Post on 20-Dec-2015
transcript
Edge Detection
Lecture 2: Edge Detection
Jeremy Wyatt
Visual pathway
The striate cortexEye-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
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
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
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
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
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 input Orientations present in cortex
Edge detection in machines
How can we extract edges from images?
Edge detection is finding significant intensity changes in the image
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
( , )f x y
[ ( , )]df
x dx
dfy dy
GG f x y
G
G
x
yG
x
y xG
yG
2 2( ) x yM G G G
1( , ) tan y
x
Gx y
G
magnitude direction
Approximating the gradient
Our image is discrete with pixels indexed by i and j
We want and to be estimated in the same place
[ , 1] [ , ]xG f i j f i j 1 1 1 1
0 1 1 1
0 0
1 1
0 0 0 1j j+1
i
i+1[ , ] [ 1, ]yG f i j f i j
-1 1
1
-1
xG yG
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
1 1 1 1
0 1 1 1
0 0
1 1
0 0 0 1j j+1
i
i+1
-1 1
-1 1xG
yG 1 1
-1 -1
Other edge detectors
Roberts
Sobel
1 0
0 -1xG yG
0 -1
1 0
xG yG
-1 0 1
-2 0 2
-1 0 1
1 2 1
0 0 0
-1 -2 -1
Convolution
This process is very general
0 1 1 3 4 5 4 5 6 7 8
0 0 2 3 3 4 5 4 6 4 5
0 0 4 6 3 5 4 7 2 4 3
0 0 0 4 4 3 5 5 4 6 4
0 0 0 3 5 2 6 7 3 4 5
0 0 0 0 5 5 6 7 8 9 8
0 0 0 0 4 3 4 5 6 7 5
-1 0 1
-2 0 2
-1 0 1
mask
image
Original After Sobel Gx Threshold =30 Threshold=100
What do these do?
After Roberts Threshold=5 Threshold=20
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
1
9
1
9
1
9
1
9
1
9
1
9
1
9
1
9
1
9
Reading
RC Jain, Chapter 5, Edge Detection