Hierarchyless simplification, stripification and compression of triangulated two-manifolds

In this paper we explore the algorithmic space in which stripification, simplification and geometric compression of triangulated 2-manifolds overlap. Edge-collapse/uncollapse based geometric simplification algorithms develop a hierarchy of collapses such that during uncollapse the reverse order has to be maintained. We show that restricting the simplification and refinement operations only to, what we call, the collapsible edges creates hierarchyless simplification in which the operations on one edge can be performed independent of those on another. Although only a restricted set of edges is used for simplification operations, we prove topological results to show that, with minor retriangulation, any triangulated 2-manifold can be reduced to either a single vertex or a single edge using the hierarchyless simplification, resulting in extreme simplification. The set of collapsible edges helps us analyze and relate the similarities between simplification, stripification and geometric compression algorithms. We show that the maximal set of collapsible edges implicitly describes a triangle strip representation of the original model. Further, these strips can be effortlessly maintained on multiresolution models obtained through any sequence of hierarchyless simplifications on these collapsible edges. Due to natural relationship between stripification and geometric compression, these multi-resolution models can also be efficiently compressed using traditional compression algorithms. We present algorithms to find the maximal set of collapsible edges and to reorganize these edges to get the minimum number of connected components of these edges. An order-independent simplification and refinement of these edges is achieved by our novel data structure and we show the results of our implementation of view-dependent, dynamic, hierarchyless simplification. We maintain a single triangle strip across all multi-resolution models created by the view-dependent simplification process. We present a new algorithm to compress the models using the triangle strips implicitly defined by the collapsible edges

Novel methods of image compression for 3D reconstruction

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