[DL]YOLO中anchor box是如何通过聚类确定的

k-means需要有数据，中心点个数是需要人为指定的，位置可以随机初始化，但是还需要度量到聚类中心的距离。这里怎么度量这个距离是很关键的。
距离度量如果使用标准的欧氏距离，大盒子会比小盒子产生更多的错误。例因此这里使用其他的距离度量公式。聚类的目的是anchor boxes和临近的ground truth有更大的IOU值，这和anchor box的尺寸没有直接关系。自定义的距离度量公式：

到聚类中心的距离越小越好，但IOU值是越大越好，所以使用 1 – IOU，这样就保证距离越小，IOU值越大。

代码实现主要是AlexeyAB/darknet中scripts/gen_anchors.py，这里根据yolov2，yolov3的版本不同进行部分修改。yolov2的配置文件yolov2.cfg需要的anchors是相对特征图的，值很小基本都小于13；yolov3的配置文件yolov3.cfg需要的3个anchors是相对于原图来说的，相对都比较大。还有输入图片的大小（32的倍数）对于输出也是有影响的。
例：
yolov2.cfg中[region] anchors =  0.57273, 0.677385, 1.87446, 2.06253, 3.33843, 5.47434, 7.88282, 3.52778, 9.77052, 9.16828
yolov3.cfg中[region] anchors = 10,13,  16,30,  33,23,  30,61,  62,45,  59,119,  116,90,  156,198,  373,326

from os import listdir
from os.path import isfile, join
import argparse
#import cv2
import numpy as np
import sys
import os
import shutil
import random 
import math
 
def IOU(x,centroids):
    '''
    :param x: 某一个ground truth的w,h
    :param centroids:  anchor的w,h的集合[(w,h),(),...]，共k个
    :return: 单个ground truth box与所有k个anchor box的IoU值集合
    '''
    IoUs = []
    w, h = x  # ground truth的w,h
    for centroid in centroids:
        c_w,c_h = centroid   #anchor的w,h
        if c_w>=w and c_h>=h:   #anchor包围ground truth
            iou = w*h/(c_w*c_h)
        elif c_w>=w and c_h<=h:    #anchor宽矮
            iou = w*c_h/(w*h + (c_w-w)*c_h)
        elif c_w<=w and c_h>=h:    #anchor瘦长
            iou = c_w*h/(w*h + c_w*(c_h-h))
        else: #ground truth包围anchor     means both w,h are bigger than c_w and c_h respectively
            iou = (c_w*c_h)/(w*h)
        IoUs.append(iou) # will become (k,) shape
    return np.array(IoUs)
 
def avg_IOU(X,centroids):
    '''
    :param X: ground truth的w,h的集合[(w,h),(),...]
    :param centroids: anchor的w,h的集合[(w,h),(),...]，共k个
    '''
    n,d = X.shape
    sum = 0.
    for i in range(X.shape[0]):
        sum+= max(IOU(X[i],centroids))  #返回一个ground truth与所有anchor的IoU中的最大值
    return sum/n    #对所有ground truth求平均
 
def write_anchors_to_file(centroids,X,anchor_file,input_shape,yolo_version):
    '''
    :param centroids: anchor的w,h的集合[(w,h),(),...]，共k个
    :param X: ground truth的w,h的集合[(w,h),(),...]
    :param anchor_file: anchor和平均IoU的输出路径
    '''
    f = open(anchor_file,'w')
    
    anchors = centroids.copy()
    print(anchors.shape)
 
    if yolo_version=='yolov2':
        for i in range(anchors.shape[0]):
            #yolo中对图片的缩放倍数为32倍，所以这里除以32，
            # 如果网络架构有改变，根据实际的缩放倍数来
            #求出anchor相对于缩放32倍以后的特征图的实际大小（yolov2）
            anchors[i][0]*=input_shape/32.
            anchors[i][1]*=input_shape/32.
    elif yolo_version=='yolov3':
        for i in range(anchors.shape[0]):
            #求出yolov3相对于原图的实际大小
            anchors[i][0]*=input_shape
            anchors[i][1]*=input_shape
    else:
        print("the yolo version is not right!")
        exit(-1)
 
    widths = anchors[:,0]
    sorted_indices = np.argsort(widths)
 
    print('Anchors = ', anchors[sorted_indices])
        
    for i in sorted_indices[:-1]:
        f.write('%0.2f,%0.2f, '%(anchors[i,0],anchors[i,1]))
 
    #there should not be comma after last anchor, that's why
    f.write('%0.2f,%0.2f\n'%(anchors[sorted_indices[-1:],0],anchors[sorted_indices[-1:],1]))
    
    f.write('%f\n'%(avg_IOU(X,centroids)))
    print()
 
def kmeans(X,centroids,eps,anchor_file,input_shape,yolo_version):
    
    N = X.shape[0] #ground truth的个数
    iterations = 0
    print("centroids.shape",centroids)
    k,dim = centroids.shape  #anchor的个数k以及w,h两维，dim默认等于2
    prev_assignments = np.ones(N)*(-1)    #对每个ground truth分配初始标签
    iter = 0
    old_D = np.zeros((N,k))  #初始化每个ground truth对每个anchor的IoU
 
    while True:
        D = []
        iter+=1           
        for i in range(N):
            d = 1 - IOU(X[i],centroids)
            D.append(d)
        D = np.array(D) # D.shape = (N,k)  得到每个ground truth对每个anchor的IoU
        
        print("iter {}: dists = {}".format(iter,np.sum(np.abs(old_D-D))))  #计算每次迭代和前一次IoU的变化值
            
        #assign samples to centroids 
        assignments = np.argmin(D,axis=1)  #将每个ground truth分配给距离d最小的anchor序号
        
        if (assignments == prev_assignments).all() :  #如果前一次分配的结果和这次的结果相同，就输出anchor以及平均IoU
            print("Centroids = ",centroids)
            write_anchors_to_file(centroids,X,anchor_file,input_shape,yolo_version)
            return
 
        #calculate new centroids
        centroid_sums=np.zeros((k,dim),np.float)   #初始化以便对每个簇的w,h求和
        for i in range(N):
            centroid_sums[assignments[i]]+=X[i]         #将每个簇中的ground truth的w和h分别累加
        for j in range(k):            #对簇中的w,h求平均
            centroids[j] = centroid_sums[j]/(np.sum(assignments==j)+1)
        
        prev_assignments = assignments.copy()     
        old_D = D.copy()  
 
def main(argv):
    parser = argparse.ArgumentParser()
    parser.add_argument('-filelist', default = r'E:\BaiduNetdiskDownload\darknetHG8245\scripts\train.txt',
                        help='path to filelist\n' )
    parser.add_argument('-output_dir', default = r'E:\BaiduNetdiskDownload\darknetHG8245', type = str,
                        help='Output anchor directory\n' )
    parser.add_argument('-num_clusters', default = 0, type = int, 
                        help='number of clusters\n' )
    '''
    需要注意的是yolov2输出的值比较小是相对特征图来说的，
    yolov3输出值较大是相对原图来说的，
    所以yolov2和yolov3的输出是有区别的
    '''
    parser.add_argument('-yolo_version', default='yolov2', type=str,
                        help='yolov2 or yolov3\n')
    parser.add_argument('-yolo_input_shape', default=416, type=int,
                        help='input images shape，multiples of 32. etc. 416*416\n')
    args = parser.parse_args()
    
    if not os.path.exists(args.output_dir):
        os.mkdir(args.output_dir)
 
    f = open(args.filelist)
  
    lines = [line.rstrip('\n') for line in f.readlines()]
    
    annotation_dims = []
 
    for line in lines:
        line = line.replace('JPEGImages','labels')
        line = line.replace('.jpg','.txt')
        line = line.replace('.png','.txt')
        print(line)
        f2 = open(line)
        for line in f2.readlines():
            line = line.rstrip('\n')
            w,h = line.split(' ')[3:]            
            #print(w,h)
            annotation_dims.append((float(w),float(h)))
    annotation_dims = np.array(annotation_dims) #保存所有ground truth框的(w,h)
  
    eps = 0.005
 
    if args.num_clusters == 0:
        for num_clusters in range(1,11): #we make 1 through 10 clusters 
            anchor_file = join( args.output_dir,'anchors%d.txt'%(num_clusters))
 
            indices = [ random.randrange(annotation_dims.shape[0]) for i in range(num_clusters)]
            centroids = annotation_dims[indices]
            kmeans(annotation_dims,centroids,eps,anchor_file,args.yolo_input_shape,args.yolo_version)
            print('centroids.shape', centroids.shape)
    else:
        anchor_file = join( args.output_dir,'anchors%d.txt'%(args.num_clusters))
        indices = [ random.randrange(annotation_dims.shape[0]) for i in range(args.num_clusters)]
        centroids = annotation_dims[indices]
        kmeans(annotation_dims,centroids,eps,anchor_file,args.yolo_input_shape,args.yolo_version)
        print('centroids.shape', centroids.shape)
 
if __name__=="__main__":
    main(sys.argv)

这是其中的yolov3的结果