Lecture 3 - Intensity transformation

Transcription

1 Computer Vision Lecture 3 - Intensity transformation Instructor: Ha Dai Duong duonghd@mta.edu.vn 22/09/ Today s class 1. Gray level transformations 2. Bit-plane slicing 3. Arithmetic/logic operators 4. Discussion 22/09/

2 Today s class 1. Gray level transformations 2. Bit-plane slicing 3. Arithmetic/logic operators 4. Discussion 22/09/ Spatial domain The term spatial domain refers to the aggregate of pixels composing an image. Spatial domain methods are procedures that operate directly on these pixels. Spatial domain processes will be denoted by the expression where f(x,y) is the input image, g(x,y) is the processed image, and T is an operator on f, defined over some neighborhood of (x,y) 22/09/

3 Spatial domain The principal approach in defining a neighborhood about a (x,y) is to use a square subimage area centered at (x, y), as Fig /09/ Spatial domain The operator T is applied at each location (x,y) to yield the output, g, at that location. The simplest form of T is when the neighborhood is of size 1*1 (that is, a single pixel). In this case, g depends only on the value of f at (x, y), and T becomes a gray-level transformation function 22/09/

4 Spatial domain Example 22/09/ Some basic gray-level transformations 22/09/

5 Image negative Definition: or 22/09/ Image negative Definition: Example or 22/09/

6 Example of performing f Negative g L-1 = 4 22/09/ Example of performing f Negative g L-1 = 4 22/09/

7 Example of performing f Negative g L-1 = 4 22/09/ Example of performing f Negative g L-1 = 4 22/09/

8 Example of performing f Negative g L-1 = 4 22/09/ Example of performing f Negative g L-1 = 4 22/09/

9 Example of performing f Negative g L-1 = 4 22/09/ Example of performing f Negative g L-1 = 4 22/09/

10 Discussion C/C++ and OpenCV implementation More on project 22/09/ Look Up Table The size of image is M N => Function T(r) is called M N times. Create and compute LUT[r] = T(r), r=0.. L-1 => Function T(r) is called L ( L<< M N ) times s = LUT[r] LUT - Look Up Table 22/09/

11 Example LUT f g L-1 = 4 22/09/ Example LUT f g L-1 = 4 22/09/

12 Example LUT f g L-1 = 4 22/09/ Example LUT f g L-1 = 4 22/09/

13 Log Transformations Definition: or where c is a constant, and it is assumed that r>=0 22/09/ Definition: Example or where c is a constant, and it is assumed that r>=0 22/09/

14 Power-Law Transformations Definition: or 22/09/ Power-Law Transformations Definition: or 22/09/

15 Example Definition: or 22/09/ Definition: Example or 22/09/

16 Contrast stretching Definition: 22/09/ Example 22/09/

17 Gray-level slicing Definition 22/09/ Example 22/09/

18 Gray-level slicing Definition 22/09/ Today s class 1. Gray level transformations 2. Bit-plane slicing 3. Arithmetic/logic operators 4. Discussion 22/09/

19 Bit-plane Often by isolating particular bits of the pixel values in an image We can highlight interesting aspects of that image 22/09/ Example [ ] [ ] [ ] [ ] [ ] [ ] 22/09/

20 Example 22/09/ Higher-order bits usually contain most of the significant visual information Lower-order bits contain subtle details Lower-order bit-plane 22/09/

21 Higher-order bit-plane Higher-order bits usually contain most of the significant visual information Lower-order bits contain subtle details 22/09/ Bit-plane slicing Reconstructed image using only bit planes 8 and 7 Reconstructed image using only bit planes 8, 7 and 6 Reconstructed image using only bit planes 7, 6 and 5 22/09/

22 Today s class 1. Gray level transformations 2. Bit-plane slicing 3. Arithmetic/logic operators 4. Discussion 22/09/ Definition: Image Subtraction g(x,y) = f(x,y) h(x,y) Extraction of the differences between images 22/09/

23 Image Subtraction Example 22/09/ Image Averaging Consider a noisy image g(x,y) formed by the addition of noise (x,y) to an original image f(x,y) g(x,y) = f(x,y) + (x,y) If noise has zero mean and be uncorrelated then it can be shown that if K 1 g( x, y) gi ( x, y) K i 1 image formed by averaging K different noisy images 22/09/

24 Image Averaging Then 2 1 g ( x, y) K 2 ( x, y) 2 2 g ( x, y ), ( x, y ) = variances of g and if K increase, it indicates that the variability (noise) of the pixel at each location (x,y) decreases. 22/09/ Image Averaging Thus E{ g( x, y)} f ( x, y) E { g ( x, y)} = expected value of g (output after averaging) = original image f(x,y) 22/09/

25 (a) Image of Galaxy Pair NGC 3314 (b) Image corrupted by additive Gauss-ian noise with zero mean and a standard deviation of 64 gray levels 22/09/ (c) Results of averaging K=8 (d) Results of averaging K=16 22/09/

26 (e) Results of averaging K=64 (f) Results of averaging K=128 22/09/ (a) Image of Galaxy Pair NGC 3314 (f) Results of averaging K=128 22/09/

27 Logical operators 22/09/ Today s class 1. Gray level transformations 2. Bit-plane slicing 3. Arithmetic/logic operators 4. Discussion 22/09/