非极大值抑制算法

1. 算法原理

  非极大值抑制算法（Non-maximum suppression, NMS）的本质是搜索局部极大值，抑制非极大值元素。

2. 3邻域情况下NMS的实现

  3邻域情况下的NMS即判断一维数组I[W]的元素I[i](2<=i<=W-1)是否大于其左邻元素I[i-1]和右邻元素I[i+1]，算法流程如下图所示：

  

  a. 算法流程3-5行判断当前元素是否大于其左邻与右邻元素，如符合条件，该元素即为极大值点。对于极大值点I[i]，已知I[i]>I[i+1]，故无需对i+1位置元素做进一步处理，直接跳至i+2位置，对应算法流程第12行。

    

  b. 若元素I[i]不满足算法流程第3行判断条件，将其右邻I[i+1]作为极大值候选，对应算法流程第7行。采用单调递增的方式向右查找，直至找到满足I[i]>I[i+1]的元素，若i<=W-1，该点即为极大值点，对应算法流程第10-11行。

    

3. NMS在物体检测中的应用

  物体检测中应用NMS算法的主要目的是消除多余（交叉重复）的窗口，找到最佳物体检测位置。

  

  如上图所示，人脸检测中，虽然每个窗口均检测到人脸，但仅需给出一个最有可能表征人脸的窗口。

4. 算法程序

function pickLocate = nms(boxes, overlap)

% Non-maximum suppression.
% In object detect algorithm, select high score detections and skip windows
% covered by a previously selected detection.
%
% input - boxes : object detect windows.
%                 xMin yMin xMax yMax score.
%         overlap : suppression threshold.
% output - pickLocate : number of local maximum score.

boxes = double(boxes);

if isempty(boxes)
    pickLocate = [];
else
    xMin = boxes(:, 1);
    yMin = boxes(:, 2);
    xMax = boxes(:, 3);
    yMax = boxes(:, 4);
    
    s = boxes(:, end);
    
    % area of every detected windows.
    area = (xMax - xMin + 1) .* (yMax - yMin + 1);
    
    % sort detected windows based on the score.
    [vals, I] = sort(s);
    
    pickLocate = [];
    while ~isempty(I)
        last = length(I);
        i = I(last);
        
        pickLocate = [pickLocate; i];
        suppress = [last];
        
        for pos = 1 : last - 1
            j = I(pos);  
            
            % covered area.
            xx1 = max(xMin(i), xMin(j));
            yy1 = max(yMin(i), yMin(j));
            xx2 = min(xMax(i), xMax(j));
            yy2 = min(yMax(i), yMax(j));
            
            w = xx2 - xx1 + 1;
            h = yy2 - yy1 + 1;
            
            if ((w > 0) && (h > 0))
                % compute overlap.
                o = w * h / min(area(i), area(j));
                
                if (o > overlap)
                    suppress = [suppress; pos];
                end
            end
            
            % 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;
            % o = inter ./ (area(i) + area(I(1:last-1)) - inter);
            
            % saving the windows which o less than threshold.
            % I = I(o <= overlap);
        end
        I(suppress) = [];
    end
end