Chapter 2

CHAPTER 3

Chapter 4

 3.1. INTRODUCTION

This chapter is an introduction to the experimental tests and the results shown in the next chapters 4, 5 and 6 and in appendix B; the tests will concern experiments done on particular AutoMERS-based images and on wavelet coefficients matrices obtained from them. As an introduction to the statistics and results obtained from the tests, we must to explain some features regarding the kind of software programs, images and parameters used in these tests.

Almost all processes developed in the trials have been made using Matlab Vers. 5 [S.1, P.2, V.1 and M.2]; this is an algorithm development environment widely used for audio, video, still images and in general digital signal processing around the world, apart from its use in many other application fields. This commercial software package, produced by “The MathWorks Inc.“ , has a command line interface. Its programming language is a vectored language, very useful for image processing because it can perform many operations on numbers grouped as vectors or matrices without explicit loop statements; for this reason this could be compact, efficient and parallelizable. Moreover, it is possible to convert native Matlab code into C or C++ code, compile it and link it with Matlab libraries, so the code could become much faster. A lot of useful toolboxes are available providing application specific function libraries; the most important for the work are Signal Processing Toolbox, Image Processing Toolbox and Wavelet Toolbox.

Some universities and research centres have created toolboxes of simple functionality, useful for Matlab users; an example of these is the WaveLab , a toolbox developed by Stanford University, that will be used in the tests on wavelets. Other software programs used for the compression tests on AutoMERS images are useful application such as WinZip for Windows operating system and Gzip for Unix system. Some specific programs like JasPer  Software by M.D. Adams, a collection of JPEG 2000 based software for the coding and decoding of images written in C programming language, and SPIHT  image compression and decompression program by A. Said and W.A. Pearlman using the SPIHT coding algorithm will be used. All these software programs and applications will be explored in more detail in the next chapters and appendices.

In the tests statistical results will be obtained using some images taken from a high-definition image called “Cross.bmp”, shown in Figure 3.1. The “Cross” image is a typical image taken by a 35 mm camera at deep sea level in the AutoMERS Project and scanned at high resolution to obtain a digital format copy; this image is a RGB bitmap windows image with a size of 3710 x 2440 pixels and a file size of 25.89 Mbytes. From that image 5 different images are obtained, named “Ima1.bmp”, “Ima2.bmp” etc., all with the same size, 512 x 512 pixels, and showing different parts of the cross image that are characteristic for shape, texture and colour. Their saving in “.bmp”, bitmap windows image format, is useful and gives the possibility to have a 3-matrices RGB 24 bit/pixel colour image, for a file size of 768 Kbytes.

Looking in more detail at these 5 different images, shown also in Figure 3.2, “Ima1” shows a background area, the bottom of the sea, with a quite uniform grey colour and some darker spots; “Ima2” shows a part of the black-and-white cross with its shadow and the background; in this image it is possible to find rectangular edges, and well-defined change of shape and colour. “Ima4” and “Ima5” show apart from the cross, the shadows and the background, also the black part of the centre sinker; within these images edges and changes of colour and shape are found on detail. “Ima3”, showing the centre part of the sinker and the cross, is the most detailed image, with a lot of edges and big changes of luminance and colour in small areas within the image. It is important for our intentions and the tests to begin with these different and well-defined kind of images, because each of them shows its own features, different from the others.

Within the various tests developed on these 5 images, some parameters are important to show and to differentiate some characteristic features; the main parameters are:

• File Size, the real size in Kbits or Kbytes (as specified from time to time) of the image compressed and uncompressed, original or reconstructed and of the various files obtained, such as the zip-compressed files,
• Compression Ratio, a parameter that shows the quantity and the power of the compression of a particular file; 3 different, but linked, ways to represent this parameter exist:
• The Ratio “X”, a number obtained by dividing the file size of the original image by the file size of the compressed image; this parameter is usually utilised in the expression “ X : 1 ”, and shows directly how much a file could be compressed,
• The Inverse Value “Y” of the ratio X, utilised sometimes as the parameter of compression ratio within software programs, for example in the JasPer JPEG 2000 coding software; obviously the relation is Y = 1 / X,
• The Bit Rate “B”, measured as bit per pixel, bpp, or bit per sample, bps, that shows how many bits, or part of bit, of the compressed image are used for coding each sample or pixel of the original image; the relation with the compression ratio value X depends on the type of the image, in fact for a 8 bit/pixel depth grey scale image the relation is B = 8 / X bpp, in a 24 bit/pixel colour image B = 24 / X bpp; for this reason sometimes the utilisation of X and Y are more used.
• Flops, that represents the number of floating point operations used by an algorithm, a function or an operation to obtain the desired result; this value is a number that helps to evaluate the complexity of an algorithm, even if it is only a rough indication of it. Sometimes the evaluation of the complexity is a difficult issue, because it means different things for different applications; other useful parameters could be the memory bandwidth, the total working memory, the number of CPU cycles, the number of hardware gates for example. These numbers are quite often very dependent on the optimisation, targeted applications and different implementation factors,
• PSNR, meaning Peak Signal to Noise Ratio, is one of the most important parameters utilised to estimate the quality of the image reconstructed with respect to the original image; it is calculated, for 8-bit depth images by:




PSNR = 10 log₁₀ (255² / MSE)

where MSE is the Mean Square Error calculated as:

MSE = (1 / N) Sum_[1,N] (x_i - x’_i)²

where x_i and x’_i are the values of the original and reconstructed image samples and N is the number of samples of the image.

This parameter, even if sometimes it does not represent faithfully the visual quality of the image, is the only established and well-known measure of the visual quality of the images; it works reasonably well across a wide range of compression ratios and for this reason is widely used.