--- /dev/null
+/**
+
+IIR Gauss Filter v1.0
+By Stephan Soller <stephan.soller@helionweb.de>
+Based on the paper "Recursive implementaion 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 blurrs 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 implementaion 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 way to
+construct a filter so that each pixel can change all others no mater the distance between them (infinite impulse
+response, IIR for short). Other (convolution based) gauss filters do that by distributing the value of each pixel
+across all it's neighbors. This takes more and more time with a larger sigma ("blur radius") because the value of
+a pixel has to be propagates across a larger area. This gets quadratically slower with higher radii.
+This IIR based implementation instead gets all the propagation 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 suppost 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 `raidus1` 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 thost estimates by applying different sigmas (0.5 to 100) to a test image and measuring the effects with
+GIMP. So take it with a grain of salt (or many). The'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
+#ifdef __cplusplus
+ extern "C" {
+#endif
+
+void iir_gauss_blur(unsigned int width, unsigned int height, unsigned char components, unsigned char* image, float sigma);
+
+#ifdef __cplusplus
+ }
+#endif
+#endif // IIR_GAUSS_BLUR_HEADER
+
+#ifdef IIR_GAUSS_BLUR_IMPLEMENTATION
+#include <stdlib.h>
+#include <math.h>
+
+void iir_gauss_blur(unsigned int width, unsigned int height, unsigned char components, unsigned char* 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
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