Assessment - Image Decimation and Interpolation Using Discrete Transforms

Assessment

1. Introduction

The objective of this assessment is for each student to undertake investigative review of literature and study the techniques for image analysis using a discrete transform. A significant number of discrete transforms may be used for image analysis including the discrete cosine, discrete sine, discrete Fourier transform, Walsh and Hadamard transforms. This assessment is limited to the application of only one of these transforms.

2. Part A: Review of Image Decimation and Interpolation Algorithms

The techniques a.k.a. algorithms for image and video analysis are well published and investigated by engineers. Image analysis find applications in mobile communication devices (eg. handsets), the Internet and in normal mobile communication services. To understand how discrete transforms are used for the specific process of image size reduction (size reduction) and expansion (interpolation), undertake a detailed review of algorithms for image interpolation using the following transforms: Discrete cosine transform (DCT) and fast Fourier transform (FFT). You will find a reasonable number of good publications in the IEEEXplore in the Library. Describe the methods using the DCT and FFT. Compare and contrast the various methods in use in a written report of not less than four (4) A4 pages with single line spacing length. Do not use the Wikipedia for this assessment.

3. Part B: Image Decimation and Interpolation Using Matlab

Through your review of image interpolation and decimation algorithms in journal articles, undertake the analysis specified below and provide a written report. Add this report to Part A report and include how you decimated and interpolated your image using the discrete cosine transform.

Matlab provides functions and commands which allow you to decimate and interpolate images. Discrete cosine transform (DCT) is in many ways similar to the fast Fourier transform with one major exception. The DCT provides real coefficients as outputs while the FFT coefficients are complex numbers. The following equation describes the forward DCT for an image in one dimension:

2 _N1 n1 2k
X k_n0 x_ncos N

Where x_n are pixels taken from an image and N is the number of pixels being transformed. There are various forms of the DCT and you should identify and review them too. Since an image is a twodimensional matrix consisting of rows and columns, the DCT need to be applied row and column wise.

It does not matter if you undertake the DCT along the rows first or along the columns first, the results will be the same.

a. Perform the DCT of the image given to you (use Matlab). Show your algorithm and its Matlab source code. Decimate the image by half by keeping only the first quarter of the two-dimensional coefficients returned by Matlab and display the interpolated image in your report. You will be required to demonstrate how this code runs to your unit lecturer and tutor in class.

b. Show how you will use the inverse DCT for interpolation to give an output image of the same size as the input image. The decimated image and the interpolated image should be visibly displayed in your report. Compare the original full-size and the interpolated images and comment on your results.

What are the major advantages and disadvantages for interpolating images using the DCT method?

4. Format of Report
Your report should be in three parts: Part I, literature review report; Part II (Decimation) of your image showing that your Matlab code works and Part III (Interpolation) of the decimated image showing the algorithm used and the Matlab code as well. Your report should have a reference list at the end of the report. The report should not be more than 10 A4 pages long (11 point font size using Calibri font type).