原理

对于Bounding Box的列表B及其对应的置信度S,采用下面的计算方式.选择具有最大score的检测框M,将其从B集合中移除并加入到最终的检测结果D中.通常将B中剩余检测框中与M的IoU大于阈值Nt的框从B中移除.重复这个过程,直到B为空。

实现步骤

（1）将所有框的得分排序，选中最高分及其对应的框
（2）遍历其余的框，如果和当前最高分框的重叠面积(IOU)大于一定阈值，我们就将框删除。
（3）从未处理的框中继续选一个得分最高的，重复上述过程。

实现代码

MATLAB

%% NMS:non maximum suppression
function pick = nms(boxes,threshold,type)
% boxes: m x 5,表示有m个框，5列分别是[x1 y1 x2 y2 score]
% threshold: IOU阈值
% type：IOU阈值的定义类型% 输入为空，则直接返回if isempty(boxes)pick = [];return;end% 依次取出左上角和右下角坐标以及分类器得分(置信度)x1 = boxes(:,1);y1 = boxes(:,2);x2 = boxes(:,3);y2 = boxes(:,4);s = boxes(:,5);% 计算每一个框的面积area = (x2-x1+1) .* (y2-y1+1);%将得分升序排列[vals, I] = sort(s);%初始化pick = s*0;counter = 1;% 循环直至所有框处理完成while ~isempty(I)last = length(I); %当前剩余框的数量i = I(last);%选中最后一个，即得分最高的框pick(counter) = i;counter = counter + 1;  %计算相交面积xx1 = max(x1(i), x1(I(1:last-1)));yy1 = max(y1(i), y1(I(1:last-1)));xx2 = min(x2(i), x2(I(1:last-1)));yy2 = min(y2(i), y2(I(1:last-1)));  w = max(0.0, xx2-xx1+1);h = max(0.0, yy2-yy1+1); inter = w.*h;%不同定义下的IOUif strcmp(type,'Min')%重叠面积与最小框面积的比值o = inter ./ min(area(i),area(I(1:last-1)));else%交集/并集o = inter ./ (area(i) + area(I(1:last-1)) - inter);end%保留所有重叠面积小于阈值的框，留作下次处理I = I(find(o<=threshold));endpick = pick(1:(counter-1));
end

Python

import numpy as np
cimport numpy as npcdef inline np.float32_t max(np.float32_t a, np.float32_t b):return a if a >= b else bcdef inline np.float32_t min(np.float32_t a, np.float32_t b):return a if a <= b else bdef cpu_soft_nms(np.ndarray[float, ndim=2] boxes, float sigma=0.5, float Nt=0.3, float threshold=0.001, unsigned int method=0):cdef unsigned int N = boxes.shape[0]cdef float iw, ih, box_areacdef float uacdef int pos = 0cdef float maxscore = 0cdef int maxpos = 0cdef float x1,x2,y1,y2,tx1,tx2,ty1,ty2,ts,area,weight,ovfor i in range(N):maxscore = boxes[i, 4]maxpos = itx1 = boxes[i,0]ty1 = boxes[i,1]tx2 = boxes[i,2]ty2 = boxes[i,3]ts = boxes[i,4]pos = i + 1# get max boxwhile pos < N:if maxscore < boxes[pos, 4]:maxscore = boxes[pos, 4]maxpos = pospos = pos + 1# add max box as a detection boxes[i,0] = boxes[maxpos,0]boxes[i,1] = boxes[maxpos,1]boxes[i,2] = boxes[maxpos,2]boxes[i,3] = boxes[maxpos,3]boxes[i,4] = boxes[maxpos,4]# swap ith box with position of max boxboxes[maxpos,0] = tx1boxes[maxpos,1] = ty1boxes[maxpos,2] = tx2boxes[maxpos,3] = ty2boxes[maxpos,4] = tstx1 = boxes[i,0]ty1 = boxes[i,1]tx2 = boxes[i,2]ty2 = boxes[i,3]ts = boxes[i,4]pos = i + 1# NMS iterations, note that N changes if detection boxes fall below thresholdwhile pos < N:x1 = boxes[pos, 0]y1 = boxes[pos, 1]x2 = boxes[pos, 2]y2 = boxes[pos, 3]s = boxes[pos, 4]area = (x2 - x1 + 1) * (y2 - y1 + 1)iw = (min(tx2, x2) - max(tx1, x1) + 1)if iw > 0:ih = (min(ty2, y2) - max(ty1, y1) + 1)if ih > 0:ua = float((tx2 - tx1 + 1) * (ty2 - ty1 + 1) + area - iw * ih)ov = iw * ih / ua #iou between max box and detection boxif method == 1: # linearif ov > Nt: weight = 1 - ovelse:weight = 1elif method == 2: # gaussianweight = np.exp(-(ov * ov)/sigma)else: # original NMSif ov > Nt: weight = 0else:weight = 1boxes[pos, 4] = weight*boxes[pos, 4]# if box score falls below threshold, discard the box by swapping with last box# update Nif boxes[pos, 4] < threshold:boxes[pos,0] = boxes[N-1, 0]boxes[pos,1] = boxes[N-1, 1]boxes[pos,2] = boxes[N-1, 2]boxes[pos,3] = boxes[N-1, 3]boxes[pos,4] = boxes[N-1, 4]N = N - 1pos = pos - 1pos = pos + 1keep = [i for i in range(N)]return keepdef cpu_nms(np.ndarray[np.float32_t, ndim=2] dets, np.float thresh):cdef np.ndarray[np.float32_t, ndim=1] x1 = dets[:, 0]cdef np.ndarray[np.float32_t, ndim=1] y1 = dets[:, 1]cdef np.ndarray[np.float32_t, ndim=1] x2 = dets[:, 2]cdef np.ndarray[np.float32_t, ndim=1] y2 = dets[:, 3]cdef np.ndarray[np.float32_t, ndim=1] scores = dets[:, 4]cdef np.ndarray[np.float32_t, ndim=1] areas = (x2 - x1 + 1) * (y2 - y1 + 1)cdef np.ndarray[np.int_t, ndim=1] order = scores.argsort()[::-1]cdef int ndets = dets.shape[0]cdef np.ndarray[np.int_t, ndim=1] suppressed = \np.zeros((ndets), dtype=np.int)# nominal indicescdef int _i, _j# sorted indicescdef int i, j# temp variables for box i's (the box currently under consideration)cdef np.float32_t ix1, iy1, ix2, iy2, iarea# variables for computing overlap with box j (lower scoring box)cdef np.float32_t xx1, yy1, xx2, yy2cdef np.float32_t w, hcdef np.float32_t inter, ovrkeep = []for _i in range(ndets):i = order[_i]if suppressed[i] == 1:continuekeep.append(i)ix1 = x1[i]iy1 = y1[i]ix2 = x2[i]iy2 = y2[i]iarea = areas[i]for _j in range(_i + 1, ndets):j = order[_j]if suppressed[j] == 1:continuexx1 = max(ix1, x1[j])yy1 = max(iy1, y1[j])xx2 = min(ix2, x2[j])yy2 = min(iy2, y2[j])w = max(0.0, xx2 - xx1 + 1)h = max(0.0, yy2 - yy1 + 1)inter = w * hovr = inter / (iarea + areas[j] - inter)if ovr >= thresh:suppressed[j] = 1return keep

参考博客：http://blog.csdn.net/shuzfan/article/details/52711706
　　　　　http://www.cnblogs.com/makefile/p/nms.html

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NMS非极大值抑制的原理

原理

实现步骤

实现代码

MATLAB

Python

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