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| -rw-r--r-- | svg-flatten/include/iir_gauss_blur.h | 210 |
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diff --git a/svg-flatten/include/iir_gauss_blur.h b/svg-flatten/include/iir_gauss_blur.h new file mode 100644 index 0000000..b448750 --- /dev/null +++ b/svg-flatten/include/iir_gauss_blur.h @@ -0,0 +1,210 @@ +/** + +IIR Gauss Filter v1.0 +By Stephan Soller <stephan.soller@helionweb.de> +Based on the paper "Recursive implementation of the Gaussian filter" by Ian T. Young and Lucas J. van Vliet. +Licensed under the MIT license + +QUICK START + + #include ... + #include ... + #define IIR_GAUSS_BLUR_IMPLEMENTATION + #include "iir_gauss_blur.h" + ... + int width = 0, height = 0, components = 1; + uint8_t* image = stbi_load("foo.png", &width, &height, &components, 0); + float sigma = 10; + iir_gauss_blur(width, height, components, image, sigma); + stbi_write_png("foo.blurred.png", width, height, components, image, 0); + +This example uses stb_image.h to load the image, then blurs it and writes the result using stb_image_write.h. +`sigma` controls the strength of the blur. Higher values give you a blurrier image. + +DOCUMENTATION + +This is a single header file library. You'll have to define IIR_GAUSS_BLUR_IMPLEMENTATION before including this file to +get the implementation. Otherwise just the header will be included. + +The library only has a single function: iir_gauss_blur(width, height, components, image, sigma). + +- `width` and `height` are the dimensions of the image in pixels. +- `components` is the number of bytes per pixel. 1 for a grayscale image, 3 for RGB and 4 for RGBA. + The function can handle an arbitrary number of channels, so 2 or 7 will work as well. +- `image` is a pointer to the image data with `width * height` pixels, each pixel having `components` bytes (interleaved + 8-bit components). There is no padding between the scanlines of the image. + This is the format used by stb_image.h and stb_image_write.h and easy to work with. +- `sigma` is the strength of the blur. It's a number > 0.5 and most people seem to just eyeball it. + Start with e.g. a sigma of 5 and go up or down until you have the blurriness you want. + There are more informed ways to choose this parameter, see CHOOSING SIGMA below. + +The function mallocs an internal float buffer with the same dimensions as the image. If that turns out to be a +bottleneck fell free to move that out of the function. The source code is quite short and straight forward (even if the +math isn't). + +The function is an implementation of the paper "Recursive implementation of the Gaussian filter" by Ian T. Young and +Lucas J. van Vliet. It has nothing to do with recursive function calls, instead it's a special way to construct a +filter. Other (convolution based) gauss filters apply a kernel for each pixel and the kernel grows as sigma gets larger. +Meaning their performance degrades the more blurry you want your image to be. + +Instead The algorithm in the paper gets it done in just a few passes: A horizontal forward and backward pass and a +vertical forward and backward pass. The work done is independent of the blur radius and so you can have ridiculously +large blur radii without any performance impact. + +CHOOSING SIGMA + +There seem to be several rules of thumb out there to get a sigma for a given "blur radius". Usually this is something +like `radius = 2 * sigma`. So if you want to have a blur radius of 10px you can use `sigma = (1.0 / 2.0) * radius` to +get the sigma for it (5.0). I'm not sure what that "radius" is supposed to mean though. + +For my own projects I came up with two different kinds of blur radii and how to get a sigma for them: Given a big white +area on a black background, how far will the white "bleed out" into the surrounding black? How large is the distance +until the white (255) gets blurred down to something barely visible (smaller than 16) or even to nothing (smaller than +1)? There are to estimates to get the sigma for those radii: + + sigma = (1.0 / 1.42) * radius16; + sigma = (1.0 / 3.66) * radius1; + +Personally I use `radius16` to calculate the sigma when blurring normal images. Think: I want to blur a pixel across a +circle with the radius x so it's impact is barely visible at the edges. + +When I need to calculate padding I use `radius1`: When I have a black border of 100px around the image I can use a +`radius1` of 100 and be reasonable sure that I still got black at the edges. So given a `radius1` blur strength I can +use it as a padding width as well. + +I created those estimates by applying different sigmas (1 to 100) to a test image and measuring the effects with GIMP. +So take it with a grain of salt (or many). They're reasonable estimates but by no means exact. I tried to solve the +normal distribution to calculate the perfect sigma but gave up after a lot of confusion. If you know an exact solution +let me know. :) + +VERSION HISTORY + +v1.0 2018-08-30 Initial release + +**/ +#ifndef IIR_GAUSS_BLUR_HEADER +#define IIR_GAUSS_BLUR_HEADER + +template <typename T> +void iir_gauss_blur(unsigned int width, unsigned int height, unsigned char components, T* image, float sigma); + +#endif // IIR_GAUSS_BLUR_HEADER + +#ifdef IIR_GAUSS_BLUR_IMPLEMENTATION +#include <stdlib.h> +#include <math.h> + +template <typename T> +void iir_gauss_blur(unsigned int width, unsigned int height, unsigned char components, T* image, float sigma) { + // Create IDX macro but push any previous definition (and restore it later) so we don't overwrite a macro the user has possibly defined before us + #pragma push_macro("IDX") + #define IDX(x, y, n) ((y)*width*components + (x)*components + n) + + // Allocate buffers + float* buffer = (float*)malloc(width * height * components * sizeof(buffer[0])); + + // Calculate filter parameters for a specified sigma + // Use Equation 11b to determine q, do nothing if sigma is to small (should have no effect) or negative (doesn't make sense) + float q; + if (sigma >= 2.5) + q = 0.98711 * sigma - 0.96330; + else if (sigma >= 0.5) + q = 3.97156 - 4.14554 * sqrtf(1.0 - 0.26891 * sigma); + else + return; + + // Use equation 8c to determine b0, b1, b2 and b3 + float b0 = 1.57825 + 2.44413*q + 1.4281*q*q + 0.422205*q*q*q; + float b1 = 2.44413*q + 2.85619*q*q + 1.26661*q*q*q; + float b2 = -( 1.4281*q*q + 1.26661*q*q*q ); + float b3 = 0.422205*q*q*q; + // Use equation 10 to determine B + float B = 1.0 - (b1 + b2 + b3) / b0; + + // Horizontal forward pass (from paper: Implement the forward filter with equation 9a) + // The data is loaded from the byte image but stored in the float buffer + for(unsigned int y = 0; y < height; y++) { + float prev1[components], prev2[components], prev3[components]; + for(unsigned char n = 0; n < components; n++) { + prev1[n] = image[IDX(0, y, n)]; + prev2[n] = prev1[n]; + prev3[n] = prev2[n]; + } + + for(unsigned int x = 0; x < width; x++) { + for(unsigned char n = 0; n < components; n++) { + float val = B * image[IDX(x, y, n)] + (b1 * prev1[n] + b2 * prev2[n] + b3 * prev3[n]) / b0; + buffer[IDX(x, y, n)] = val; + prev3[n] = prev2[n]; + prev2[n] = prev1[n]; + prev1[n] = val; + } + } + } + + // Horizontal backward pass (from paper: Implement the backward filter with equation 9b) + for(unsigned int y = height-1; y < height; y--) { + float prev1[components], prev2[components], prev3[components]; + for(unsigned char n = 0; n < components; n++) { + prev1[n] = buffer[IDX(width-1, y, n)]; + prev2[n] = prev1[n]; + prev3[n] = prev2[n]; + } + + for(unsigned int x = width-1; x < width; x--) { + for(unsigned char n = 0; n < components; n++) { + float val = B * buffer[IDX(x, y, n)] + (b1 * prev1[n] + b2 * prev2[n] + b3 * prev3[n]) / b0; + buffer[IDX(x, y, n)] = val; + prev3[n] = prev2[n]; + prev2[n] = prev1[n]; + prev1[n] = val; + } + } + } + + // Vertical forward pass (from paper: Implement the forward filter with equation 9a) + for(unsigned int x = 0; x < width; x++) { + float prev1[components], prev2[components], prev3[components]; + for(unsigned char n = 0; n < components; n++) { + prev1[n] = buffer[IDX(x, 0, n)]; + prev2[n] = prev1[n]; + prev3[n] = prev2[n]; + } + + for(unsigned int y = 0; y < height; y++) { + for(unsigned char n = 0; n < components; n++) { + float val = B * buffer[IDX(x, y, n)] + (b1 * prev1[n] + b2 * prev2[n] + b3 * prev3[n]) / b0; + buffer[IDX(x, y, n)] = val; + prev3[n] = prev2[n]; + prev2[n] = prev1[n]; + prev1[n] = val; + } + } + } + + // Vertical backward pass (from paper: Implement the backward filter with equation 9b) + // Also write the result back into the byte image + for(unsigned int x = width-1; x < width; x--) { + float prev1[components], prev2[components], prev3[components]; + for(unsigned char n = 0; n < components; n++) { + prev1[n] = buffer[IDX(x, height-1, n)]; + prev2[n] = prev1[n]; + prev3[n] = prev2[n]; + } + + for(unsigned int y = height-1; y < height; y--) { + for(unsigned char n = 0; n < components; n++) { + float val = B * buffer[IDX(x, y, n)] + (b1 * prev1[n] + b2 * prev2[n] + b3 * prev3[n]) / b0; + image[IDX(x, y, n)] = val; + prev3[n] = prev2[n]; + prev2[n] = prev1[n]; + prev1[n] = val; + } + } + } + + // Free temporary buffers and restore any potential IDX macro + free(buffer); + #pragma pop_macro("IDX") +} +#endif // IIR_GAUSS_BLUR_IMPLEMENTATION |