disable-test-package: true diff --git a/docs/Features/Geometry/Geometry.md b/docs/Features/Geometry/Geometry.md index 4c5374b0..53bf3534 100644 --- a/docs/Features/Geometry/Geometry.md +++ b/docs/Features/Geometry/Geometry.md @@ -8,10 +8,11 @@ Geometric operations in image processing involve transforming the spatial coordi ### Methods -| Can be applied on | Images | Masks | -| -------------------------------------------------------------------------------------------------------- | ------- | -------- | -| [Flip(`flip`)](./Flip.md 'internal link on flip') | ✅ | ❌ | -| [Resize(`resize`)](./Resize.md 'internal link on resize') | ✅ | ❌ | -| [Rotate(`rotate`)](./Rotate.md 'internal link on rotate') | ✅ | ❌ | -| [Transform(`transform`)](./Transform.md 'internal link on transform') | ✅ | ❌ | -| [Transform and rotate(`transformRotate`)](./Transform%20and%20Rotate 'internal link on transformRotate') | ✅ | ❌ | +| Can be applied on | Images | Masks | +| --------------------------------------------------------------------------------------------------------------------------------- | ------- | -------- | +| [Flip(`flip`)](./Flip.md 'internal link on flip') | ✅ | ❌ | +| [Resize(`resize`)](./Resize.md 'internal link on resize') | ✅ | ❌ | +| [Rotate(`rotate`)](./Rotate.md 'internal link on rotate') | ✅ | ❌ | +| [Transform(`transform`)](./Transform.md 'internal link on transform') | ✅ | ❌ | +| [Transform and rotate(`transformRotate`)](./Transform%20and%20Rotate 'internal link on transformRotate') | ✅ | ❌ | +| [Get perspective warp matrix(`getPerspectiveWarp`)](./Get%20Perspective%20Warp%20Matrix.md 'internal link on getPerspectiveWarp') | - | - | diff --git a/docs/Features/Geometry/Get Perspective Warp Matrix.md b/docs/Features/Geometry/Get Perspective Warp Matrix.md new file mode 100644 index 00000000..5319b4b2 --- /dev/null +++ b/docs/Features/Geometry/Get Perspective Warp Matrix.md @@ -0,0 +1,51 @@ +--- +sidebar_position: 41 +--- + +# Get perspective warp matrix + +_Returns a perspective transformation matrix from source points that transforms a quadrilateral._ + +`getPerspectiveWarp` function takes 4 corner points (source quadrilateral) and then calculates the 3×3 perspective transformation matrix that allows removing [perspective distortion](https://en.wikipedia.org/wiki/Perspective_distortion). +The function also returns width and height of the new image. +If they were put as option's parameters it just returns indicated width and height, otherwise it calculates new width and height from given source points. + +### Basic use case + +```ts +const image = readSync('path/to/file.png'); +// Define source corners (original image points) and destination image width and height. +// In this case they correspond to credit card's corner points. +const sourcePoints = [ + [ + { column: 55, row: 140 }, + { column: 680, row: 38 }, + { column: 840, row: 340 }, + { column: 145, row: 460 }, + ], + { width: 725, height: 425 }, +]; + +// Get transformation matrix using 4 points and `getPerspectiveWarp` function. +const projectionMatrix = getPerspectiveWarp(sourcePoints); +const projectedImage = image.transform(matrix.matrix, { + width: matrix.width, + height: matrix.height, + inverse: true, +}); +``` + +![Basic use case of perspectiveWarp](./images/cardPerspective.png) + +### Parameters and default values + +- `sourcePoints` + +- `options` + +#### Options + +| Property | Required | Default value | +| -------------------------------------------------------------------------------------------------- | -------- | ------------- | +| [`width`](https://image-js.github.io/image-js-typescript/interfaces/ResizeOptions.html#borderType) | no | - | +| [`height`](https://image-js.github.io/image-js-typescript/interfaces/ResizeOptions.html#height) | no | - | diff --git a/docs/Features/Geometry/images/cardPerspective.png b/docs/Features/Geometry/images/cardPerspective.png new file mode 100644 index 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function on images.md +++ b/docs/Tutorials/Applying transform function on images.md @@ -2,7 +2,72 @@ In a broader sense of the term, image transformation refers to the process of mo In ImageJS, however, `transform()` function does transformations that can be accomplished through [matrix multiplication](https://en.wikipedia.org/wiki/Matrix_multiplication). -In this tutorial we will cover and explain basic transformation techniques as well as explain how `transform()` function allows us to modify images. +In this tutorial we will cover and explain basic geometric transformation techniques as well as explain how `transform()` function allows us to modify images. + +## How image transformations work + +[Geometric transformation](https://www.geeksforgeeks.org/electronics-engineering/geometric-transformation-in-image-processing-1/) modifies the location of pixels in an image. It consists of two main steps: + +- Spatial transformation of pixels or coordinates and intensity interpolation. +- Intensity interpolation is used to assign the intensity value of pixels after spatial transformation. + +In a geometric transformation a pixel at coordinate $$(x, y)$$ will be moved to coordinate $$(x', y')$$. That is the coordinate (x', y') of the output image which will have the intensity value of the coordinate (x, y) in the input image. + +In this tutorial we will focus more on spatial transformation and talk more about interpolation another time. Basic geometric transformation is given by the equation in matrix form: + +$$ +\begin{bmatrix} +x' \\ +y' \\ +z' +\end{bmatrix} = A \begin{bmatrix} +x \\ +y \\ +z\end{bmatrix} +=\begin{bmatrix} +a & b & c\\ +d & e & f \\ +g & h & i\\ +\end{bmatrix} +\begin{bmatrix} +x \\ +y \\ +z +\end{bmatrix} +$$ + +where + +- $$(x, y,z)$$ is the input coordinate +- $$(x', y',z')$$ is the output coordinate +- $$A$$ is the affine transformation matrix + +:::note + +### Example of matrix multiplication + +If you are interested to look a bit deeper into matrix multiplications, take a look at the [`ml-matrix`](https://mljs.github.io/matrix/index.html 'link on ml-matrix api') package. +It facilitates basic matrix operations in ImageJS, as well as something more advanced like inverting a matrix. +Here is a basic demo on how to upscale a pixel coordinate by 2 using `ml-matrix` library. + +```ts +import { Matrix } from 'ml-matrix'; + +const matrix = new Matrix([[10], [10], [1]]); + +const transform = new Matrix([ + [2, 0, 0], + [0, 2, 0], + [0, 0, 1], +]); + +const result = transform.mmul(matrix); +/* +gives [20,20,1] as a new coordinate of a pixel. +*/ +``` + +::: ## Types of transformation @@ -80,6 +145,11 @@ const stretchedImage = image.transform(transformationMatrix); ![Stretched image](./images/transformations/lennaStretched.png) +:::note +ImageJS also has [`resize`](../Features/Geometry/Resize.md) function that allows to scale an image. +Current tutorial just demonstrates the basic principle behind transformation of such kind. +::: + #### Common Scaling Examples ```ts @@ -114,6 +184,10 @@ const flippedImage = image.transform(flipMatrix); ``` ![Flipped image](./images/transformations/lennaFlipped.png) +:::note +ImageJS also has [`flip`](../Features/Geometry/Flip.md) function that allows to flip an image. +Current tutorial just demonstrates the basic principle behind transformation of such kind. +::: ### Translation @@ -225,9 +299,8 @@ return image.transform(matrix); ![Rotated by center image](./images/transformations/lennaRotatedCenter.png) :::note -Image-js also has `rotate()` and `transformRotate()` functions. `rotate()` function allows rotating an image by multiple of 90 degrees. +Image-js also has [`rotate()`](../Features/Geometry/Rotate.md) and [`transformRotate()`](../Features/Geometry/Transform%20and%20Rotate.md) functions. `rotate()` function allows rotating an image by multiple of 90 degrees. `transformRotate()` allows rotating an image by any degree. It also allows choosing the axe of rotation. So, for rotation, you have other functions that allow you to perform it. -Current tutorial just demonstrates the basic principle behind transformation of such kind. ::: ## Projective Transformations @@ -286,9 +359,9 @@ const sourcePoints = [ // Get transformation matrix using 4 points and `getPerspectiveWarp` function. const projectionMatrix = getPerspectiveWarp(sourcePoints); -const projectedImage = image.transform(matrix.matrix, { - width: matrix.width, - height: matrix.height, +const projectedImage = image.transform(projectionMatrix.matrix, { + width: projectionMatrix.width, + height: projectionMatrix.height, inverse: true, }); ``` diff --git a/project-words.txt b/project-words.txt index 62066311..5a5b7e36 100644 --- a/project-words.txt +++ b/project-words.txt @@ -30,3 +30,4 @@ electrometric Grayscaling Avgs Collinearity +mmul \ No newline at end of file From f760d2e20520fe85f08c6228b632c7e9b9234a32 Mon Sep 17 00:00:00 2001 From: EscapedGibbon Date: Fri, 4 Jul 2025 14:44:43 +0200 Subject: [PATCH 10/16] docs: explain z value of a coordinate --- docs/Tutorials/Applying transform function on images.md | 2 ++ 1 file changed, 2 insertions(+) diff --git a/docs/Tutorials/Applying transform function on images.md b/docs/Tutorials/Applying transform function on images.md index 6be08438..cbd97f92 100644 --- a/docs/Tutorials/Applying transform function on images.md +++ b/docs/Tutorials/Applying transform function on images.md @@ -42,6 +42,8 @@ where - $$(x', y',z')$$ is the output coordinate - $$A$$ is the affine transformation matrix +It is worth mentioning that we will be working with 2D coordinates, so $$z$$ will be 1 in most cases. + :::note ### Example of matrix multiplication From 9e400c3147f111545075f49625dd2a920282fd8e Mon Sep 17 00:00:00 2001 From: EscapedGibbon Date: Fri, 4 Jul 2025 14:54:17 +0200 Subject: [PATCH 11/16] docs: fix getPerspectiveWarp options --- docs/Features/Geometry/Get Perspective Warp Matrix.md | 8 ++++---- 1 file changed, 4 insertions(+), 4 deletions(-) diff --git a/docs/Features/Geometry/Get Perspective Warp Matrix.md b/docs/Features/Geometry/Get Perspective Warp Matrix.md index 5319b4b2..c07910cd 100644 --- a/docs/Features/Geometry/Get Perspective Warp Matrix.md +++ b/docs/Features/Geometry/Get Perspective Warp Matrix.md @@ -45,7 +45,7 @@ const projectedImage = image.transform(matrix.matrix, { #### Options -| Property | Required | Default value | -| -------------------------------------------------------------------------------------------------- | -------- | ------------- | -| [`width`](https://image-js.github.io/image-js-typescript/interfaces/ResizeOptions.html#borderType) | no | - | -| [`height`](https://image-js.github.io/image-js-typescript/interfaces/ResizeOptions.html#height) | no | - | +| Property | Required | Default value | +| ----------------------------------------------------------------------------------------------------------- | -------- | ------------- | +| [`width`](https://image-js.github.io/image-js-typescript/interfaces/GetPerspectiveWarpOptions.html#width) | no | - | +| [`height`](https://image-js.github.io/image-js-typescript/interfaces/GetPerspectiveWarpOptions.html#height) | no | - | From 4cadbab6e4e989c1e7f26e3e716dd9e2e0117ed2 Mon Sep 17 00:00:00 2001 From: EscapedGibbon Date: Fri, 4 Jul 2025 15:13:18 +0200 Subject: [PATCH 12/16] docs: update getPerspectiveWarp --- .../Geometry/Get Perspective Warp Matrix.md | 4 +- package-lock.json | 8056 +++++++++-------- package.json | 2 +- 3 files changed, 4285 insertions(+), 3777 deletions(-) diff --git a/docs/Features/Geometry/Get Perspective Warp Matrix.md b/docs/Features/Geometry/Get Perspective Warp Matrix.md index c07910cd..3f071922 100644 --- a/docs/Features/Geometry/Get Perspective Warp Matrix.md +++ b/docs/Features/Geometry/Get Perspective Warp Matrix.md @@ -6,6 +6,8 @@ sidebar_position: 41 _Returns a perspective transformation matrix from source points that transforms a quadrilateral._ +[Options and parameters of `getPerspectiveWarp` function](https://image-js.github.io/image-js-typescript/functions/getPerspectiveWarp.html) + `getPerspectiveWarp` function takes 4 corner points (source quadrilateral) and then calculates the 3×3 perspective transformation matrix that allows removing [perspective distortion](https://en.wikipedia.org/wiki/Perspective_distortion). The function also returns width and height of the new image. If they were put as option's parameters it just returns indicated width and height, otherwise it calculates new width and height from given source points. @@ -39,7 +41,7 @@ const projectedImage = image.transform(matrix.matrix, { ### Parameters and default values -- `sourcePoints` +- `pts` - `options` diff --git a/package-lock.json b/package-lock.json index cc132827..4e5504cf 100644 --- a/package-lock.json +++ b/package-lock.json @@ -16,7 +16,7 @@ "@orama/plugin-secure-proxy": "^3.0.5", "clsx": "^1.2.1", "hast-util-is-element": "^1.1.0", - "image-js": "0.0.0-next-646dc2b006", + "image-js": "0.0.0-next-1a96bf38e6", "immer": "^9.0.19", "prism-react-renderer": "^2.1.0", "react": "^18.2.0", @@ -43,15 +43,6 @@ "node": ">=18" } }, - "node_modules/@aashutoshrathi/word-wrap": { - "version": "1.2.6", - "resolved": "https://registry.npmjs.org/@aashutoshrathi/word-wrap/-/word-wrap-1.2.6.tgz", - "integrity": "sha512-1Yjs2SvM8TflER/OD3cOjhWWOZb58A2t7wpE2S9XfBYTiIl+XFhQG2bjy4Pu1I+EAlCNUzRDYDdFwFYUKvXcIA==", - 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"main": "docusaurus.config.js", - "exports": { - ".": "./docusaurus.config.js", - "./config": "./docusaurus.config.js" - }, "scripts": { "build": "docusaurus build", "clear": "docusaurus clear", @@ -33,7 +28,7 @@ "@orama/plugin-secure-proxy": "^3.0.5", "clsx": "^1.2.1", "hast-util-is-element": "^1.1.0", - "image-js": "0.0.0-next-1a96bf38e6", + "image-js": "0.0.0-next-646dc2b006", "immer": "^9.0.19", "prism-react-renderer": "^2.1.0", "react": "^18.2.0", From 9799bd3e4a1c042fa9e7c1ac0a3af484f941c840 Mon Sep 17 00:00:00 2001 From: EscapedGibbon Date: Tue, 8 Jul 2025 09:05:50 +0200 Subject: [PATCH 14/16] docs: move ml-matrix explanation --- .../Applying transform function on images.md | 79 ++++++++++++------- 1 file changed, 52 insertions(+), 27 deletions(-) diff --git a/docs/Tutorials/Applying transform function on images.md b/docs/Tutorials/Applying transform function on images.md index cbd97f92..56ac4ac9 100644 --- a/docs/Tutorials/Applying transform function on images.md +++ b/docs/Tutorials/Applying transform function on images.md @@ -44,33 +44,6 @@ where It is worth mentioning that we will be working with 2D coordinates, so $$z$$ will be 1 in most cases. -:::note - -### Example of matrix multiplication - -If you are interested to look a bit deeper into matrix multiplications, take a look at the [`ml-matrix`](https://mljs.github.io/matrix/index.html 'link on ml-matrix api') package. -It facilitates basic matrix operations in ImageJS, as well as something more advanced like inverting a matrix. -Here is a basic demo on how to upscale a pixel coordinate by 2 using `ml-matrix` library. - -```ts -import { Matrix } from 'ml-matrix'; - -const matrix = new Matrix([[10], [10], [1]]); - -const transform = new Matrix([ - [2, 0, 0], - [0, 2, 0], - [0, 0, 1], -]); - -const result = transform.mmul(matrix); -/* -gives [20,20,1] as a new coordinate of a pixel. -*/ -``` - -::: - ## Types of transformation Here, we distinguish between two primary types of transformations: @@ -305,6 +278,58 @@ Image-js also has [`rotate()`](../Features/Geometry/Rotate.md) and [`transformRo `transformRotate()` allows rotating an image by any degree. It also allows choosing the axe of rotation. So, for rotation, you have other functions that allow you to perform it. ::: +

    + + Example of matrix multiplication + +As mentioned previously, to rotate an image around its center, you need to translate your image to the origin, rotate it, and translate it back to its original position. + +Performing these operations separately would require three different matrix multiplications on your image, which is computationally expensive. The optimal solution is to combine all three transformations into a single matrix by multiplying the transformation matrices together first, then applying the result to your image, as was shown in the previous example. + +To accomplish this, you can use the [`ml-matrix`](https://mljs.github.io/matrix/index.html 'link on ml-matrix api') package. It facilitates basic matrix operations in ImageJS, as well as more advanced operations like matrix inversion. + +Here's a step-by-step code example showing how to create a complex transformation matrix: + +```ts +import { Matrix } from 'ml-matrix'; + +const angle = Math.PI / 4; +const center = image.getCoordinates('center'); + +const cos = Math.cos(angle); +const sin = Math.sin(angle); +// Step 1: Translate to center. +const translateToOrigin = new Matrix([ + [1, 0, center.column], + [0, 1, center.row], + [0, 0, 1], +]); + +// Step 2: Rotation matrix +const rotation = new Matrix([ + [cos, -sin, 0], + [sin, cos, 0], + [0, 0, 1], +]); + +// Step 3: Translate back +const translateBack = new Matrix([ + [1, 0, -center.column], + [0, 1, -center.row], + [0, 0, 1], +]); + +const rotateAroundCenterMatrix = translateToOrigin + .mmul(rotation) + .mmul(translateBack); + +const rotateAroundCenterImage = image.transform( + rotateAroundCenterMatrix.to2DArray(), +); +``` + +
    + ## Projective Transformations Projective transformations use the full 3×3 matrix, including the bottom row parameters `g`, `h`, and `i`. These create perspective effects and can map rectangular images onto quadrilaterals. From fe5a02e0519e4191a2e16ca9153593f59cab15ac Mon Sep 17 00:00:00 2001 From: Daniel Kostro Date: Tue, 8 Jul 2025 10:45:08 +0200 Subject: [PATCH 15/16] chore: use same node version in CI --- .github/workflows/nodejs.yml | 1 + 1 file changed, 1 insertion(+) diff --git a/.github/workflows/nodejs.yml b/.github/workflows/nodejs.yml index d4284274..70b509f7 100644 --- a/.github/workflows/nodejs.yml +++ b/.github/workflows/nodejs.yml @@ -10,6 +10,7 @@ jobs: nodejs: uses: zakodium/workflows/.github/workflows/nodejs.yml@nodejs-v1 with: + node-version: 18.x lint-check-types: true npm-test-command: npm run build node-version-matrix: '[18]' From 2712e93d7ad6789009d3ac31958c88857c3878f4 Mon Sep 17 00:00:00 2001 From: EscapedGibbon Date: Tue, 8 Jul 2025 11:48:08 +0200 Subject: [PATCH 16/16] docs: resolve conversations --- docs/Features/Geometry/Transform.md | 3 -- .../Applying transform function on images.md | 42 ++++--------------- 2 files changed, 8 insertions(+), 37 deletions(-) diff --git a/docs/Features/Geometry/Transform.md b/docs/Features/Geometry/Transform.md index 0f108eed..9fba1267 100644 --- a/docs/Features/Geometry/Transform.md +++ b/docs/Features/Geometry/Transform.md @@ -30,9 +30,6 @@ If 2x3 matrix is passed, the algorithm will consider it as [affine transformatio For more information take a look at the tutorial about [image transformations](../../Tutorials/Applying%20transform%20function%20on%20images.md) -:::note -`transform()` function can accept 2x3 as well as 3x3 matrix. If matrix's size is 2x3 that it becomes an affine transformation. This means that transformation happens on the same -::: :::caution Matrix cannot be singular. Otherwise it cannot be inverted. Click [here](https://en.wikipedia.org/wiki/Invertible_matrix 'wikipedia link on invertible matrices') to learn more. ::: diff --git a/docs/Tutorials/Applying transform function on images.md b/docs/Tutorials/Applying transform function on images.md index 56ac4ac9..0ac91fd5 100644 --- a/docs/Tutorials/Applying transform function on images.md +++ b/docs/Tutorials/Applying transform function on images.md @@ -253,39 +253,8 @@ const combinedShearImage = image.transform(combinedShearMatrix); ### Complex Affine Transformations You can combine multiple transformations by multiplying matrices or applying them sequentially: -For example, to rotate around the image center instead of the origin, combine translation with rotation: - -```ts -const angle = Math.PI / 4; //45 degrees -const center = image.getCoordinates('center'); - -const cos = Math.cos(angle); -const sin = Math.sin(angle); - -// Translate to origin, rotate, translate back -const matrix = [ - [cos, -sin, center.column * (1 - cos) + center.row * sin], - [sin, cos, center.row * (1 - cos) - center.column * sin], -]; - -return image.transform(matrix); -``` - -![Rotated by center image](./images/transformations/lennaRotatedCenter.png) - -:::note -Image-js also has [`rotate()`](../Features/Geometry/Rotate.md) and [`transformRotate()`](../Features/Geometry/Transform%20and%20Rotate.md) functions. `rotate()` function allows rotating an image by multiple of 90 degrees. -`transformRotate()` allows rotating an image by any degree. It also allows choosing the axe of rotation. So, for rotation, you have other functions that allow you to perform it. -::: - -
    - - Example of matrix multiplication - -As mentioned previously, to rotate an image around its center, you need to translate your image to the origin, rotate it, and translate it back to its original position. - -Performing these operations separately would require three different matrix multiplications on your image, which is computationally expensive. The optimal solution is to combine all three transformations into a single matrix by multiplying the transformation matrices together first, then applying the result to your image, as was shown in the previous example. - +For example, to rotate around the image center instead of the origin, combine translation with rotation. So, you need to translate the image to the center, rotate it and translate it back. You can obviously use a separate matrix for each of the transformations. +But a more optimized approach is to create a matrix which combines all three transformations into one. To accomplish this, you can use the [`ml-matrix`](https://mljs.github.io/matrix/index.html 'link on ml-matrix api') package. It facilitates basic matrix operations in ImageJS, as well as more advanced operations like matrix inversion. Here's a step-by-step code example showing how to create a complex transformation matrix: @@ -328,7 +297,12 @@ const rotateAroundCenterImage = image.transform( ); ``` -
    +![Rotated by center image](./images/transformations/lennaRotatedCenter.png) + +:::note +Image-js also has [`rotate()`](../Features/Geometry/Rotate.md) and [`transformRotate()`](../Features/Geometry/Transform%20and%20Rotate.md) functions. `rotate()` function allows rotating an image by multiple of 90 degrees. +`transformRotate()` allows rotating an image by any degree. It also allows choosing the axe of rotation. So, for rotation, you have other functions that allow you to perform it. +::: ## Projective Transformations
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