MATLAB conv2卷积的实现

二维卷积的算法原理比較简单，參考随意一本数字信号处理的书籍，而matlab的conv2函数的滤波有个形状參数，用以下的一张图非常能说明问题：

这里给出一种最原始的实现方案。这样的实现对于数据矩阵大小为1000x1000，卷积核矩阵大小为20x20，在我的机器上须要大约1秒钟的时间。而matlab採用的MKL库最快仅仅须要将近0.1s的时间。

以下的代码用到了自己眼下开发的FastIV中的一些函数接口。详细代码例如以下：

#include "fiv_core.h"

typedef enum{
	FIV_CONV2_SHAPE_FULL,
	FIV_CONV2_SHAPE_SAME,
	FIV_CONV2_SHAPE_VALID
}FIV_CONV_SHAPE;

void fIv_conv2(fIvMat** dst_mat, fIvMat* src_mat, fIvMat* kernel_mat, FIV_CONV_SHAPE shape)
{
	int src_row = src_mat->rows;
	int src_cols = src_mat->cols;
	int kernel_row = kernel_mat->rows;
	int kernel_cols = kernel_mat->cols;
	int dst_row = 0, dst_cols = 0, edge_row = 0, edge_cols = 0;
	int i,j, kernel_i,kernel_j,src_i,src_j;
	fIvMat* ptr_dst_mat = NULL;

	switch(shape){
		case FIV_CONV2_SHAPE_FULL:	

			dst_row = src_row + kernel_row - 1;
			dst_cols = src_cols + kernel_cols - 1;
			edge_row = kernel_row - 1;
			edge_cols = kernel_cols - 1;
			break;

		case FIV_CONV2_SHAPE_SAME:

			dst_row = src_row;
			dst_cols = src_cols;
			edge_row = (kernel_row - 1) / 2;
			edge_cols = (kernel_cols - 1) / 2;
			break;

		case FIV_CONV2_SHAPE_VALID:

			dst_row = src_row - kernel_row + 1;
			dst_cols = src_cols - kernel_cols + 1;
			edge_row = edge_cols = 0;
			break;

	}

	ptr_dst_mat = fIv_create_mat(dst_row, dst_cols, FIV_64FC1);
	*dst_mat = ptr_dst_mat;

	for (i = 0; i < dst_row; i++) {
		ivf64* ptr_dst_line_i = (ivf64* )fIv_get_mat_data_at_row(ptr_dst_mat, i);
		for (j = 0; j < dst_cols; j++) {
			ivf64 sum = 0;

			kernel_i = kernel_row - 1 - FIV_MAX(0, edge_row - i);
			src_i = FIV_MAX(0, i - edge_row);

			for (; kernel_i >= 0 && src_i < src_row; kernel_i--, src_i++) {

				ivf64* ptr_src_line_i,*ptr_kernel_line_i;

				kernel_j = kernel_cols - 1 - FIV_MAX(0, edge_cols - j);
				src_j = FIV_MAX(0, j - edge_cols);

				ptr_src_line_i = (ivf64*)fIv_get_mat_data_at_row(src_mat, src_i);
				ptr_kernel_line_i = (ivf64*)fIv_get_mat_data_at_row(kernel_mat, kernel_i);

				ptr_src_line_i += src_j;
				ptr_kernel_line_i += kernel_j;

				for (; kernel_j >= 0 && src_j < src_cols; kernel_j--, src_j++){
					sum += *ptr_src_line_i++ * *ptr_kernel_line_i--;
					}
			}
			ptr_dst_line_i[j] = sum;
		}
	}
}

FIV_ALIGNED(16) ivf64 ker_data[4*4] = {0.1,0.2,0.3,0.4,
									   0.5,0.6,0.7,0.8,
									   0.9,1.0,1.1,1.2,
									   1.3,1.4,1.5,1.6};

void test_conv2()
{
	fIvMat* src_mat = fIv_create_mat_magic(8, FIV_64FC1); // 8x8 magic matrix
	fIvMat* kernel_mat = fIv_create_mat_header(4, 4, FIV_64FC1);

	fIvMat* dst_mat = NULL;
	fIv_set_mat_data(kernel_mat, ker_data, (sizeof(ivf64)) * 4 * 4);

	fIv_conv2(&dst_mat, src_mat, kernel_mat, FIV_CONV2_SHAPE_FULL);

	fIv_export_matrix_data_file(dst_mat,"dst_mat_4x4-full.txt", 1);

	fIv_release_mat(&src_mat);
	fIv_release_mat(&kernel_mat);
	fIv_release_mat(&dst_mat);

}

int main()
{
	test_conv2();

	return 0;
}

 10月24日更新:

眼下FastIV中的实现已经经过优化，最高速度在我的机器上已经超越MATLAB。