3D MODELING USING PARTIAL DIFFERENTIAL EQUATIONS - Essay Example

First, I am grateful to the University for granting me the opportunity to pursue the Doctor of Philosophy Degree in this institution. Second, I wish to thank to my Supervisor for the guidance and committed support offered to see me through my doctorate studies. Third, I remain indebted to all the persons, corporate and individual for volunteering their time to provide the requisite information, which has been processed to form the substance of this Thesis. Finally, I acknowledge the support of my academic colleagues for their positive critique of my work, for advising me and keeping me company throughout the academic journey.

To all those who supported me in one way or another but have not been mentioned individually, accept my gratitude. ABSTRACT The mathematical modeling of the real world images is mostly dominated by partial differential equations. The major challenge that has disturbed most players in this industry of geometric modeling and use of computer graphics is the manufacture of representative human facial geometrical images. Such geometries are crucial for an extensive range of uses, such as in 3D face recognition.

The same can be used in virtual realism presentations, facial appearance simulations and computer-based plastic surgery applications. The main objective of this paper was to address methods used for the construction of 3D geometry/modeling of human faces founded on the use of Partial Differential Equations (PDE) and to enable the compression of those 3D data for faster transmission over the internet. In this study, the corresponding geometry to a face is applied as a set of surface patches, with each patch represented using boundary curves in the 3-space thus, formulating the suitable boundary settings for the selected PDE.

The boundary curves are removed automatically by the use of 3D information of human faces acquired by means of a 3D scanner. In this study, through the use of certain experimental confirmations it is shown that the effectiveness of the partial differential equations (PDE) based method for 3D facial surface reconstruction using scanned data effectively addresses the topic of this study. Additionally, I have also shown that the methodology makes available a well-organized way of representing facial images by the use of small sets of restrictions that could be exploited for effectual storage of the facial data and quick verification of the same.

For further research, the study recommends the need for its replication in other universities or scaling up to the national or international levels. Chapter 3 Efficient 3D Data Compression through Parameterization of Free-Form Surface Patches This study seeks to present a new technique for 3D data compression centered on the parameterization of surface patches. The successful usage of the procedure requires that it be applied to data which can be easily defined as single-valued functions. Such a scenario is the case for 3D patches that are obtained by the use of standard 3D scanners.

Another significant feature with this technique is that, it defines the number of mesh cutting planes, while the connection or intersection of the planes on the mesh defines a set of sampling points. An explicit structure that allows for the parametrical definition of both x and