1 / 30

# Image Features - I - PowerPoint PPT Presentation

Image Features - I. Hao Jiang Computer Science Department Sept. 22, 2009. Outline. Summary of convolution and linear systems Image features Edges Corners Programming Corner Detection. Properties of Convolution. 1. Commutative: f * g = g * f 2. Associative

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.

## PowerPoint Slideshow about ' Image Features - I' - fedella-jerome

An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript

### Image Features - I

Hao Jiang

Computer Science Department

Sept. 22, 2009

• Summary of convolution and linear systems

• Image features

• Edges

• Corners

• Programming Corner Detection

1. Commutative:

f * g = g * f

2. Associative

(f * g) * h = f *(g * h)

3. Superposition

(f + g) * h = f * h + g * h

N

M

full

(N+M-1)x(N+M-1)

f

h

g = f * h

Linear:

a f1+ b f2 => a g1 + b g2

where the response of f1 is g1

and the response of f2 is g2

Shift invariant:

if f => g, then f(n-m) => g(n-m)

f

h1

h2

h1 + h2

f

h1

h2

h1*h2

• Neighborhood filtering can be nonlinear

• Median Filtering

• 1 1

• 1 2 1

• 1 1 1

Mask [1 1 1 ]

• 1 1

• 1 1 1

• 1 1 1

Original Image

Add 10% pepper noise

Median filter with 3x3

square structure element

Median filter with 5x5

square structure element

Kernel size 5x5 and sigma 3

Kernel size 11x11 and sigma 5

Step

Ridge

Valley

Peak

Corner

Junction

Line

Structures:

“Edge”

Step

Ridge

Valley

Point

Structures:

“Corners”

Peak

Corner

Junction

edge

Region

corners

>> im = imread('flower.jpg');

>> im = im2double(im);

>> im = rgb2gray(im);

>> ed = edge(im, 'canny', 0.15);

A 1D edge

f’(x)

f’’(x)

b

There is a direction in which

image f(x,y) increases the

fastest. The direction is called

Magnitude: sqrt(fx^2 + fy^2)

Direction: atan2(fy, fx)

a

• Approximating derivatives using finite difference.

• Finite difference and convolution

0.01 noise

0.03 noise

image

h * (g * f) = (h * g) * f

Difference of

Gaussian Kernel

Difference Kernel

Gaussian Kernel

• Gaussian smoothed filtering in x and y directions: Ix, Iy

• Non-maximum suppression for |Ix|+|Iy|

• Edge Tracing – double thresholding.

• Canny edge detector:

edge(image, ‘canny’, threshold)

• Sobel edge detector:

edge(image, ‘sobel’, threshold)

• Prewitt edge detector:

edge(image, ‘prewitt’, threshold)

D. Martin, C. Fowlkes, D. Tal, J. Malik. "A Database of Human Segmented Natural Images and its Application to Evaluating Segmentation Algorithms and Measuring Ecological Statistics”, ICCV, 2001

• Corner is a point feature that has large changing rate in all directions.

Peak

Step

Line

Flat region

Compute matrix H =

Ix2 Ixy

Ixy Iy2

=

in each window. If the ratio

(Ix2 * Iy2 – Ixy ^2 )

------------------------ > T

(Ix2 + Iy2 + eps)

We have a corner