This program implements color quantization with K-means clustering using Lloyd's algorithm

kmeans_color_quantization.cpp

/*

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*/

/*
  This program implements color quantization with K-means clustering using Lloyd's algorithm.
  Based on the article
  https://en.wikipedia.org/wiki/K-means_clustering

  The only dependency is lodepng. You compile and run in g++ with the line

  g++ -o quantize -std=c++11 main.cpp lodepng.cpp -O2 && ./quantize

 */


#include "lodepng.h"

#include <stdio.h>
#include <stdlib.h>
#include <math.h>

#include <vector>
#include <set>
#include <map>

#define NUM_QUANTIZATION_COLORS 16 // number of colors to quantize into
#define MAX_ITERATIONS 200
#define EPSILON 0.001f
#define RANDOM_SEED 1

#define INPUT_FILE "smallcat.png"
#define OUTPUT_FILE "quantized_cat.png"

class vec3 {
public:
    float x, y, z;
    vec3(float x, float y, float z) { this->x = x; this->y = y; this->z = z; }
    vec3(float v) { this->x = v; this->y = v; this->z = v; }
    vec3() { this->x = this->y = this->z = 0; }
    vec3& operator+=(const vec3& b) { (*this) = (*this) + b; return (*this); }
    friend vec3 operator-(const vec3& a, const vec3& b) { return vec3(a.x - b.x, a.y - b.y, a.z - b.z); }
    friend vec3 operator+(const vec3& a, const vec3& b) { return vec3(a.x + b.x, a.y + b.y, a.z + b.z); }
    friend vec3 operator*(const float s, const vec3& a) { return vec3(s * a.x, s * a.y, s * a.z); }
    friend vec3 operator*(const vec3& a, const float s) { return s * a; }

    static float length(const vec3& a) { return sqrt(vec3::dot(a, a)); }
    static float dot(const vec3& a, const vec3& b) { return a.x*b.x + a.y*b.y + a.z*b.z; }
    static float distance(const vec3& a, const vec3& b) { return length(a - b); }
};

int main() {
    srand(RANDOM_SEED); // use different seed, for different initial means

    std::vector<unsigned char> image;
    unsigned width, height;
    unsigned error = lodepng::decode(image, width, height, INPUT_FILE);
    if(error) {
        printf("could not open input image: %s\n", lodepng_error_text(error));
        exit(1);
    }

    const int k = NUM_QUANTIZATION_COLORS;

    // we treat every color value in the image, as a point 3D-space that should be quantized.
    std::vector<vec3> pl;
    for(int i = 0; i < image.size(); i+=4) {
        pl.push_back(vec3(image[i + 0] / 255.0f,image[i + 1] / 255.0f,image[i + 2] / 255.0f));
    }

    // set the initial means to random samples from pl.
    // we use an std::set to ensure that these samples are unique.
    std::vector<vec3> m;
    {
        std::set<int> im;
        while(im.size() < k) {
            im.insert(rand() % pl.size());
        }

        for(const int i: im) {
            m.push_back(pl[i]);
        }
    }

    std::vector<std::vector<int> > clusters;
    for(int i = 0; i < k; ++i) {
        clusters.push_back(std::vector<int>());
    }

    for(int iter = 0; iter < MAX_ITERATIONS; ++iter) {
        printf("iteration %d\n", iter);
        for(int i = 0; i < k; ++i) {
            clusters[i].clear();
        }

        // we will assign every single point to a cluster.
        // every cluster has a mean, and the point is assigned
        // to the cluster whose mean it is closest to(in terms of
        // the euclidean distance)
        for(int i_point = 0; i_point < pl.size(); ++i_point) {

            int i_closest = -1;
            float i_dist = -1;

            for(int i_cluster = 0; i_cluster < k; ++i_cluster) {
                float dist = vec3::distance(pl[i_point], m[i_cluster]);
                if(i_closest == -1 || dist < i_dist) {
                    i_dist = dist;
                    i_closest = i_cluster;
                }
            }

            clusters[i_closest].push_back(i_point);
        }

        bool different_enough = false;

        // now all the points have been assigned to clusters.
        // this means that k clusters have been formed.
        // now we update the means of these clusters.
        for(int i_cluster = 0; i_cluster < k; ++i_cluster) {
            float w = 1.0 / clusters[i_cluster].size();

            vec3 avg = vec3(0.0);

            for(int i = 0; i < clusters[i_cluster].size(); ++i) {
                avg += w * pl[clusters[i_cluster][i]];
            }

            if(vec3::distance(m[i_cluster],avg) > EPSILON) {
                different_enough = true;
            }

            m[i_cluster] = avg;
        }

        // if all the updated means barely moved at all, then we have attained
        // local maximum. we can't do any better, so terminate.
        if(!different_enough) {
            printf("Found local maximum. Done!\n");
            break;
        }
    }
    printf("Clustering done!\n");

    std::map<int, int> color_map; // maps the original colors to their quantized clors.
    for(int i_cluster = 0; i_cluster < k; ++i_cluster) {
        for(int i = 0; i < clusters[i_cluster].size(); ++i) {
            color_map[clusters[i_cluster][i]] = i_cluster;
        }
    }

    // finally, output the quantized image.
    image.clear();
    for(int i = 0; i < pl.size(); ++i) {
        vec3 col = m[color_map[i]];

        unsigned char r = (unsigned char)(col.x * 255.0f);
        unsigned char g = (unsigned char)(col.y * 255.0f);
        unsigned char b = (unsigned char)(col.z * 255.0f);

        image.push_back(r);
        image.push_back(g);
        image.push_back(b);
        image.push_back(255);
    }

    lodepng::encode(OUTPUT_FILE, image, width, height);
}