Curve Reconstruction, the Traveling Salesman Problem, and Menger's Theorem on Length

We give necessary and sufficient regularity conditions under which the curve reconstruction problem is solved by a traveling salesman tour or path, respectively. For the proof we have to generalize a theorem of Menger [12], [13] on arc lengt

Vision based curve reconstruction algorithms and their application to graphical password

Curve reconstruction is the problem of approximating a curve or multiple curves from a point cloud. Curve reconstruction problem has received numerous attention over the last few decades due to its significant application in geometric modeling. In this thesis, based on the relationship between human vision and curve reconstruction, two Gestalt laws have been identified for the curve reconstruction: the law of proximity indicating that our vision tends to perceptually group near objects together and the law of continuation pointing out that objects following a consistent continuous direction are perceptually grouped together. Two algorithms have been proposed to implement these two laws in curve reconstruction. This first algorithm, DISCUR, connects points based on the law of proximity. The second algorithm, VICUR, considers both laws. The algorithms have been compared to the main curve reconstruction algorithms available in the literature. Another contribution of this thesis is a new application of curve reconstruction in the field of cryptography. In the thesis, a new graphical password scheme is introduced. The proposed scheme requires users to create their secret by selecting individual points or by connecting points into curves from a given set of points. It is reasonable to assume that the users will connect points into curves that look natural to their vision so that they can recall easily. Consequently, the password may be a part of the reconstructed results of the human-vision based curve reconstruction algorithms and the attacker can use these results to crack the password. We present the application of curve reconstruction algorithm in the evaluation of our graphical password scheme

Quantification of two Gestalt Laws using curve resconstruction

Visual perception is the ability to interpret, process, and comprehend all the information received through the sense of sight by association with earlier experiences. Researchers have long struggled to explain what visual processing does to create what we actually see, and brought many theoretical approaches explaining how human beings see the world. The theoretical approaches of visual perception differ widely and their coverage ranges from early theories such as Gestalt theory to recent computational theory in the field of Artificial Intelligence. According to the characteristics of visual perception, human beings tend to classify the ambient environment objects into different categories described by various symbols or objects. Similar symbols or even quite dissimilar symbols may be perceived as belonging together or belonging to different groups according to people's judgment. It must follow certain rules when human beings set up relationships between those objects and symbols, and finally obtain the unambiguous perceptual results through the process of visual perception. To find out the mechanisms underlying these properties of visual perception, this present thesis conducts experiments on perception using curve reconstructions as test cases. The perception model developed through the experiment is implemented in a curve reconstruction algorithm. It is assumed that a good perception model will reconstruct curves in the same manner as human beings perceive them. In the present thesis, a series of methods from Design of Experiments (DOE), ANOVA and the multivariate nonlinear regression model are applied to investigate the relationships between the points and curves. The results show that our perception model conforms to the pattern human perceives the points

A Holmes and Doyle Bibliography, Volume 5: Periodical Articles--Secondary References, Alphabetical Listing

This bibliography is a work in progress. It attempts to update Ronald B. De Waal’s comprehensive bibliography, The Universal Sherlock Holmes, but does not claim to be exhaustive in content. New works are continually discovered and added to this bibliography. Readers and researchers are invited to suggest additional content. Volume 5 includes "passing" or "secondary" references, i.e. those entries that are passing in nature or contain very brief information or content

A Holmes and Doyle Bibliography, Volume 6: Periodical Articles, Subject Listing, By De Waal Category

This bibliography is a work in progress. It attempts to update Ronald B. De Waal’s comprehensive bibliography, The Universal Sherlock Holmes, but does not claim to be exhaustive in content. New works are continually discovered and added to this bibliography. Readers and researchers are invited to suggest additional content. Volume 6 presents the periodical literature arranged by subject categories (as originally devised for the De Waal bibliography and slightly modified here)

A Holmes and Doyle Bibliography, Volume 9: All Formats—Combined Alphabetical Listing

This bibliography is a work in progress. It attempts to update Ronald B. De Waal’s comprehensive bibliography, The Universal Sherlock Holmes, but does not claim to be exhaustive in content. New works are continually discovered and added to this bibliography. Readers and researchers are invited to suggest additional content. This volume contains all listings in all formats, arranged alphabetically by author or main entry. In other words, it combines the listings from Volume 1 (Monograph and Serial Titles), Volume 3 (Periodical Articles), and Volume 7 (Audio/Visual Materials) into a comprehensive bibliography. (There may be additional materials included in this list, e.g. duplicate items and items not yet fully edited.) As in the other volumes, coverage of this material begins around 1994, the final year covered by De Waal's bibliography, but may not yet be totally up-to-date (given the ongoing nature of this bibliography). It is hoped that other titles will be added at a later date. At present, this bibliography includes 12,594 items