Description
Objectives:
Understand different concepts of convolution along with its applications.
Prerequisites:
Linear Convolution
2D – Convolution
Circular Convolution
Problems
1. Explore command conv2 in Matlab. Take input of 2 Matrix from user and Find 2D
convolution of the same. Also explore the properties of conv2 command and analyze the
result.
For an example
A
[
]
B = [
]
2. Application of 2D convolution on image processing applications
a) Take a standard test image “Lenna.png” from shared folder. Explore following
commands and apply for given image.
imread
rgb2gray
imshow
b) Now in order to perform 2D convolution, Given image becomes first input as matrix
and second input will be a sets of kernel matrix performing different operations on
image which are mentioned below:
2
List of different kernels:
In image processing, a kernel, convolution matrix, or mask is a small matrix useful for
averaging, sharpening, embossing, edge-detection, and more. This is accomplished by
means of convolution between a kernel and an image.
Average (blur, smooth) 3×3 convolution kernel
A = [
]
Sharpen 3×3 convolution kernel
S = [
]
Edge detection 3×3 convolution kernel
E= [
] EH = [
] EV= [
]
Gradient detection 3×3 convolution kernel
GH = [
] GV = [
]
Sobel Operator 3×3 convolution kernel
SH = [
] SV = [
]
3
3. Develop a MATLAB function to obtain circular convolution of two sequences. Verify the
function for following sequence. Write a script file to use the developed function.
1. x1(n) = {1,-1,-2,3,-1} and x2(n) = {1,2,3}
2. x1(n) = {1, 2, 1, 2} and x2(n)= {3,2,1,4}
3. x1(n)= (
) and x2(n)= (
), .for N=8
4. Write a MATLAB program to find circular convolution of two sequences using Matrix
Multiplication method.
1. x1(n) = {1,-1,-2,3,-1} and x2(n) = {1,2,3}
2. x1(n) = {1, 2, 1, 2} and x2(n)= {3,2,1,4}
3. x1(n)= (
) and x2(n)= (
), .for N=8
