1. Edge Detection Lecture 2: Edge Detection Jeremy Wyatt

2. Visual pathway

3. The striate cortex Eye-cortex mapping has certain properties Neighbouring areas in the retina are approximately mapped to neighbouring areas in the cortex Half the image in each half of the cortex Middle of retinal image on the outer edge of the relevant half of the cortex Mapping is spatial distorted

4. Hypercolumns & Hyperfields 3-4mm 0.5-1mm Surface Each hypercolumn processes information about one area of the retina, its hyperfield. 400-600 columns in each hypercolumn. Each column has its own receptive field. All the cells in one column are excited by line stimuli of the same orientation. Column

5. Cells within a column Light on the right and dark on the left of this cell causes excitation The less the contrast the lower the excitation Different cells in a single column respond to different patterns with the same orientation

6. Orientation across columns Different columns are tuned to different orientations Adjacent columns are tuned to similar orientations Cells can be excited to different degrees More excited Less excited

7. Slabs and Hyperfields Each hypercolumn is composed of about 20 slabs of columns Each slab is tuned to one orientation Each column in a slab is centred on a different portion of the hyperfield But each column takes input from the whole hyperfield Columns in each slab Slabs

8. Learning We learn the orientation selectivity of cells in the early months of life This has been shown by depriving animals of certain orientations of input Sole visual inputOrientations present in cortex

9. Edge detection in machines How can we extract edges from images? Edge detection is finding significant intensity changes in the image

10. Images and intensity gradients The image is a function mapping coordinates to intensity The gradient of the intensity is a vector We can think of the gradient as having an x and a y component  magnitude direction

11. Approximating the gradient Our image is discrete with pixels indexed by i and j We want and to be estimated in the same place 1111 0111 0011 0001 j j+1 i i+1 1 1

12. Approximating the gradient So we use 2x2 masks instead For each mask of weights you multiply the corresponding pixel by the weight and sum over all pixels 1111 0111 0011 0001 j j+1 i i+1 1 1 1 1

13. Other edge detectors Roberts Sobel 10 0 0 10 01 -202 01 121 000 -2

14. Convolution This process is very general 01134545678 00233454645 00463547243 00044355464 00035267345 00005567898 00004345675 01 -202 01 mask image

15. Original After Sobel G x Threshold =30 Threshold=100 What do these do? After Roberts Threshold=5 Threshold=20

16. Noise It turns out we will need to remove noise There are many noise filters We can implement most of them using the idea of convolution again e.g. Mean filter

17. Reading RC Jain, Chapter 5, Edge Detection