1. CHAPTER 7 Template Filters IMAGE ANALYSIS A. Dermanis

2. g ij = f i–1,j–1 h –1,–1 + f i–1,j h –1,0 + f i–1,j+1 h –1,1 + + f i,j–1 h 0,–1 + f i,j h 0,0 + f i,j+1 h 0,1 + + f i+1,j–1 h 1,–1 + f i+1,j h 1,0 + f i+1,j+1 h 1,1 g ij = f i–1,j–1 h –1,–1 + f i–1,j h –1,0 + f i–1,j+1 h –1,1 + + f i,j–1 h 0,–1 + f i,j h 0,0 + f i,j+1 h 0,1 + + f i+1,j–1 h 1,–1 + f i+1,j h 1,0 + f i+1,j+1 h 1,1 Moving templates for image filtering The discrete convolution process in template filtering A. Dermanis

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

4. localized g ij = h i,j;k,m f km  k=i–p m=j–p i+p j+p Template filters = Localized position-invariant linear transformations of an image Using a (p+1)  (p+1) template linear g ij = h i,j;k,m f km    k m position-invariant h i,j;k,m = h k–i,m – j g ij = h k–i,m – j f km    k m A. Dermanis

5. Template filters = Localized position-invariant linear transformations of an image renamed (i = 0, j = 0, k = k, m = m) Combination of all properties g ij = h k–i,m–j f km  k=i–p m=j–p i+p j+p k = k – i m = m – j g ij = h k,m f i+k,j+m  k = –p m = –p p g 00 = h k,m f k,m  k = –p m = –p p A. Dermanis

6. Template filters = Localized position-invariant linear transformations of an image renamed j–1j–1jj+1j+1 i+1i+1 i i–1i–1 h ij f ij 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 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 g 00 = h k,m f k,m  k = –p m = –p p A. Dermanis

7. Examples homogeneous areas are set to zero high values emphasize high frequencies f km = C  g 00 = h k,m C = 0  k = –p m = –p p h k,m = 0  k = –p m = –p p Examples 1 25 1 9 homogeneous (low frequency) areas preserve their value f km = C  g 00 = h k,m C = C  k = –p m = –p p 11111 11111111 11111111 11111111 11111 11 11 11 1 22 1 11 8 11 22 4 22 11 11 11 1 22 1 High-pass filters h k,m = 1  k = –p m = –p p Low-pass filters A. Dermanis

8. 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 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  3Moving mean 5  5 A. Dermanis

9. 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 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  3high pass filtering 3  3 (negative) A. Dermanis

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

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

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

13. The Roberts and Sobel filters for edge detection Original (TM band 4) Roberts Sobel Roberts filter Sobel filter 000 010 00 000 001 0 0 XY 01 -202 01 -2 000 121 XY X 2+Y 2X 2+Y 2 X 2+Y 2X 2+Y 2 A. Dermanis