【Computer Vision 3】Filters

公式：

卷积的性质：

• Linearity: filter(f1 + f2) = filter(f1) + filter(f2)
• Shift invariance: same behavior regardless of pixel location: filter(shift(f)) = shift(filter(f))

卷积运算规律：

• Commutative: a * b = b * a
  • Conceptually no difference between filter and signal
• Associative: a * (b * c) = (a * b) * c
  • Often apply several filters one after another: (((a * b1) * b2) * b3)
  • This is equivalent to applying one filter: a * (b1 * b2 * b3)
• Distributes over addition: a * (b + c) = (a * b) + (a * c)
• Scalars factor out: ka * b = a * kb = k (a * b)
• Identity: unit impulse e = […, 0, 0, 1, 0, 0, …], a * e = a

高斯滤波器

特性：

• 去除图像中高频率的部分
• 高斯滤波与自身卷积的结果仍为高斯滤波：重复做高斯滤波的结果等同于更大的。
• 多维的可离散为更低维度的：可以降低复杂度

噪声noise

中值滤波

对椒盐噪声的处理效果更好。

MATLAB函数

filter2(g, f, shape)

• shape = ‘full’ | ‘same’ | ‘valid’

卷积时，补零会产生黑边轮廓，所以有时候采取周期|外圈复制|对称插取的方法。

imfilter(f, g, filtering mode)

• clip filter (black): imfilter(f, g, 0)
• wrap around: imfilter(f, g, ‘circular’)
• copy edge: imfilter(f, g, ‘replicate’)
• reflect across edge: imfilter(f, g, ‘symmetric’)

medfilt2(image, [h w])