EECS490: Digital Image Processing. Lecture #4. Image Warping Spatial & gray level interpolation Intensity transformations

Transcription

1 Lecture #4 Image Warping Spatial & gray level interpolation Intensity transformations

2 Geometric Transformations [ x y 1]= [ v w 1]T = [ v w 1] t 11 t 12 0 t 21 t 22 0 t 31 t 32 1

3 Rotation and motion blur by Richard Alan Peters II

4 Image Registration

5 EECS490: Digital Image Processing Image Warping by Richard Alan Peters II

6 Geometric Transformations (Warping)

7 Spatial Warping

8 Polynomial Spatial Warp Represent the coordinate transformations as polynomials in x and y G(x, y) = F(x', y') = F(ax + by + cxy + d,ex + fy + gxy + h) Using corresponding point pairs write the coordinate transformations as systems of linear equations and put them in matrix form x 1 ' = ax 1 + by 1 + cx 1 y 1 + d x 2 ' = ax 2 + by 2 + cx 2 y 2 + d x 3 ' = ax 3 + by 3 + cx 3 y 3 + d x 4 ' = ax 4 + by 4 + cx 4 y 4 + d x 1 ' x 1 y 1 x 1 y 1 1 a x 2 ' x 2 y 2 x 2 y 2 1 b = x 3 ' x 3 y 3 x 3 y 3 1 c x 4 ' x 4 y 4 x 4 y 4 1 d solve for the unknown coefficients a b c d

9 Simple Rotation Example original image transformed image original pixel nearest neighbor rotated pixel Forward mapping with nearest neighbor assignment of intensity value

10 EECS490: Digital Image Processing

11 Gray Level Interpolation forward mapping f(x,y) f(x',y') 1. Can result in pixels mapping to pixels outside the image 2. Complex transforms can map several input pixels to the same output pixel 3. Does not guarantee that all output pixels will have a value

12 Gray Level Interpolation backward mapping (pixel filling) f(x,y) f(x',y') 1. for EACH output pixel (x,y ) determine corresponding location (x,y) in input image 2. Use gray level interpolation* for pixels surrounding (x,y) to assign a pixel value f(x,y ) to selected output pixel 3. Guarantees that all pixels in output image will have a value *can be nearest neighbor, bilinear, etc.

13 Gray Level Interpolation Nearest Neighbor Assigns output f(x,y ) the value of the closest pixel Can produce artifacts when input f(x,y) changes rapidly

14 Gray level interpolation bilinear

15 Bilinear Intensity Interpolation Linearly interpolate along y=0 Linearly interpolate along y=1 Interpolate along x Combine equations f( x,0)= f ( 0,0)+ x f( 1, 0) f 0,0 f( x, y)= f ( 1, 0) f ( 0,0) x + f ( 0,1 ) f ( 0,0 ) y + f ( 1,1 )+ f ( 0,0) f ( 0,1) f ( 1, 0 ) ( ) f( x,1)= f ( 0,1)+ x f( 1,1) f 1, 0 ( ) f( x, y)= f( x,0)+ y f( x,1) f( x,0) xy + f ( 0,0 )

16 Results of interpolation methods

17 Interpolation can be applied to vectors

18 Point Processing of Images In a digital image, point = pixel. Point processing transforms a pixel s value as a function of its value alone; pixel s value does not depend on the values of the pixel s neighbors by Richard Alan Peters II

19 Point Processing of Images Brightness and contrast adjustment Gamma correction Histogram equalization Histogram matching Color correction by Richard Alan Peters II

20 Image Contrast

21 Negative Transformation

22 Negative Transformation

23 More Intensity Transformations

24 Log Transformation s = clog( 1 + r)

25 Log Transformation

26 Gamma Transformation s = cr

27 Gamma Transformation input intensity input intensity input intensity input intensity

28 Gamma Transformation dark bright input intensity

29 Gamma Transformation dark bright input intensity

30 Piece-wise Linear Transformations

31 Piece-wise Linear Transformations

32 Piece-wise Linear Transformations dark bright input intensity dark bright input intensity

33 Piece-wise Linear Transformations

34 EECS490: Digital Image Processing

35 EECS490: Digital Image Processing

36 Brightness & Contrast