ECE 468: Digital Image Processing. Lecture 2

Transcription

1 ECE 468: Digital Image Processing Lecture 2 Prof. Sinisa Todorovic sinisa@eecs.oregonstate.edu Outline Image interpolation MATLAB tutorial Review of image elements Affine transforms of images Spatial-domain filtering 2

2 Image Interpolation Bilinear N Bicubic N 3 f(, ) N N a ij i j i0 j0 3 MATLAB Image Processing Toolbo 4

3 Basic MATLAB Commands imread size whos imshow imwrite double, uint8 im2uint8, im2bw plot(img(size(img,)/2,:)) zeros(m,n), ones(m,n), rand(m,n), randn(m,n) function outputs name_func(inputs), return 5 Basic MATLAB Commands ismember, isempt intersect, union for, while meshgrid imadjust imhist 6

4 Image Structure 7 Image Elements Piels, 4-adjacenc, 8-adjacenc, m-adjacenc Path -- directed, undirected, loop Region Connected set of piels Region boundar, inner and outer contour Foreground - background Edge Connected piels with high derivative values Interest points: T-junction, Y-junction Highlights or specularities Lambertian surface isotropic reflectance Specular surface zero reflectance ecept at an angle 8

5 9 0

6 Spatial Image Transformations Affine transforms: Translation Scaling Rotation Shear Eample (, )T {(, )} T 2

7 2D Translation displacement t t t 3 2D Translation displacement t t t P P + t + t + t 0 t 0 t 3

8 2D Translation P + t P + t + t displacement t t t 0 t 0 t homogeneous coordinates 3 2D Translation P P + t P + t + t + t + t displacement t t t 0 t 0 t 0 t 0 t 0 0 homogeneous coordinates 3

9 2D Translation P P + t P + t + t + t + t displacement t t t 0 t 0 t 0 t 0 t 0 0 homogeneous coordinates translation matri 3 2D Scaling s s 4

10 2D Scaling s s s s s s D Scaling s s s s s s scaling matri 4

11 2D Scaling s s s s S s s scaling matri 4 2D Scaling + Translation Is the ordering important? P S P P T P P (T S) P 5

12 2D Scaling + Translation P S P P T P 0 t 0 t 0 0 Is the ordering important? s s P (T S) P 5 2D Scaling + Translation Is the ordering important? A P S P P T P 0 t 0 t 0 0 s 0 t 0 s t 0 0 s s P (T S) P scaling + translation matri 5

13 2D Rotation counter-clockwise b angle θ P cos θ sin θ sin θ + cos θ θ P cos θ sin θ 0 sin θ cos θ D Rotation counter-clockwise b angle θ P cos θ sin θ sin θ + cos θ θ P cos θ sin θ 0 sin θ cos θ rotation matri 6

14 2D Rotation counter-clockwise b angle θ P cos θ sin θ sin θ + cos θ θ P R cos θ sin θ 0 sin θ cos θ rotation matri 6 2D Rotation + Scaling + Translation R cos θ sin θ 0 sin θ cos θ t 0 t 0 t 0 0 S s s rotation matri translation matri scaling matri RS t 0 7

15 Estimating the Spatial Transform input transformed input inverse transform estimation error 8 Estimating the Spatial Transform t t 2 t 3 t 2 t 22 t What is the minimum number of point pairs to find matri T? AX B if det(a) 0 X A B or if det(a T A) 0 X (A T A) A T B 9

16 Re-writing the Equation of Transformation t t 2 t 3 t 2 t 22 t Re-writing the Equation of Transformation t t 2 t 3 t 2 t 22 t i t + i t 2 + t t t t 23 i 0 t + 0 t t 3 + i t 2 + i t 22 + t 23 i 20

17 Re-writing the Equation of Transformation t t 2 t 3 t 2 t 22 t i t + i t 2 + t t t t 23 i 0 t + 0 t t 3 + i t 2 + i t 22 + t 23 i i i i i t t 2 t 3 t 2 t 22 t 23 i i 20 Summar of Affine Transforms 2

18 Spatial-Domain Filtering of Images 22 Spatial-Domain Filtering of Images g(, ) T {f(, )} transformed input input 23

19 Basic Operations on Images Addition Multiplication 24 Eample: Averaging Nois Measurements g(, ) f(, )+η(, ) ḡ(, ) K g i (, ) K i 25

20 Eample: Shading Correction g(, ) f(, )h(, ) 26 Eample: Masking g(, ) f(, )h(, ) 27

21 Eample: Rescaling Intensit Values g(, ) K f(, ) minf(, ) maf(, ) minf(, ) input output 28 Eample: Local Averaging - Smoothing g(, ) f(, ) mn (, ) N 29

22 Eample: Image Negatives g(, ) L f(, ) 30 Eample: Gamma Correction s cr γ 3

23 Eample: Gamma Correction input!.6 input!3!.4!.3!4!5 32 Net Class Homework due Histogram equalization (Tetbook: 3.3.); Histogram specification (Tetbook: 3.3.2); Spatial convolution and correlation (Tetbook: 3.4.2); Smoothing and sharpening spatial filters (Tetbook: 3.5); Homework 2 33