| Summary: | Data compression techniques are widely used in the transmission and storage of 2D image, video and 3D data structures. The thesis addresses two aspects of data compression: 2D images and 3D structures by focusing research on solving the problem of compressing structured light images for 3D reconstruction. It is useful then to describe the research by separating the compression of 2D images from the compression of 3D data. Concerning image compression, there are many types of techniques and among the most popular are JPEG and JPEG2000. The thesis addresses different types of discrete transformations (DWT, DCT and DST) thatcombined in particular ways followed by Matrix Minimization algorithm,which is achieved high compression ratio by converting groups of data into a single value. This is an essential step to achieve higher compression ratios reaches to 99%. It is demonstrated that the approach is superior to both JPEG and JPEG2000 for compressing 2D images used in 3D reconstruction. The approach has also been tested oncompressing natural or generic 2D images mainly through DCT followed by Matrix Minimization and arithmetic coding. Results show that the method is superior to JPEG in terms of compression ratios and image quality, and equivalent to JPEG2000 in terms of image quality. Concerning the compression of 3D data structures, the Matrix Minimization algorithm is used to compress geometry and connectivity represented by a list of vertices and a list of triangulated faces. It is demonstrated that the method can compress vertices very efficiently compared with other 3D formats. Here the Matrix Minimization algorithm converts each vertex (X, Y and Z) into a single value without the use of any prior discrete transformation (as used in 2D images) and without using any coding algorithm. Concerningconnectivity,the triangulated face data are also compressed with the Matrix Minimizationalgorithm followed by arithmetic coding yielding a stream of compressed data. Results show compression ratiosclose to 95% which are far superior to compression with other 3D techniques. The compression methods presented in this thesis are defined as per-file compression. The methods to generate compression keys depend on the data to be compressed. Thus, each file generates their own set of compression keys and their own set of unique data. This feature enables application in the security domain for safe transmission and storage of data. The generated keys together with the set of unique data can be defined as an encryption key for the file as, without this information, the file cannot be decompressed.
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