Image decimation and interpolation using discrete transforms

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Reference no: EM131951728

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).

Reference no: EM131951728

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Reviews

len1951728

4/21/2018 1:53:47 AM

Explanation All elements are present and well integrated. Components present with good cohesion Components present and mostly well integrated Most components present Lacks structure. Reference style Clear styles with excellent source of references. Clear referencing/ style Generally good referencing/style Unclear referencing/style Lacks consistency with many errors Report structure and report presentation Proper writing. Professionally presented Properly written, with some minor deficiencies Mostly good, but some structure or presentation problems Acceptable presentation Poor structure, careless presentation

len1951728

4/21/2018 1:53:41 AM

Excellent Very Good Good Satisfactory Unsatisfactory Evaluation Logic is clear and easy to follow with strong arguments Consistency logical and convincing Mostly consistent and convincing Adequate cohesion and conviction Argument is confused and disjointed Sophistication and effectivity The presented solution demonstrated an extreme degree of sophistication The presented solution demonstrated a high degree of sophistication The presented solution demonstrated an average degree of sophistication and effectivity to secure The presented solution demonstrated a low degree of sophistication and effectivity to secure The presented solution demonstrated a poor degree of sophistication and effectivity to secure

len1951728

4/21/2018 1:53:35 AM

Image interpolation Working Matlab code for image decimation demonstration of working code and presentation 25 Reference style Correct IEEE referencing 10 Poor writing Poor writing style, not putting captions and figure numbers, not numbering equations, copy and pasting of figures without referencing them, inability to explain concepts, wrong grammar and typographical errors will lead to loss of marks. 10 Plagiarism Type of plagiarism • Copying of Matlab codes • Copy of other peoples works and journal articles - Contract cheating -100%

len1951728

4/21/2018 1:53:26 AM

Extension If an extension of time to submit work is required, a Special Consideration Application must be submitted directly through the AMS. You must submit this application three working days prior to the due date of the assignment. Further information is available at: Part I, II and III: Marks are allocated as follows: Section to be included in the report Description of the section Marks Literature Review Review analysis of image decimation and interpolation using discrete transforms and Fourier transform 30 Image decimation Working Matlab code for image decimation, demonstration of working code and presentation 25

len1951728

4/21/2018 1:53:12 AM

Submission Guidelines • All work must be submitted on Moodle by the due date along with a completed Assignment Cover Page. • The assignment must be in MS Word format, single line spacing, 11-pt Calibri (Body) font and 2 cm margins on all four sides of your page with appropriate section headings. • Reference sources must be cited in the text of the report, and listed appropriately at the end in a reference list using IEEE referencing style for School of Business and School of Information Technology and Engineering respectively.

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