1. CS 376b Introduction to Computer Vision 03 / 18 / 2008 Instructor: Michael Eckmann

2. Michael Eckmann - Skidmore College - CS 376b - Spring 2008 Today’s Topics Comments/Questions Enhancing images (Chap. 5)‏ –Fourier transform Chapter 6 –color histograms

3. Michael Eckmann - Skidmore College - CS 376b - Spring 2008 More comments on Fourier transforms Can anyone give examples of images that contain high frequencies? Low frequencies?

4. Michael Eckmann - Skidmore College - CS 376b - Spring 2008 More comments on Fourier transforms high/low frequencies in images –low frequencies are in constant or near constant areas –high frequencies are in highly textured areas --- e.g. grass, with lots of abrupt changes in intensities

5. Michael Eckmann - Skidmore College - CS 376b - Spring 2008 More comments on Fourier transforms What are the basis functions? –on the board How to calculate the weights of basis functions? –just like any other basis –by the dot product of the image with each basis –on the board Let's look here at some simple examples: http://www.cs.ioc.ee/~khoros2/linear/dft-pulse-example/front-page.html

6. Michael Eckmann - Skidmore College - CS 376b - Spring 2008 A note about assignments/labs Another assignment is to come real soon --- spend time this week getting the previous assignments done.

7. Michael Eckmann - Skidmore College - CS 376b - Spring 2008 More comments on Fourier transforms recall the power spectrum ccd setup from chapter 1 –it integrated all the values in either a wedge or a curved section wedge tells us what directions the dominant features in the image have curved section tells us how much high low or medium, etc. frequencies there are in the original image

8. Michael Eckmann - Skidmore College - CS 376b - Spring 2008 More comments on Fourier transforms low pass, high pass, bandpass filtering –compute DFT of an image –operate in the frequency domain –keep only certain areas of the power spectrum –take IDFT of the altered spectrum in the frequency domain to get an altered image with whatever frequencies you decided to keep in.

9. Michael Eckmann - Skidmore College - CS 376b - Spring 2008 More comments on Fourier transforms Let's continue going over the handouts

10. Michael Eckmann - Skidmore College - CS 376b - Spring 2008 Color and Shading I already covered most of what is found in the first 3 sections of chapter 6 earlier this semester. –read about HSI (aka HSV) color system H = hue S = saturation I (or V) = Intensity (or Value)‏ there is an algorithm to convert RGB to HSI in our text –understand what's the use of YIQ and YUV

11. Michael Eckmann - Skidmore College - CS 376b - Spring 2008 Color Histograms One use of histograms is for similarity comparisons. For example, compare the histogram of an input image with some stored image to determine how similar they are. –let's look at exercise 6.12 on page 200

12. Michael Eckmann - Skidmore College - CS 376b - Spring 2008 Color Histograms If our pixels contain 8 bits each for R G and B, we have 24bits which leads to 2 24 different colors possible for each pixel. Would I want to store a histogram with 2 24 different bins? –why or why not?

13. Michael Eckmann - Skidmore College - CS 376b - Spring 2008 Color Histograms If our pixels contain 8 bits each for R G and B, we have 24bits which leads to 2 24 different colors possible for each pixel. Would I want to store a histogram with 2 24 different bins? –maybe but if you really only care about how many pixels are red(dish) or blue(ish) etc., but not how many specifically have RGB=200,189,3 then you wouldn't Some options –use only the two highest bits from each of R G and B yielding 2 6 different bins –make three different histograms, one for each of R G and B each with say 16 bins (16*3=48 total bins)‏ –use HSV color space (maybe ignore saturation and only consider Hue and Value or only consider Hue)‏

14. Michael Eckmann - Skidmore College - CS 376b - Spring 2008 Color Histograms If when trying to determine if a model (e.g. a car) is in an image (e.g. of a driveway) the image can contain the model but it might have been taken under different lighting conditions (sunny vs. cloudy or foggy or rainy), at a different angle, or partially obscured by some other object (e.g. a person or a bush) in the image or a host of other problematic things (e.g. distortions, noise). color histogram matching is relatively invariant to translation, rotation about the imaging axis, small off-axis rotations, scale, and partial occlusion.

15. Michael Eckmann - Skidmore College - CS 376b - Spring 2008 Color Histograms To determine some match value between two image's histograms (say a largish input image and a smallish model image to try to determine if the model image is in the input image) we can do the following: compute the intersection of the histograms by –sum up over all bins the min histogram value in each bin then divide this sum by the number of pixels in the model image to get a match value –this value is not diminished due to background pixel colors in the input image that are not in the model the idea is that the higher the match value the more likely the model is contained within the image

16. Michael Eckmann - Skidmore College - CS 376b - Spring 2008 Color Histograms Other measures include distance measures where smaller values (little distance) implies similarity –sum of absolute value of differences –ssd = sum of squared differences –Euclidean distance = sqrt(ssd)‏ –...