非极大值抑制 （NMS）及其matlab代码实现

非极大值抑制（Non Maximum Suppression）最常用的领域就是目标检测，比如人脸检测，物体检测等。下面也就其在目标检测领域的应用及其代码实现。

目标检测的基本流程如下：

具体示意图如下：

所以，在输出的ScoreMap中，像素数为numel(ScoreMap)，则输出检测到的Box数目为numel(ScoreMap)个，其维数为（4，numel(ScoreMap)），那么在这么多个输出的detBox(检测到的Box)中，哪一个（假设图像中只含一个目标）呢？这就需要采用非极大值抑制去除冗余的detBox，抑制的过程是一个迭代-遍历-消除的过程。具体如下代码实现：

im = imread(testImages{3}) ;
im = im2single(im) ;

% Compute detections
[detections, scores] = detect(im, w, hogCellSize, scales) ;

% Non-maxima suppression
keep = boxsuppress(detections, scores, 0.25) ;

detections = detections(:, keep) ;
scores = scores(keep) ;

% Further keep only top detections
detections = detections(:, 1:10) ;
scores = scores(1:10) ;

function keep = boxsuppress(boxes, scores, threshold)
% BOXSUPPRESS Box non-maxima suprression（非最大值抑制）
%   KEEP = BOXSUPPRESS(BOXES, SCORES, THRESHOLD)

% remove any empty box (xmax < xmin or ymax < ymin)
scores(any([-1 0 1 0 ; 0 -1 0 1] * boxes < 0)) = -inf ;

keep = false(1, size(boxes,2)) ;
while true
  [score, best] = max(scores) ;
  if score == -inf, break ; end
  keep(best) = true ;
  remove = boxinclusion(boxes(:,best), boxes, 'pascalFormat', true) >= threshold ;
  scores(remove) = -inf ;
  scores(best) = -inf ; % `best` is not in `remove` if threshold > 1
end

function dist = calcBoxInclusion(A, B, varargin)
%%boxinclusion
 % GETBOXOVERLAP
%   A and B have a box for each column, in the format [xmin ymin xmax
%   ymax]. The resulting matrix dist has A's boxes along the rows
%   and B's boxes along the columns and contains the percentage of
%   the area of each box B contained in the box A.

opts.pascalFormat = false ;
opts = vl_argparse(opts, varargin) ;

m = size(A,2) ;
n = size(B,2) ;
O = [] ;

if m==0 || n==0, dist = zeros(m,n) ; return ; end

om = ones(1,m) ;
on = ones(1,n) ;

if opts.pascalFormat
  A(3:4,:) = A(3:4,:) + 1 ;
  B(3:4,:) = B(3:4,:) + 1 ;
end

% find length Ox of the overlap range [x1, x2] along x
% x1 cannot be smaller than A.xmin B.xmin
% x2 cannot be larger  than A.xmax B.xmax
% Ox is x2 - x1 or 0

x1 = max(A(1*on,:)', B(1*om,:)) ;
x2 = min(A(3*on,:)', B(3*om,:)) ;
Ox = max(x2 - x1, 0) ;

y1 = max(A(2*on,:)', B(2*om,:)) ;
y2 = min(A(4*on,:)', B(4*om,:)) ;
Oy = max(y2 - y1, 0) ;

% are of the intersection
areaInt = Ox .* Oy ;

% area of the union is sum of areas - inersection
areaA = prod(A(3:4,:) - A(1:2,:)) ;
areaB = prod(B(3:4,:) - B(1:2,:)) ;

% final distance matrix
dist = areaInt ./ (areaB(om,:) + eps) ;

重点部分注释：

scores(any([-1 0 1 0 ; 0 -1 0 1] * boxes < 0)) = -inf ;

这里要注意的是boxes的格式，即为[xmin,ymin,xmax,ymax]，其与[-1 0 1 0;0 -1 0 1]相乘，如果其值小于零，也就是xmax

x1 = max(A(1*on,:)', B(1*om,:)) ;
x2 = min(A(3*on,:)', B(3*om,:)) ;

y1 = max(A(2*on,:)', B(2*om,:)) ;
y2 = min(A(4*on,:)', B(4*om,:)) ;

要理解此段代码，见下图所示：

重叠部分的面积即为左上角(x21,y21)（框2的坐标小值）到右下角(x12,y12)（框1坐标的大值）矩形的面积。因为框1已经是按照Score的较大值像素点检测出的Box，框2是按照次较大值检测的Box，如果两者的Box有较大面积重合（设定一个阈值），此时可以说明框1和框2都在目标附近，但是框1更准确一点定位到目标，那么框2也就没必要保留了。继续迭代下一个检测到的Box，是否满足消除条件决定是否保留Box，这就是非最大值抑制。

参考：

1. NMS——非极大值抑制