参考书目：Forsyth and Ponce, Computer Vision, Chapter 7

Filtering

用原始图像的像素点的组合构造新的图像。

Form a new image whose pixels are a combination of the original pixel values.

目的:

  • 提取图像中有用的信息
    • 特征(edges, corners, blobs)
  • 修改，增强图像的某些属性
    • Super-resolution; in-painting; de-noising.

举例：

  • Moving average

    • 用相邻像素的平均值替换掉这个像素的值
    • 平滑滤波，去掉sharp features.

  • Image segmentation

    • 定义一个阈值，大于的取255，小于的取0

离散卷积(descret convolution)

符号 *

步骤：

  • Fold h[k,l] about origin to form h[−k,−l], 模板翻转
  • Shift the folded results by n,m to form h[n − k,m − l] 模板平移
  • Multiply h[n − k,m − l] by f[k, l]
  • Sum over all k,l
  • Repeat for every n,m

original - blurred = detailed.

original + detailed = sharped.

也就是说

2倍的original - blurred = sharpped

假如图像是N1xM1，模板是N2xM2，卷积之后的结果是(N1+N2-1)x(M1+M2-1).

对原始图像超出了N1xM1的部分有多种处理方式:

  • 补0(zero padding), matlab使用这种方式

假如矩阵是:

补0后:

  • 复制边界像素(edge replication)
  • Mirror extension
  • …

互相关(cross correlation)

符号 **

步骤：

互相关跟卷积的唯一不同就是模板不需要翻转。

性质:

  • 交换律(commutative)
  • 结合律(Associative)
  • 分配率(Distributive)
  • 移不变(shift-invariant)

卷积和互相关

A convolution is an integral that expresses the amount of overlap of one function as it is shifted over another function.

  • convolution is a filtering operation

Correlation compares the similarity of two sets of data. Correlation computes a measure of similarity of two input signals as they are shifted by one another. The correlation result reaches a maximum at the time when the two signals match best.

  • correlation is a measure of relatedness of two signals

Normalized Cross-Correlation

参考: http://scribblethink.org/Work/nvisionInterface/nip.html

在模板和图像的每个片段相乘之前，先把图像的这个片段的值做标乘(scaled)和平移(offset)，使之均值为0，方差为1. 这个过程称之为归一化（Normalized）.

如果图像片段的灰度值过高，跟模板的模式不匹配，这个过程可以提高精度。在matlab中采用normxcorr2完成这个过程。