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.
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