论文PCANet: A Simple Deep Learning Baseline for Image Classification?的matlab源码解读（三）

<span style="font-family:Times New Roman;font-size:18px;"><span style="font-family:Times New Roman;font-size:14px;"><span style="font-family: Arial, Helvetica, sans-serif;">function [f BlkIdx] = HashingHist(PCANet,ImgIdx,OutImg)</span></span></span>

<span style="font-family:Times New Roman;font-size:18px;"><span style="font-family:Times New Roman;font-size:14px;">% Output layer of PCANet (Hashing plus local histogram)
% ========= INPUT ============
% PCANet  PCANet parameters (struct)
%       .PCANet.NumStages      
%           the number of stages in PCANet; e.g., 2  
%       .PatchSize
%           the patch size (filter size) for square patches; e.g., [5 3]
%           means patch size equalt to 5 and 3 in the first stage and second stage, respectively 
%       .NumFilters
%           the number of filters in each stage; e.g., [16 8] means 16 and
%           8 filters in the first stage and second stage, respectively
%       .HistBlockSize 
%           the size of each block for local histogram; e.g., [10 10]
%       .BlkOverLapRatio 
%           overlapped block region ratio; e.g., 0 means no overlapped 
%           between blocks, and 0.3 means 30% of blocksize is overlapped 
%       .Pyramid
%           spatial pyramid matching; e.g., [1 2 4], and [] if no Pyramid
%           is applied
% ImgIdx  Image index for OutImg (column vector) 
% OutImg  PCA filter output before the last stage (cell structure) 这里的OutImg为
% ========= OUTPUT ===========
% f       PCANet features (each column corresponds to feature of each image)
% BlkIdx  index of local block from which the histogram is compuated
% ============================
addpath('./Utils')


NumImg = max(ImgIdx);% 求每一列的最大值，相当于求总共有多少输入图片，这里的输入图片数目是最后一层的输入，不是初始的图片样本数
f = cell(NumImg,1);% 这里的NUmImg=L2*L1*NumImg
% 这部分就是进行二值化哈希编码时候的权重，权重设置为 2 的 i 次幂。
% PCANet.NumFilters(end)-1 对应论文中的2^(l-1),l=1...L2
% ((PCANet.NumFilters(end)-1):-1:0)就是以-1为间隔取到0
map_weights = 2.^((PCANet.NumFilters(end)-1):-1:0); % weights for binary to decimal conversion 权重从二进制转换到十进制 


for Idx = 1:NumImg %外层循环对每一幅图片进行
    % ImgIdx大小为（NumFilters*NumImg）*1，是一个列向量；每个输入图片都有L1*L2个索引
    Idx_span = find(ImgIdx == Idx);%分别找到每一幅样本图片的索引1~N
    % find函数返回ImgIdx矩阵中为Idx元素的索引，索引跨度为L1*L2
    NumOs = length(Idx_span)/PCANet.NumFilters(end); % the number of "O"s ；这里是N个图形经一层PCA的L1个滤波器后的输出个数
    Bhist = cell(NumOs,1);% 对矩阵T,将其分成B块，得到的分块矩阵大小为 （k1k2）* B，NumOs = L1
    
    for i = 1:NumOs % 内层循环第一阶段的滤波器L1，对应论文中的For each of the L1 images T_li;l = 1...L1, we partition it into B blocks
        
        T = 0;
        ImgSize = size(OutImg{Idx_span(PCANet.NumFilters(end)*(i-1) + 1)});%此处的size应该还是m*n
        % 这里需要此次循环的样本图片在第i个L1中的滤波器输出开始的索引号，Idx_span跨度为L1*L2
        for j = 1:PCANet.NumFilters(end)
        % 第三层循环L2层滤波器
            T = T + map_weights(j)*Heaviside(OutImg{Idx_span(PCANet.NumFilters(end)*(i-1)+j)}); 
            % weighted combination; hashing codes to decimal number conversion
            % heaviside(x) has the value 0 for x < 0, 1 for x > 0, and 0.5 for x == 0. 
            
            OutImg{Idx_span(PCANet.NumFilters(end)*(i-1)+j)} = [];%清空缓存
        end
        
        
        if isempty(PCANet.HistBlockSize)%判断HistBlockSize是否被赋值，如果有赋值返回0
            NumBlk = ceil((PCANet.ImgBlkRatio - 1)./PCANet.BlkOverLapRatio) + 1;
            HistBlockSize = ceil(size(T)./PCANet.ImgBlkRatio);
            OverLapinPixel = ceil((size(T) - HistBlockSize)./(NumBlk - 1));
            NImgSize = (NumBlk-1).*OverLapinPixel + HistBlockSize;
            Tmp = zeros(NImgSize);
            Tmp(1:size(T,1), 1:size(T,2)) = T;
            Bhist{i} = sparse(histc(im2col_general(Tmp,HistBlockSize,...
            OverLapinPixel),(0:2^PCANet.NumFilters(end)-1)')); 
        else %当HistBlockSize被赋值时执行
            
            stride = round((1-PCANet.BlkOverLapRatio)*PCANet.HistBlockSize); %round（）四舍五入,stride为X和y轴的间隔
            blkwise_fea = sparse(histc(im2col_general(T,PCANet.HistBlockSize,...
              stride),(0:2^PCANet.NumFilters(end)-1)')); 
            % calculate histogram for each local block in "T"
            % histc函数制定数值边界为分界条件，这里是2^L2-1为分界
            % S = sparse(A) 将矩阵A转化为稀疏矩阵形式，即矩阵A中任何0元素被去除，非零元素及其下标组成矩阵S。
            % 这里sparse的作用是计算在图片的编码值在每个区间的个数
			 
           if ~isempty(PCANet.Pyramid)
                x_start = ceil(PCANet.HistBlockSize(2)/2);
                y_start = ceil(PCANet.HistBlockSize(1)/2);
                x_end = floor(ImgSize(2) - PCANet.HistBlockSize(2)/2);
                y_end = floor(ImgSize(1) - PCANet.HistBlockSize(1)/2);
                
                sam_coordinate = [...
                    kron(x_start:stride:x_end,ones(1,length(y_start:stride: y_end))); 
                    kron(ones(1,length(x_start:stride:x_end)),y_start:stride: y_end)];               
                
                blkwise_fea = spp(blkwise_fea, sam_coordinate, ImgSize, PCANet.Pyramid)';
                %spp()函数对灰度值进行二进制编码
           else% PCANet.Pyramid未设置时执行
                blkwise_fea = bsxfun(@times, blkwise_fea, ...
                    2^PCANet.NumFilters(end)./sum(blkwise_fea)); 
           end
           
           Bhist{i} = blkwise_fea;
        end
        
    end           
    f{Idx} = vec([Bhist{:}]');
    
    if ~isempty(PCANet.Pyramid)
        f{Idx} = sparse(f{Idx}/norm(f{Idx}));
    end
end
f = [f{:}];

if ~isempty(PCANet.Pyramid)
    BlkIdx = kron((1:size(Bhist{1},1))',ones(length(Bhist)*size(Bhist{1},2),1));
else
    BlkIdx = kron(ones(NumOs,1),kron((1:size(Bhist{1},2))',ones(size(Bhist{1},1),1)));
end

%-------------------------------
function X = Heaviside(X) % binary quantization
X = sign(X);
X(X<=0) = 0;

function x = vec(X) % vectorization
x = X(:);


function beta = spp(blkwise_fea, sam_coordinate, ImgSize, pyramid)

[dSize, ~] = size(blkwise_fea);

img_width = ImgSize(2);
img_height = ImgSize(1);

% spatial levels
pyramid_Levels = length(pyramid);
pyramid_Bins = pyramid.^2;
tBins = sum(pyramid_Bins);

beta = zeros(dSize, tBins);
cnt = 0;

for i1 = 1:pyramid_Levels,
    
    Num_Bins = pyramid_Bins(i1);
    
    wUnit = img_width / pyramid(i1);
    hUnit = img_height / pyramid(i1);
    
    % find to which spatial bin each local descriptor belongs
    xBin = ceil(sam_coordinate(1,:) / wUnit);
    yBin = ceil(sam_coordinate(2,:) / hUnit);
    idxBin = (yBin - 1)*pyramid(i1) + xBin;
    
    for i2 = 1:Num_Bins,     
        cnt = cnt + 1;
        sidxBin = find(idxBin == i2);
        if isempty(sidxBin),
            continue;
        end      
        beta(:, cnt) = max(blkwise_fea(:, sidxBin), [], 2);
    end
end</span></span>

此函数实现哈希编码并画成直方图