Models of statistical self-similarity for signal and image synthesis

Statistical self-similarity of random processes in continuous-domains is defined through invariance of their statistics to time or spatial scaling. In discrete-time, scaling by an arbitrary factor of signals can be accomplished through frequency warping, and statistical self-similarity is defined by the discrete-time continuous-dilation scaling operation. Unlike other self-similarity models mostly relying on characteristics of continuous self-similarity other than scaling, this model provides a way to express discrete-time statistical self-similarity using scaling of discrete-time signals. This dissertation studies the discrete-time self-similarity model based on the new scaling operation, and develops its properties, which reveals relations with other models. Furthermore, it also presents a new self-similarity definition for discrete-time vector processes, and demonstrates synthesis examples for multi-channel network traffic. In two-dimensional spaces, self-similar random fields are of interest in various areas of image processing, since they fit certain types of natural patterns and textures very well. Current treatments of self-similarity in continuous two-dimensional space use a definition that is a direct extension of the 1-D definition. However, most of current discrete-space two-dimensional approaches do not consider scaling but instead are based on ad hoc formulations, for example, digitizing continuous random fields such as fractional Brownian motion. The dissertation demonstrates that the current statistical self-similarity definition in continuous-space is restrictive, and provides an alternative, more general definition. It also provides a formalism for discrete-space statistical self-similarity that depends on a new scaling operator for discrete images. Within the new framework, it is possible to synthesize a wider class of discrete-space self-similar random fields

Fuzzy Logic Classification of Handwritten Signature Based Computer Access and File Encryption

Often times computer access and file encryption is successful based on how complex a password will be, how often users could change their complex password, the length of the complex password and how creative users are in creating a complex passsword to stand against unauthorized access to computer resources or files. This research proposes a new way of computer access and file encryption based on the fuzzy logic classification of handwritten signatures. Feature extraction of the handwritten signatures, the Fourier transformation algorithm and the k-Nearest Algorithm could be implemented to determine how close the signature is to the signature on file to grant or deny users access to computer resources and encrypted files. lternatively implementing fuzzy logic algorithms and fuzzy k-Nearest Neighbor algorithm to the captured signature could determine how close a signature is to the one on file to grant or deny access to computer resources and files. This research paper accomplishes the feature recognition firstly by extracting the features as users sign their signatures for storage, and secondly by determining the shortest distance between the signatures. On the other hand this research work accomplish the fuzzy logic recognition firstly by classifying the signature into a membership groups based on their degree of membership and secondly by determining what level of closeness the signatures are from each other. The signatures were collected from three selected input devices- the mouse, I-Pen and the IOGear. This research demonstrates which input device users found efficient and flexible to sign their respective names. The research work also demonstrates the security levels of implementing the fuzzy logic, fuzzy k-Nearest Neighbor, Fourier Transform.Master'sCollege of Arts and Sciences: Computer ScienceUniversity of Michiganhttp://deepblue.lib.umich.edu/bitstream/2027.42/117719/1/Kwarteng.pd