卷积神经网络车牌识别

function net = cnnbp2(net, y) % CNN网络,反向传播(批处理算法)(C串行风格) n = numel(net.layers); % CNN网络层数 E = net.layers{n}.X - y; % 输出误差: 预测值-期望值 net.layers{n}.Delta = E .* dy(net.layers{n}.X); % 输出层灵敏度(残差) net.err = 1/2* sum(E(:) .^ 2); % 代价函数是均方误差,已对样本数做平均 % net.err = 1/2* sum(E(:) .^ 2) / size(E, 2); % 代价函数是均方误差,已对样本数做平均 %% 灵敏度(残差)的反向传播 if strcmp(net.layers{2}.type, 'f') % 当第二层就是全连接层时,相当于输入图片拉成一个特征矢量形成的BP网络,考虑到必须计算net.layers{1}.X_Array,所以L的下限必须到1 tmp = 1; else % 其它情况L下限是2就可以 tmp = 2; end for L = (n - 1) : -1 : tmp %====================================================================== % 以下代码对“下一层”为“全连接层”时有效 if (strcmp(net.layers{L+1}.type, 'f')) if (strcmp(net.layers{L}.type, 'f')) %------------------------------------------------------------------ % 以下代码对第7层(全连接层)有效 % 典型的BP网络输出层对隐层的灵敏度(残差)的反向传播公式 net.layers{L}.Delta = (net.layers{L+1}.W' * net.layers{L+1}.Delta) .* dy(net.layers{L}.X); elseif (strcmp(net.layers{L}.type, 's') || strcmp(net.layers{L}.type, 'c') || strcmp(net.layers{L}.type, 'i')) %------------------------------------------------------------------ % 以下代码对第6层(过渡全连接层)有效 sa = size(net.layers{L}.X{1}); % 每个输出通道图像尺寸(三维矢量,前两维是尺寸,第三维是批处理样本个数) fvnum = sa(1) * sa(2); % 输出图像像素个数 % 典型的BP网络输出层对隐层的灵敏度(残差)的反向传播公式 net.layers{L}.Delta_Array = (net.layers{L+1}.W' * net.layers{L+1}.Delta); if strcmp(net.layers{L}.type, 'c') net.layers{L}.Delta_Array = net.layers{L}.Delta_Array .* dy(net.layers{L}.X_Array); end for J = 1 : net.layers{L}.iChannel % 将本层长矢量灵敏度(残差),每一列为一个样本,reshape成通道表示 (矢量化全连接 -> 通道化全连接) net.layers{L}.Delta{J} = reshape(net.layers{L}.Delta_Array (((J - 1) * fvnum + 1) : J * fvnum, :), sa(1), sa(2)); % net.layers{L}.Delta{J} = reshape(net.layers{L}.Delta_Array (((J - 1) * fvnum + 1) : J * fvnum, :), sa(1), sa(2), sa(3)); end %------------------------------------------------------------------ end end %====================================================================== % 以下代码对“下一层”为“下采样层”时有效 if (strcmp(net.layers{L+1}.type, 's')) for J = 1 : net.layers{L}.iChannel % 对本层输出通道数做循环 tmp1 = dy(net.layers{L}.X{J}); % 为本层导数 % 为上采样函数,这里用expand函数代替文献中的kron(kron仅适用二维情况) tmp2 = up(net.layers{L + 1}.Delta{J}, net.layers{L + 1}.iSample); % tmp2 = expand(net.layers{L + 1}.Delta{J}, [net.layers{L + 1}.iSample,net.layers{L + 1}.iSample,1]); % net.layers{L}.Delta{J} = net.layers{L}.X{J} .* (1 - net.layers{L}.X{J}) .* (expand(net.layers{L + 1}.Delta{J}, [net.layers{L + 1}.iSample net.layers{L + 1}.iSample 1]) / net.layers{L + 1}.iSample ^ 2); % 与上式相比, 这里我认为最好不除以net.layers{L + 1}.iSample ^ 2, 因为在CNN正向计算函数cnnff中只做了下采样处理, 可以认为灵敏度(残差)是直接复制过去的. %############################################################## % 后改，以下代码用于下采样层的计算 net.layers{L}.Delta{J} = tmp1 .* tmp2; net.layers{L}.Delta{J} = net.layers{L+1}.Beta{J} * net.layers{L}.Delta{J}; end end %====================================================================== % 以下代码对“下一层”为“卷积层”时有效 if (strcmp(net.layers{L+1}.type, 'c')) for I = 1 : net.layers{L}.iChannel % 对本层输出通道数做循环 z = zeros(size(net.layers{L}.X{1})); for J = 1 : net.layers{L+1}.iChannel % 对下一层输出通道数做循环 % 当前层灵敏度(残差)net.layers{L}.Delta{J}计算 z = z + conv2(net.layers{L + 1}.Delta{J}, rot180(net.layers{L + 1}.Ker{I}{J},2), 'full'); % z = z + convn(net.layers{L + 1}.Delta{J}, rot180(net.layers{L + 1}.Ker{I}{J},2), 'full'); end net.layers{L}.Delta{I} = z; % net.layers{L}.Delta{I} = dy(net.layers{L}.X{I}) .* net.layers{L}.Delta{I}; end end %====================================================================== end %% 求训练参数的梯度 % 特别注意：与Matlab并行版本不同，由于C采用是串行机制，以下训练参数在这里需要累加，之后在函数cnngradmean()中对一批样本做平均 % net.layers{L}.Ker_grad{I}{J} % net.layers{L}.B_grad{J} % net.layers{L}.W_grad % net.layers{L}.B_grad % % 这里与 Notes on Convolutional Neural Networks 中不同，这里的 子采样 层没有参数，也没有 % 激活函数，所以在子采样层是没有需要求解的参数的 for L = 2 : n % 对CNN网络层数做循环(注意:这里实际上可以从第2层开始) %====================================================================== if (strcmp(net.layers{L}.type, 'c')) for J = 1 : net.layers{L}.iChannel % 对本层输出通道数做循环 for I = 1 : net.layers{L-1}.iChannel % 对上一层输出通道数做循环 % 特别注意: % (1)等价关系 rot180(conv2(a,rot180(b),'valid')) = conv2(rot180(a),b,'valid') % (2)若ndims(a)=ndims(b)=3,则convn(filpall(a),b,'valid')表示三个维度上同时相关运算 % (3)若size(a,3)=size(b,3),则上式输出第三维为1,表示参与训练样本的叠加和(批处理算法),结果要对样本数做平均 net.layers{L}.Ker_grad{I}{J} = net.layers{L}.Ker_grad{I}{J} + conv2(rot180(net.layers{L - 1}.X{I},2), net.layers{L}.Delta{J}, 'valid'); % net.layers{L}.Ker_grad{I}{J} = convn(rot180(net.layers{L - 1}.X{I},3), net.layers{L}.Delta{J}, 'valid') / size(net.layers{L}.Delta{J}, 3); end % 对所有net.layers{L}.Delta{J}的叠加,结果要对样本数做平均 net.layers{L}.B_grad{J} = net.layers{L}.B_grad{J} + sum(net.layers{L}.Delta{J}(:)); % net.layers{L}.B_grad{J} = sum(net.layers{L}.Delta{J}(:)) / size(net.layers{L}.Delta{J}, 3); end end %###################################################################### % 后改，以下代码用于下采样层的计算 if (strcmp(net.layers{L}.type, 's')) for J = 1 : net.layers{L}.iChannel % 对本层输出通道数做循环 net.layers{L}.Beta_grad{J} = net.layers{L}.Beta_grad{J} + sum(net.layers{L}.Delta{J}(:) .* net.layers{L}.X_down{J}(:)); % net.layers{L}.Beta_grad{J} = sum(net.layers{L}.Delta{J}(:) .* net.layers{L}.X_down{J}(:)) / size(net.layers{L}.Delta{J}, 3); % 对所有net.layers{L}.Delta{J}的叠加,结果要对样本数做平均 net.layers{L}.B_grad{J} = net.layers{L}