Review Spatial Filtering Basics · Review Spatial Filtering Basics Outline 1 Review 2 Spatial Filtering Basics Convolution and Correlation Filter Masks Dr. Praveen Sankrana DIP Winter

ReviewSpatial Filtering Basics

Spatial Filtering

Dr. Praveen Sankaran

Department of ECE

NIT Calicut

January 6, 2013

Dr. Praveen Sankaran DIP Winter 2013


Outline

1 Review

2 Spatial Filtering Basics

Convolution and Correlation

Filter Masks



Review

A pixel is a small image area indexed by [m,n];

g [m,n] is the associated pixel value;

A digital image is an M×N array of gray levels.



Neighbors, Adjacency, Regions, Connectivity, Boundaries,

Edges

We took ξ = 1. We are essentially de�ning our neighbors in this

step.



Spatial Domain

Refers to the image plane itself.

↓Direct manipulation of image pixels.

Figure: Spatial Filtering with a 3×3 mask (kernel, template or window)



Convolution and CorrelationFilter Masks

Outline

1 Review



Filter Masks




Spatial Filter




Correlation and Convolution - In 1D




Correlation and Convolution - In 2D




Correlation and Convolution - Representations

Correlation

w (m,n)�g (m,n) =a

∑s=−a

b

∑t=−b

w (s, t)g (m+ s, y + t)

Convolution

w (m,n)?g (m,n) =a

∑s=−a

b

∑t=−b

w (s, t)g (m− s, y − t)




Outline

1 Review



Filter Masks




Vector Representation

w1 w2 w3

w4 w5 w6

w7 w8 w9

→3×3 �lter mask

g1 g2 g3g4 g5 g6g7 g8 g9

→image

Linear Representation

R5 = w1g1+w2g2+ · · ·+w9g9 =9

∑k=1

wkgk =wTg

where, w and g are 9-dimensional vectors formed from the

mask and the image respectively.




Generating a Mask

Creating a �lter essentially boils down to specifying the values

of mask coe�cients.

Remember - All we are doing is a sum-of-products.

Creating an averaging �lter - replace pixel with average intensity in

neighborhood

Average = 19

9

∑i=1

gi =9

∑i=1

19gi

19

19

19

19

19

19

19

19

19

→averaging mask!




Gaussian Mask

Basic form →h (x ,y) = e

− x2+y2

2σ2

sample,quantize

⇓

h (m,n) = e−m

2+n2

2σ2

Sample the continuous function about its center.w1 w2 w3

w4 w5 w6

w7 w8 w9

=

h (−1,−1) h (0,−1) h (1,−1)h (−1,0) h (0,0) h (1,0)h (−1,1) h(0,1) h (1,1)




Summary

Pixel relationships.

Correlation and Convolution.

Vector representation.

Generating a mask for �ltering.




Questions

3.1, 3.2, 3.3, 3.4, 3.5

3.6, 3.7, 3.11

3.13, 3.14


Review Spatial Filtering Basics · Review Spatial Filtering Basics Outline 1 Review 2 Spatial Filtering Basics Convolution and Correlation Filter Masks Dr. Praveen Sankrana DIP Winter

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