Swift/Metal Image Processing
1. Edge Detection
Edge detection is one of spatial filtering.
Edge is the outside limit of an object. At edges, the image’s luminance changes drastically.
Edge detection is to calculate a position luminance changes drastically in the image.
How to calculate the position? Use differential. In continuous domain, the image’s derivatives is
where f(x, y) is input image, same as I(i, j) in the previous section. Current calculation will be performed in discrete domain so approximation is needed.
(x, y) means each pixel’s index, gid in metal. So these values’ delta is enough small. The following approximation can be used.
This is just a subtraction!! simple.
Think again the following case.
Target pixel is I(2, 2). Then the deltas of both sides of target pixel are
- Horizontal: I(2, 3) - I(2, 1)
- Vertical: I(3, 2) - I(1, 2)
The horizontal and vertical kernels become
Try this filter.
SwiftImageProcessor/Shader/Edge/derivatives.metal is prepared as following.
The double for-loops is convolution. The latter part is color conversion.
This generate landscape_derivatives.jpg .
Could get edges.
Some special filters are defined depending on kernel and prepared in my project.
Prewitt Filter
Sobel Filter
Laplace
Laplace filter is different from Prewitt and Sobel in using second derivatives.
Derivatives is approximated by delta in image processing so second derivatives is
In mathematics, laplacian is defined as following equation
This equation is important, but not much as the below kernel matrix here.
SwiftImageProcessor/Shader/Edge/laplace.metal is prepared. So try this.
