# HOG(Histograms of Oriented Gradients) 代码

Source from

http://hi.baidu.com/timehandle/blog/item/9a395c370e69980591ef3943.html

```function F = hogcalculator(img, cellpw, cellph, nblockw, nblockh,...
nthet, overlap, isglobalinterpolate, issigned, normmethod)
% HOGCALCULATOR calculate R-HOG feature vector of an input image using the
% procedure presented in Dalal and Triggs's paper in CVPR 2005.
%

% Author:   timeHandle
% Time:     March 24, 2010
%           May 12，2010 update.
%
%       this copy of code is written for my personal interest, which is an
%       original and inornate realization of [Dalal CVPR2005]'s algorithm
%       without any optimization. I just want to check whether I understand
%       the algorithm really or not, and also do some practices for knowing
%       matlab programming more well because I could be called as 'novice'.
%       OpenCV 2.0 has realized Dalal's HOG algorithm which runs faster
%       than mine without any doubt, ╮(╯▽╰)╭ . Ronan pointed a error in
%       the code，thanks for his correction. Note that at the end of this
%
% F = hogcalculator(img, cellpw, cellph, nblockw, nblockh,
%    nthet, overlap, isglobalinterpolate, issigned, normmethod)
%
% IMG:
%       IMG is the input image.
%
% CELLPW, CELLPH:
%       CELLPW and CELLPH are cell's pixel width and height respectively.
%
% NBLOCKW, NBLCOKH:
%       NBLOCKW and NBLCOKH are block size counted by cells number in x and
%       y directions respectively.
%
% NTHET, ISSIGNED:
%       NTHET is the number of the bins of the histogram of oriented
%       gradient. The histogram of oriented gradient ranges from 0 to pi in
%       'unsigned' condition while to 2*pi in 'signed' condition, which can
%       be specified through setting the value of the variable ISSIGNED by
%       the string 'unsigned' or 'signed'.
%
% OVERLAP:
%       OVERLAP is the overlap proportion of two neighboring block.
%
% ISGLOBALINTERPOLATE:
%       ISGLOBALINTERPOLATE specifies whether the trilinear interpolation
%       is done in a single global 3d histogram of the whole detecting
%       window by the string 'globalinterpolate' or in each local 3d
%       histogram corresponding to respective blocks by the string
%       'localinterpolate' which is in strict accordance with the procedure
%       proposed in Dalal's paper. Interpolating in the whole detecting
%       window requires the block's sliding step to be an integral multiple
%       of cell's width and height because the histogram is fixing before
%       interpolate. In fact here the so called 'global interpolation' is
%       a notation given by myself. at first the spatial interpolation is
%       done without any relevant to block's slide position, but when I was
%       doing calculation while OVERLAP is 0.75, something occurred and
%       confused me o__O"… . This let me find that the operation I firstly
%       did is different from which mentioned in Dalal's paper. But this
%       does not mean it is incorrect ^◎^, so I reserve this. As for name,
%       besides 'global interpolate', any others would be all ok, like 'Lady GaGa'
%       or what else, :-).
%
% NORMMETHOD：
%       NORMMETHOD is the block histogram normalized method which can be
%       set as one of the following strings:
%               'none', which means non-normalization;
%               'l1', which means L1-norm normalization;
%               'l2', which means L2-norm normalization;
%               'l1sqrt', which means L1-sqrt-norm normalization;
%               'l2hys', which means L2-hys-norm normalization.
% F：
%       F is a row vector storing the final histogram of all of the blocks
%       one by one in a top-left to bottom-right image scan manner, the
%       cells histogram are stored in the same manner in each block's
%       section of F.
%
% Note that CELLPW*NBLOCKW and CELLPH*NBLOCKH should be equal to IMG's
% width and height respectively.
%
% Here is a demonstration, which all of parameters are set as the
% best value mentioned in Dalal's paper when the window detected is 128*64
% size(128 rows, 64 columns):
%       F = hogcalculator(window, 8, 8, 2, 2, 9, 0.5,
%                               'localinterpolate', 'unsigned', 'l2hys');
% Also the function can be called like:
%       F = hogcalculator(window);
% the other parameters are all set by using the above-mentioned "dalal's
% best value" as default.
%

if nargin < 2
% set default parameters value.
cellpw = 8;
cellph = 8;
nblockw = 2;
nblockh = 2;
nthet = 9;
overlap = 0.5;
isglobalinterpolate = 'localinterpolate';
issigned = 'unsigned';
normmethod = 'l2hys';
else
if nargin < 10
error('Input parameters are not enough.');
end
end

% check parameters's validity.
[M, N, K] = size(img);
if mod(M,cellph*nblockh) ~= 0
error('IMG''s height should be an integral multiple of CELLPH*NBLOCKH.');
end
if mod(N,cellpw*nblockw) ~= 0
error('IMG''s width should be an integral multiple of CELLPW*NBLOCKW.');
end
if mod((1-overlap)*cellpw*nblockw, cellpw) ~= 0 ||...
mod((1-overlap)*cellph*nblockh, cellph) ~= 0
str1 = 'Incorrect OVERLAP or ISGLOBALINTERPOLATE parameter';
str2 = ', slide step should be an intergral multiple of cell size';
error([str1, str2]);
end

% set the standard deviation of gaussian spatial weight window.
delta = cellpw*nblockw * 0.5;

hx = [-1,0,1];
hy = -hx';

%
if K > 1
gxtemp = zeros(M,N);
gytemp = gxtemp;
for kn = 1:K
[rowidx, colidx] = ind2sub(size(gidx),find(gidx==kn));
end
else
end

% plus small number for avoiding dividing zero.
% unsigned situation: orientation region is 0 to pi.
if strcmp(issigned, 'unsigned') == 1
or = 1;
else
% signed situation: orientation region is 0 to 2*pi.
if strcmp(issigned, 'signed') == 1
or = 2;
else
error('Incorrect ISSIGNED parameter.');
end
end

% calculate block slide step.
xbstride = cellpw*nblockw*(1-overlap);
ybstride = cellph*nblockh*(1-overlap);
xbstridend = N - cellpw*nblockw + 1;
ybstridend = M - cellph*nblockh + 1;

% calculate the total blocks number in the window detected, which is
% ntotalbh*ntotalbw.
ntotalbh = ((M-cellph*nblockh)/ybstride)+1;
ntotalbw = ((N-cellpw*nblockw)/xbstride)+1;

% generate the matrix hist3dbig for storing the 3-dimensions histogram. the
% matrix covers the whole image in the 'globalinterpolate' condition or
% covers the local block in the 'localinterpolate' condition. The matrix is
% bigger than the area where it covers by adding additional elements
% (corresponding to the cells) to the surround for calculation convenience.
if strcmp(isglobalinterpolate, 'globalinterpolate') == 1
ncellx = N / cellpw;
ncelly = M / cellph;
hist3dbig = zeros(ncelly+2, ncellx+2, nthet+2);
F = zeros(1, (M/cellph-1)*(N/cellpw-1)*nblockw*nblockh*nthet);
glbalinter = 1;
else
if strcmp(isglobalinterpolate, 'localinterpolate') == 1
hist3dbig = zeros(nblockh+2, nblockw+2, nthet+2);
F = zeros(1, ntotalbh*ntotalbw*nblockw*nblockh*nthet);
glbalinter = 0;
else
error('Incorrect ISGLOBALINTERPOLATE parameter.')
end
end

% generate the matrix for storing histogram of one block;
sF = zeros(1, nblockw*nblockh*nthet);

% generate gaussian spatial weight.
[gaussx, gaussy] = meshgrid(0:(cellpw*nblockw-1), 0:(cellph*nblockh-1));
weight = exp(-((gaussx-(cellpw*nblockw-1)/2)...
.*(gaussx-(cellpw*nblockw-1)/2)+(gaussy-(cellph*nblockh-1)/2)...
.*(gaussy-(cellph*nblockh-1)/2))/(delta*delta));

% vote for histogram. there are two situations according to the interpolate
% condition('global' interpolate or local interpolate). The hist3d which is
% generated from the 'bigger' matrix hist3dbig is the final histogram.
if glbalinter == 1
xbstep = nblockw*cellpw;
ybstep = nblockh*cellph;
else
xbstep = xbstride;
ybstep = ybstride;
end
% block slide loop
for btly = 1:ybstep:ybstridend
for btlx = 1:xbstep:xbstridend
for bi = 1:(cellph*nblockh)
for bj = 1:(cellpw*nblockw)

i = btly + bi - 1;
j = btlx + bj - 1;
gaussweight = weight(bi,bj);

if glbalinter == 1
jorbj = j;
iorbi = i;
else
jorbj = bj;
iorbi = bi;
end

% calculate bin index of hist3dbig
binx1 = floor((jorbj-1+cellpw/2)/cellpw) + 1;
biny1 = floor((iorbi-1+cellph/2)/cellph) + 1;
binz1 = floor((go+(or*pi/nthet)/2)/(or*pi/nthet)) + 1;

if gs < 1E-5
continue;
end

binx2 = binx1 + 1;
biny2 = biny1 + 1;
binz2 = binz1 + 1;

x1 = (binx1-1.5)*cellpw + 0.5;
y1 = (biny1-1.5)*cellph + 0.5;
z1 = (binz1-1.5)*(or*pi/nthet);

% trilinear interpolation.
hist3dbig(biny1,binx1,binz1) =...
hist3dbig(biny1,binx1,binz1) + gs*gaussweight...
* (1-(jorbj-x1)/cellpw)*(1-(iorbi-y1)/cellph)...
*(1-(go-z1)/(or*pi/nthet));
hist3dbig(biny1,binx1,binz2) =...
hist3dbig(biny1,binx1,binz2) + gs*gaussweight...
* (1-(jorbj-x1)/cellpw)*(1-(iorbi-y1)/cellph)...
*((go-z1)/(or*pi/nthet));
hist3dbig(biny2,binx1,binz1) =...
hist3dbig(biny2,binx1,binz1) + gs*gaussweight...
* (1-(jorbj-x1)/cellpw)*((iorbi-y1)/cellph)...
*(1-(go-z1)/(or*pi/nthet));
hist3dbig(biny2,binx1,binz2) =...
hist3dbig(biny2,binx1,binz2) + gs*gaussweight...
* (1-(jorbj-x1)/cellpw)*((iorbi-y1)/cellph)...
*((go-z1)/(or*pi/nthet));
hist3dbig(biny1,binx2,binz1) =...
hist3dbig(biny1,binx2,binz1) + gs*gaussweight...
* ((jorbj-x1)/cellpw)*(1-(iorbi-y1)/cellph)...
*(1-(go-z1)/(or*pi/nthet));
hist3dbig(biny1,binx2,binz2) =...
hist3dbig(biny1,binx2,binz2) + gs*gaussweight...
* ((jorbj-x1)/cellpw)*(1-(iorbi-y1)/cellph)...
*((go-z1)/(or*pi/nthet));
hist3dbig(biny2,binx2,binz1) =...
hist3dbig(biny2,binx2,binz1) + gs*gaussweight...
* ((jorbj-x1)/cellpw)*((iorbi-y1)/cellph)...
*(1-(go-z1)/(or*pi/nthet));
hist3dbig(biny2,binx2,binz2) =...
hist3dbig(biny2,binx2,binz2) + gs*gaussweight...
* ((jorbj-x1)/cellpw)*((iorbi-y1)/cellph)...
*((go-z1)/(or*pi/nthet));
end
end

% In the local interpolate condition. F is generated in this block
% slide loop. hist3dbig should be cleared in each loop.
if glbalinter == 0
if or == 2
hist3dbig(:,:,2) = hist3dbig(:,:,2)...
+ hist3dbig(:,:,nthet+2);
hist3dbig(:,:,(nthet+1)) =...
hist3dbig(:,:,(nthet+1)) + hist3dbig(:,:,1);
end
hist3d = hist3dbig(2:(nblockh+1), 2:(nblockw+1), 2:(nthet+1));
for ibin = 1:nblockh
for jbin = 1:nblockw
idsF = nthet*((ibin-1)*nblockw+jbin-1)+1;
idsF = idsF:(idsF+nthet-1);
sF(idsF) = hist3d(ibin,jbin,:);
end
end
iblock = ((btly-1)/ybstride)*ntotalbw +...
((btlx-1)/xbstride) + 1;
idF = (iblock-1)*nblockw*nblockh*nthet+1;
idF = idF:(idF+nblockw*nblockh*nthet-1);
F(idF) = sF;
hist3dbig(:,:,:) = 0;
end
end
end

% In the global interpolate condition. F is generated here outside the
% block slide loop
if glbalinter == 1
ncellx = N / cellpw;
ncelly = M / cellph;
if or == 2
hist3dbig(:,:,2) = hist3dbig(:,:,2) + hist3dbig(:,:,nthet+2);
hist3dbig(:,:,(nthet+1)) = hist3dbig(:,:,(nthet+1)) + hist3dbig(:,:,1);
end
hist3d = hist3dbig(2:(ncelly+1), 2:(ncellx+1), 2:(nthet+1));

iblock = 1;
for btly = 1:ybstride:ybstridend
for btlx = 1:xbstride:xbstridend
binidx = floor((btlx-1)/cellpw)+1;
binidy = floor((btly-1)/cellph)+1;
idF = (iblock-1)*nblockw*nblockh*nthet+1;
idF = idF:(idF+nblockw*nblockh*nthet-1);
for ibin = 1:nblockh
for jbin = 1:nblockw
idsF = nthet*((ibin-1)*nblockw+jbin-1)+1;
idsF = idsF:(idsF+nthet-1);
sF(idsF) = hist3d(binidy+ibin-1, binidx+jbin-1, :);
end
end
F(idF) = sF;
iblock = iblock + 1;
end
end
end

% adjust the negative value caused by accuracy of floating-point
% operations.these value's scale is very small, usually at E-03 magnitude
% while others will be E+02 or E+03 before normalization.
F(F<0) = 0;

% block normalization.
e = 0.001;
l2hysthreshold = 0.2;
fslidestep = nblockw*nblockh*nthet;
switch normmethod
case 'none'
case 'l1'
for fi = 1:fslidestep:size(F,2)
div = sum(F(fi:(fi+fslidestep-1)));
F(fi:(fi+fslidestep-1)) = F(fi:(fi+fslidestep-1))/(div+e);
end
case 'l1sqrt'
for fi = 1:fslidestep:size(F,2)
div = sum(F(fi:(fi+fslidestep-1)));
F(fi:(fi+fslidestep-1)) = sqrt(F(fi:(fi+fslidestep-1))/(div+e));
end
case 'l2'
for fi = 1:fslidestep:size(F,2)
sF = F(fi:(fi+fslidestep-1)).*F(fi:(fi+fslidestep-1));
div = sqrt(sum(sF)+e*e);
F(fi:(fi+fslidestep-1)) = F(fi:(fi+fslidestep-1))/div;
end
case 'l2hys'
for fi = 1:fslidestep:size(F,2)
sF = F(fi:(fi+fslidestep-1)).*F(fi:(fi+fslidestep-1));
div = sqrt(sum(sF)+e*e);
sF = F(fi:(fi+fslidestep-1))/div;
sF(sF>l2hysthreshold) = l2hysthreshold;
div = sqrt(sum(sF.*sF)+e*e);
F(fi:(fi+fslidestep-1)) = sF/div;
end
otherwise
error('Incorrect NORMMETHOD parameter.');
end```

btly与btlx分别表示block所在位置左上角点处的坐标。对于前述假设，一个检测窗内会有105个block存在，因此第一个block左上角的坐标是(1,1),第二个是(9,1)…,此行最后一个是block的左上角坐标是(49,1),然后下一个block就需要向下滑动8个像素，并回到最左边,此时的block左上角坐标为(1,9),接着block重新开始新的横向滑动…如此这般,在检测窗内最后一个block的坐标就是(49,113).

block每滑动到一个新的位置，就需要停下来计算它内部的那四个cell中的梯度方向直方图.(bj,bi)就是来存储cell左上角的坐标的（cell的坐标以block左上角为原点）.

(j,i)就表示cell中的像素在整个检测窗（64*128的图像）中的坐标.另外，我在程序里有个jorbj与iorbi，这在Localinterpolate的情况下（也就是标准的原始HOG情况），就是bj与bi.

```binx1 = floor((jorbj-1+cellpw/2)/cellpw) + 1;
biny1 = floor((iorbi-1+cellph/2)/cellph) + 1;
binz1 = floor((go+(or*pi/nthet)/2)/(or*pi/nthet)) + 1;
binx2 = binx1 + 1;
biny2 = biny1 + 1;
binz2 = binz1 + 1;```

```x1 = (binx1-1.5)*cellpw + 0.5;
y1 = (biny1-1.5)*cellph + 0.5;
z1 = (binz1-1.5)*(or*pi/nthet);```

```if or == 2
hist3dbig(:,:,2) = hist3dbig(:,:,2) + hist3dbig(:,:,nthet+2);
hist3dbig(:,:,(nthet+1)) = hist3dbig(:,:,(nthet+1)) + hist3dbig(:,:,1);
end```

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