这个方法被应用于深度学习目标检测的经典之作selective search方法中（Selective Search for Object Recognition），用于初始化分割区域。。论文题目：《Efficient Graph-Based Image Segmentation》
查阅了许多博客，后来感觉，对于这个方法整体还是一知半解，于是花了一个下午阅读了源码，做一个笔记，如有错误，希望大家指正
源代码输入5个参数，示意如下：
sigma: Used to smooth the input image before segmenting it.k: Value for the threshold function.min: Minimum component size enforced by post-processing.input: Input image.output: Output image.大意为，sigma：使用的平滑参数，k:给出的初始化阈值，min:最小分割块大小（用于合并小块），输入图片(input)和输入图片(output)（都要为pnm格式）
参数传入segment.cpp中，如下
image<rgb> *seg = segment_image(input, sigma, k, min_size, &num_ccs); 调用segment-image.h中的 image *segment_image，函数大概注释如下：
/*
Copyright (C) 2006 Pedro FelzenszwalbThis program is free software; you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation; either version 2 of the License, or
(at your option) any later version.This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.You should have received a copy of the GNU General Public License
along with this program; if not, write to the Free Software
Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
*/#ifndef SEGMENT_IMAGE
#define SEGMENT_IMAGE#include <cstdlib>
#include <image.h>
#include <misc.h>
#include <filter.h>
#include <stdio.h>
#include "segment-graph.h"// random color
rgb random_rgb(){ rgb c;double r;c.r = (uchar)random();c.g = (uchar)random();c.b = (uchar)random();return c;
}// dissimilarity measure between pixels
// 衡量不相似度，用rgb距离
static inline float diff(image<float> *r, image<float> *g, image<float> *b,int x1, int y1, int x2, int y2) {return sqrt(square(imRef(r, x1, y1)-imRef(r, x2, y2)) +square(imRef(g, x1, y1)-imRef(g, x2, y2)) +square(imRef(b, x1, y1)-imRef(b, x2, y2)));
}/** Segment an image** Returns a color image representing the segmentation.** im: image to segment.* sigma: to smooth the image.* c: constant for treshold function.* min_size: minimum component size (enforced by post-processing stage).* num_ccs: number of connected components in the segmentation.*/
image<rgb> *segment_image(image<rgb> *im, float sigma, float c, int min_size,int *num_ccs) {//图像的宽和高int width = im->width();int height = im->height();// 初始化了三个通道的片image<float> *r = new image<float>(width, height);image<float> *g = new image<float>(width, height);image<float> *b = new image<float>(width, height);// smooth each color channel//平滑色彩通道for (int y = 0; y < height; y++) {for (int x = 0; x < width; x++) {imRef(r, x, y) = imRef(im, x, y).r;imRef(g, x, y) = imRef(im, x, y).g;imRef(b, x, y) = imRef(im, x, y).b;}}image<float> *smooth_r = smooth(r, sigma);image<float> *smooth_g = smooth(g, sigma);image<float> *smooth_b = smooth(b, sigma);delete r;delete g;delete b;// build graph//构建图，边的数组是原来的4倍，就是四个方向,计算出了全部的点和点之间的相似性//这里是初始化了width*height*4大小的数组，其实用不了这么多edge *edges = new edge[width*height*4];int num = 0;for (int y = 0; y < height; y++) {for (int x = 0; x < width; x++) {//对每个边的左右点计算权重if (x < width-1) {edges[num].a = y * width + x;edges[num].b = y * width + (x+1);edges[num].w = diff(smooth_r, smooth_g, smooth_b, x, y, x+1, y);num++;}if (y < height-1) {edges[num].a = y * width + x;edges[num].b = (y+1) * width + x;edges[num].w = diff(smooth_r, smooth_g, smooth_b, x, y, x, y+1);num++;}if ((x < width-1) && (y < height-1)) {edges[num].a = y * width + x;edges[num].b = (y+1) * width + (x+1);edges[num].w = diff(smooth_r, smooth_g, smooth_b, x, y, x+1, y+1);num++;}if ((x < width-1) && (y > 0)) {edges[num].a = y * width + x;edges[num].b = (y-1) * width + (x+1);edges[num].w = diff(smooth_r, smooth_g, smooth_b, x, y, x+1, y-1);num++;}}}
// printf("%d %d", width*height*4, num);
// printf("width is:%d height is:%d", width, height);delete smooth_r;delete smooth_g;delete smooth_b;// segment//分割步骤，。。。。跳出universe *u = segment_graph(width*height, num, edges, c);// post process small components//合并最小的块，如果边两边的块小于min_size就合并for (int i = 0; i < num; i++) {int a = u->find(edges[i].a);int b = u->find(edges[i].b);if ((a != b) && ((u->size(a) < min_size) || (u->size(b) < min_size)))u->join(a, b);}delete [] edges;*num_ccs = u->num_sets();//写入新的pnm图片image<rgb> *output = new image<rgb>(width, height);// pick random colors for each componentrgb *colors = new rgb[width*height];for (int i = 0; i < width*height; i++)colors[i] = random_rgb();for (int y = 0; y < height; y++) {for (int x = 0; x < width; x++) {int comp = u->find(y * width + x);imRef(output, x, y) = colors[comp];}} delete [] colors; delete u;return output;
}#endif
其中 segment_graph(width*height, num, edges, c); 这一步跳到 segment-graph.h中
/*
Copyright (C) 2006 Pedro FelzenszwalbThis program is free software; you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation; either version 2 of the License, or
(at your option) any later version.This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.You should have received a copy of the GNU General Public License
along with this program; if not, write to the Free Software
Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
*/#ifndef SEGMENT_GRAPH
#define SEGMENT_GRAPH#include <algorithm>
#include <cmath>
#include "disjoint-set.h"// threshold function
#define THRESHOLD(size, c) (c/size)typedef struct {float w;int a, b;
} edge;bool operator<(const edge &a, const edge &b) {//按照不相似程度从小到大排序return a.w < b.w;
}/** Segment a graph** Returns a disjoint-set forest representing the segmentation.** num_vertices: number of vertices in graph.* num_edges: number of edges in graph* edges: array of edges.* c: constant for treshold function.*/
universe *segment_graph(int num_vertices, int num_edges, edge *edges, float c) { // sort edges by weight// 将edge按照权重进行排序,权重越大越不相似，这里权重是不相似程度std::sort(edges, edges + num_edges);// make a disjoint-set forest// num_vertices 是顶点的数量universe *u = new universe(num_vertices);// init thresholds//这里阈值是为了防止刚开始的时候每个点之间全部都分开了float *threshold = new float[num_vertices];for (int i = 0; i < num_vertices; i++)//c/1threshold[i] = THRESHOLD(1,c);// for each edge, in non-decreasing weight order...for (int i = 0; i < num_edges; i++) {//遍历所有的边edge *pedge = &edges[i];// components conected by this edge// 找出这个边的左右顶点，这个顶点会随着边的合并而变动，为了保证阈值threshold[a]是最大的，就是这个域内的不相似程度最大int a = u->find(pedge->a);int b = u->find(pedge->b);// 如果 a==b 则说明在同个域里面if (a != b) {//权值小于阈值，这里a和b代表这个边链接的两个域的分别的最大不相似程度if ((pedge->w <= threshold[a]) &&(pedge->w <= threshold[b])) {//如果这个边的长度（就是这个边链接的两个点的不相似程度）比两边的最大的不相似度都小，则将这两个域链接起来u->join(a, b);
// printf("size a is:%d ", u->size(a));a = u->find(a);
// printf(" size a is:%d \n", u->size(a));//这里只更新了a的部分，这里个人理解，不太确定，应该是因为在disjoint-set.h中代码find函数中总是找到下标最靠前的那个点，然后返回threshold[a] = pedge->w + THRESHOLD(u->size(a), c);}}}// free updelete threshold;return u;
}#endif下面是 universe *u = new universe(num_vertices); 的定义。。。在disjoint-set.h中
/*
Copyright (C) 2006 Pedro FelzenszwalbThis program is free software; you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation; either version 2 of the License, or
(at your option) any later version.This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.You should have received a copy of the GNU General Public License
along with this program; if not, write to the Free Software
Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
*/#ifndef DISJOINT_SET
#define DISJOINT_SET// disjoint-set forests using union-by-rank and path compression (sort of).typedef struct {/*rank:等级，用来判定将要合并的块合在左边还是右边p:用来找到这个块最先的那个节点size:用来记录现在这个块有大*/int rank;int p;int size;
} uni_elt;class universe {
public:universe(int elements);~universe();int find(int x); void join(int x, int y);int size(int x) const { return elts[x].size; }int num_sets() const { return num; }private:uni_elt *elts;int num;
};universe::universe(int elements) {//初始化三个参数elts = new uni_elt[elements];num = elements;for (int i = 0; i < elements; i++) {elts[i].rank = 0;elts[i].size = 1;elts[i].p = i;}
}universe::~universe() {delete [] elts;
}int universe::find(int x) {int y = x;while (y != elts[y].p){// 个人理解，这里不确定。这里通过不断的链接，查找到最初的那个点，那个点作为这个域的标识y = elts[y].p;}elts[x].p = y;return y;
}void universe::join(int x, int y) {//链接两个块，如果x的rank大于y就合并在x里面，//反之则加在y里面if (elts[x].rank > elts[y].rank) {elts[y].p = x;elts[x].size += elts[y].size;} else {elts[x].p = y;elts[y].size += elts[x].size;if (elts[x].rank == elts[y].rank)elts[y].rank++;}num--;
}#endif关于如何平滑（smooth）参数，在filter.h里，就不贴了（里面涉及一些数学公式，不看代码会看的很累）
个人觉得，大概思路是，先是每个点作为一个块，对边的权重进行排序，遍历所有的边，不断结合块，把边遍历过之后，也就合并所有的块了，在把太小的块融合起来。
最后，贴上一段原始论文中的描述，供大家参考
Algorithm 1 Segmentation algorithm.
The input is a graph G = (V, E), with n vertices and m edges. The output is a
segmentation of V into components S = (C 1 , . . . , C r ).
0. Sort E into π = (o 1 , . . . , o m ), by non-decreasing edge weight.
1. Start with a segmentation S 0 , where each vertex v i is in its own component.
2. Repeat step 3 for q = 1, . . . , m.
3. Construct S q given S q?1 as follows. Let v i and v j denote the vertices connected
by the q-th edge in the ordering, i.e., o q = (v i , v j ). If v i and v j are in disjoint
components of S q?1 and w(o q ) is small compared to the internal difference of
both those components, then merge the two components otherwise do nothing.
More formally, let C i q?1 be the component of S q?1 containing v i and C j q?1 the
component containing v j . If C i q?1 6 = C j q?1 and w(o q ) ≤ M Int(C i q?1 , C j q?1 ) then
S q is obtained from S q?1 by merging C i q?1 and C j q?1 . Otherwise S q = S q?1 .
4. Return S = S m .最后的最后，代码和论文如下：这里