非極大抑制（Non-Maximum Suppression）

最近在看檢測方面的東西，Faster RCNN，其中涉及到Non-Maximum Suppression，論文中沒具體展開，我就研究下了代碼，這里做一個簡單的總結，聽這個名字感覺是一個很高深的算法，其實很簡單。
Non-Maximum Suppression就是根據score和box的坐標信息，從中找到置信度比較高的bounding box。首先，然后根據score進行排序，把score最大的bounding box拿出來。計算其余bounding box與這個box的IoU，然后去除IoU大於設定的閾值的bounding box。然后重復上面的過程，直至候選bounding box為空。說白了就是我要在一堆矩陣里面找出一些局部最大值，所以要把和這些局部最大值所代表矩陣IoU比較大的去除掉，這樣就能得到一些權值很大，而且IoU又比較小的bounding box。

function pick = nms(boxes, overlap)
% top = nms(boxes, overlap)
% Non-maximum suppression. (FAST VERSION)
% Greedily select high-scoring detections and skip detections
% that are significantly covered by a previously selected
% detection.
%
% NOTE: This is adapted from Pedro Felzenszwalb's version (nms.m),
% but an inner loop has been eliminated to significantly speed it
% up in the case of a large number of boxes


% Copyright (C) 2011-12 by Tomasz Malisiewicz
% All rights reserved.
% 
% This file is part of the Exemplar-SVM library and is made
% available under the terms of the MIT license (see COPYING file).
% Project homepage: https://github.com/quantombone/exemplarsvm




if isempty(boxes)
  pick = [];
  return;
end


x1 = boxes(:,1);
y1 = boxes(:,2);
x2 = boxes(:,3);
y2 = boxes(:,4);
s = boxes(:,end);


area = (x2-x1+1) .* (y2-y1+1);    %計算出每一個bounding box的面積
[vals, I] = sort(s);				%根據score遞增排序


pick = s*0;
counter = 1;
while ~isempty(I)
  last = length(I);
  i = I(last);  
  pick(counter) = i;			%選擇score最大bounding box加入到候選隊列
  counter = counter + 1;
  
  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;		%計算出每一bounding box與當前score最大的box的交集面積
  o = inter ./ (area(i) + area(I(1:last-1)) - inter);  %IoU（intersection-over-union）
  
  I = I(find(o<=overlap));  %找出IoU小於overlap閾值的index
end


pick = pick(1:(counter-1));