1. IMAGE 1 An image is a two dimensional Function f(x,y) where x and y are spatial coordinates And f at any x,y is related to the brightness at that point A digital image is a 2D representation of a continuous image by a 2D array of discrete samples Each element of the 2D array is a pixel.

2. Definition Histograms count the number of occurrences of each possible value CountGrey level

3. Properties Sum of all values in the histogram equals the total number of pixels

4. Properties Sum of all values between a and b equals the area of all objects in that range

5. Properties Integrated optical density Mean greylevel

6. Application: Adjusting Camera Parameters Too bright - lots of pixels at 255 (or max) Too dark - lots of pixels at 0 Gain too low - not enough of the range used

7. Application: Segmentation Can be used to separate bright objects from dark background (or vice versa)

8. Normalizing Histograms Probability density function = histogram normalized by area

9. Cumulative Histograms Counts pixels with values up to and including the specified value

10. Cumulative Density Functions Normalized cumulative histograms

11. IMAGE 1

12. Image 1: Bright

13. Image 1: Dark

14. Image 1: Low contrast

15. Image 1: High contrast

16. RESOLUTION

17. INTERPOLATION

18. HISTOGRAM EQUALIZATION

19. THRESHOLDING 104

20. 199

21. 34

22. 137

23. Inverted

57. SMOOTH 3 MEDIAN 3 SMOOTH 7 MEDIAN 5