余弦窗(汉宁窗)的作用——图像预处理

1.MOSSE（Visual Object Tracking using Adaptive Correlation Filters）

3.1 Preprocessing(文章原处) :

    One issue with the FFT convolution algorithm is that the image and the filter are mapped to the topological structure of a torus. In other words, it connects the left edge of the image to the right edge, and the top to the bottom. During convolution, the images rotate through the toroidal space instead of translating as they would in the spatial domain. Artificially connecting the boundaries of the image introducesan artifact which effects the correlation output.

    This effect is reduced by following the preprocessing steps outlined in [3]. First, the pixel values are transformed using a log function which helps with low contrast lighting situations. The pixel values are normalized to have a mean value of 0:0 and a norm of 1:0. Finally, the image is multiplied by a cosine window which gradually reduces the pixel values near the edge to zero. This also has the benefit that it puts more emphasis near the center of the target

    一个问题关于傅立叶卷积算法图片和滤波器被映射到这个拓扑结构的一个环。换句话说，就是图片的左边缘与右边缘连接，上边缘与下边缘连接。在卷积时，图像的旋转通过这个环形的空间代替了它们在时域的转换。人工的链接图像边界将影响相关输出。

    这个影响在预处理时需要减弱。首先，原始像素值通过一个对数函数转换，这将有助于低对比度照明的情况。这个原始的像素值就被规范化为0.0和1.0。最终，图像乘上一个余弦窗口将是靠近图像边缘的像素值接近于零。这同样有利于突出靠近中心的目标。

2 CSK(Exploiting the Circulant Structure of Tracking-by-detection with Kernels)

4.1 Pre-processing(文章原处)：

    The proposed method can operate directly on the pixel values, with no feature extraction.However, since the Fourier transform is periodic, it does not respectthe image boundaries. The large discontinuity between opposite edges of a nonperiodic image will result in a noisy Fourier representation. A common solutionis to band the original n*n image with a cosine (or sine) window:

    

    提出这个方法能够直接操作在原始像素上，没有特征提取。然而，傅里叶变换是周期性的，并没有考虑到图像边界。这个大的不连续的在相反的边缘个一个非周期性的图片上将产生一个噪声。一个共同的解决方法就是在原始图像n*n区域引入余弦（或正弦）窗口。

    总结：其实就是在说明引入余弦窗就是为了解决边界效应，而解决的方法就是在目标原始像素上乘一个余弦窗使接近边缘的像素值接近于零。

汉宁（Hanning）窗可以看成是升余弦窗的一个特例，汉宁窗可以看作是3个矩形时间窗的频谱之和，或者说是 3个 sinc（t）型函数之和，而括号中的两项相对于第一个谱窗向左、右各移动了π/T，从而使旁瓣互相抵消，消去高频干扰和漏能。

适用于非周期性的连续信号。

其中n属于