IMAGE ANALYSIS CHAPTER 7 Template Filters A Dermanis

IMAGE ANALYSIS CHAPTER 7 Template Filters A. Dermanis

Moving templates for image filtering gij = fi– 1, j– 1 h– 1, – 1 + fi– 1, j h– 1, 0 + fi– 1, j+1 h– 1, 1 + + fi, j– 1 h 0, – 1 + fi, j h 0, 0 + fi, j+1 h 0, 1 + + fi+1, j– 1 h 1, – 1 + fi+1, j h 1, 0 + fi+1, j+1 h 1, 1 The discrete convolution process in template filtering A. Dermanis

Typical template dimensions Non-square templates viewed as special cases of square ones A. Dermanis

Template filters = Localized position-invariant linear transformations of an image linear gij = h i, j; k, m fkm k position-invariant m hi, j; k, m = hk–i, m–j gij = h k–i, m–j fkm k i+p localized gij = m j+p h i, j; k, m fkm k=i–p m=j–p Using a (p+1) template A. Dermanis

Template filters = Localized position-invariant linear transformations of an image Combination of all properties i+p gij = j+p h k–i, m–j fkm k=i–p m=j–p k = k – i m = m – j renamed (i = 0, j = 0, k = k, m = m) p gij = p h k = –p m = –p k , m fi+k , j+m p g 00 = p k = –p hk, m fk, m m = –p A. Dermanis

Template filters = Localized position-invariant linear transformations of an image renamed p g 00 = k = –p hij p hk, m fk, m m = –p i– 1 fij i i+1 j– 1 j j+1 g 00 = h– 1, – 1 f– 1, – 1 + h – 1, 0 f– 1, +1 + h – 1, 1 f– 1, +1 + + h 0, – 1 f 0, – 1 + h 0, 0 f 0, 0 + h 0, +1 f 0, +1 + + h+1, – 1 f+1, – 1 + h+1, 0 f+1, 0 + h+1, +1 f+1, +1 A. Dermanis

Low-pass filters p High-pass filters p p h k, m k = –p h =1 k, m m = –p k = –p fkm = C p k = –p p hk, m C = C g 00 = m = –p p k = –p homogeneous (low frequency) areas preserve their value hk, m C = 0 m = –p homogeneous areas are set to zero high values emphasize high frequencies Examples 1 9 =0 fkm = C p g 00 = p Examples 1 1 1 1 1 25 1 1 1 1 1 -1 -1 -1 1 -2 1 1 1 -1 -1 -1 1 1 8 -1 4 -2 1 A. Dermanis

An example of low pass filters: The original band 3 of a TM image is undergoing low pass filtering by moving mean templates with dimensions 3 3 and 5 5 Original Moving mean 3 3 Moving mean 5 5 A. Dermanis

An example of a high pass filter: The original image is undergoing high pass filtering with a 3 3 template, which enhances edges, best viewed as black lines in its negative Original high pass filtering 3 3 (negative) A. Dermanis

Templates expressing linear operators Local interpolation and template formulation fkm interpolation h km f(x, y) A k, m gij evaluation g(0, 0) g(x, y) A. Dermanis

The Laplacian operator 2 2 A = = + x 2 y 2 Original (TM band 4) Laplacian 9 9 Examples of Laplacian filters with varying template sizes Laplacian 13 13 Laplacian 17 17 A. Dermanis

Examples of Laplacian filters with varying template sizes Original (TM band 4) Laplacian 5 5 Original + Laplacian 5 5 A. Dermanis

The Roberts and Sobel filters for edge detection Sobel filter Roberts filter X 2+Y 2 X Original (TM band 4) X 2+Y 2 Y X Y 0 0 0 -1 0 1 -1 -2 -1 0 0 0 1 -2 0 0 0 -1 0 1 1 2 1 Roberts Sobel A. Dermanis