Schmid也是一种类Gabor图像滤波器，在这篇文章[1]中有具体推导和介绍。

一种更简洁的表达公式是：

其中，r为核半径，Z为归一化参数，τ和σ是比较重要的参数，在ReID提取TextFeature中，经常使用如下一系列参数：

(2,1), (4,1), (4,2), (6,1), (6,2), (6,3), (8,1), (8,2), (8,3), (10,1), (10,2), (10,3), (10,4)

此外，还结合前面的Gabor滤波器，γ,θ,λ,σ的参数分别使用：(0.3,0,4,2), (0.3,0,8,2), (0.4,0,4,1), (0.4,0,4,1), (0.3,π/2,4,2), (0.3,π/2,8,2), (0.4,π/2 ,4,1), (0.4,π/2,4,1)

以下是11个滤波核的示意图：

生成Schmid核函数代码：

Mat getSchmidFilter(float tao, float sigma){
	float r = sigma/(4.0f*tao);
	float sigma2 = sigma*sigma;
	//int half_filter_size = int(r+0.5);
	int half_filter_size = 10;
	int filter_size = 2*half_filter_size+1;
	Mat schmid = Mat::zeros(filter_size,filter_size,CV_32F);
	float filter_sum = 0.0f;
	for(int i=0;i<filter_size;i++){
		float* s = schmid.ptr<float>(i);
		for(int j=0;j<filter_size;j++){
			float x = i-half_filter_size;
			float y = j-half_filter_size;
			r = sqrt(x*x+y*y);
			float tmp = 2*PI*tao*r/sigma;
			float tmp2 = r*r/(2.0f*sigma2);
			s[j] = cos(tmp)*exp(-tmp2);
			filter_sum += s[j];
		}
	}
	//cout<<filter_size<<" "<<filter_sum<<endl;
	//cout<<schmid<<endl;
	if(abs(filter_sum-0.0f)<1e-6){
		return schmid;
	}
	for(int i=0;i<filter_size;i++){
		float* s = schmid.ptr<float>(i);
		for(int j=0;j<filter_size;j++){
			s[j]/=filter_sum;
		}
	}
	return schmid;
}

参考文献：

[1] Schmid, Cordelia. "Constructing models for content-based image retrieval."Computer Vision and Pattern Recognition, 2001. CVPR 2001. Proceedings of the 2001 IEEE Computer Society Conference on. Vol. 2. IEEE, 2001.

[2] Gray, Douglas, and Hai Tao. "Viewpoint invariant pedestrian recognition with an ensemble of localized features." Computer Vision–ECCV 2008. Springer Berlin Heidelberg, 2008. 262-275.

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