1. Images Course web page: vision.cis.udel.edu/cv March 3, 2003  Lecture 8

2. Announcements Homework is due tonight by midnight (LaTeX broken in Smith 040) Read about convolution in Chapter 7- 7.2, 7.5-7.7 of Forsyth and Ponce for Wednesday

3. Outline Digitization will be discussed in the camera lecture (#16) Image types, basic operations in Matlab Binary images Image comparison Texture mapping

4. Matlab Image Types Note: Although we write I(x, y), remember that Matlab uses I(r, c) Intensity: m x n matrix. Can be: –uint8 : Unsigned 8-bit integer—i.e., in the range [0…255] –double : Real number in range [0…1] True color: m x n x 3 –Basically, stacked red, green, and blue intensity images (aka channels) Binary: Values are 0 or 1, type logical

5. Image Type Conversions Many functions work on just one channel –Run on each channel independently –Convert from color  grayscale weighting each channel by perceptual importance ( rgb2gray ) Some operations want the pixels to be real-valued –Type conversion: I2 = double(I1)

6. Image Arithmetic Just like matrices, we can do pixelwise arithmetic on images Some useful operations –Differencing: Measure of similarity –Averaging: Blend separate images or smooth a single one over time –Thresholding: Apply function to each pixel, test value In Matlab: imadd, imsubtract, imcomplement, imlincomb, etc. –Beware of truncation –Can do all of these with matrix operations if you pay attention to types and truncation

7. Thresholding Grayscale  Binary: Choose threshold based on histogram of image intensities (Matlab: imhist )

8. Example: Image Histograms courtesy of MathWorks

9. Derived Images: Color Similarity as Chrominance Distance Distance to red in YIQ space ( rgb2ntsc ) Can threshold on this

10. Connected Components Uniquely label each n-connected region in binary image 4- and 8-connectedness Matlab: bwfill, bwselect

11. Example: Connected Components courtesy of HIPR

12. Binary Operations Dilation, erosion (Matlab: imdilate, imerode ) –Dilation: All 0’s next to a 1  1 (Enlarge foreground) –Erosion: All 1’s next to a 0  0 (Enlarge background) OriginalDilatedEroded courtesy of Reindeer Graphics

13. Moments: Region Statistics Zeroth-order: Size/area First-order: Position (centroid) Second-order: Orientation

14. Geometric Image Comparison: SSD Given a template image I T and an image I, how to quantify the similarity between them? Vector difference: Sum of squared differences (SSD)

15. Correlation for Template Matching Note that SSD formula can be written: When the last term is big, the mismatch is small—the dot product measures correlation: By normalizing by the vectors’ lengths, we are measuring the angle between them

16. Normalized Cross-Correlation Shift template image over search image, measuring normalized correlation at each point Local maxima indicate template matches Matlab: normxcorr2 from Jain, Kasturi, & Schunck

17. Statistical Image Comparison: Color Histograms Steps –Histogram RGB/HSI triplets over two images to be compared –Normalize each histogram by respective total number of pixels to get frequencies –Similarity is Euclidean distance between color frequency vectors Insensitive to geometric changes, including different-sized images Matlab: imhist, hist

18. Image Transformations Geometric: Compute new pixel locations –Rotate –Scale –Undistort (e.g., radial distortion from lens) Photometric: How to compute new pixel values when non-integral –Nearest neighbor: Value of closest pixel –Bilinear interpolation (2 x 2 neighborhood) –Bicubic interpolation (4 x 4)

19. Bilinear Interpolation Idea: Blend four pixel values surrounding source, weighted by nearness Vertical blend Horizontal blend