Source-aggregated-poisson with applications to groupwise shape analysis and mesh segmentation

Date

2018

Author

Gençtav, Murat

Metadata

Show full item record

Item Usage Stats

47
views

0
downloads

By computing multiple solutions to Poisson’s equation with varying source functions within the shape and aggregating those solutions, we obtain a novel function for shape analysis, which we call Source-Aggregated-Poisson, or SAP. Despite the local computations, by means of specially designed source functions, our model mimics the part-coding behavior of a previous nonlocal model. We show that SAP is robust under geometric transformations and nuisance factors including topological distortions, pose changes, and occlusions. Using SAP, we address shape analysis problems in two and three dimensions. Toward this end, firstly, we exploit the evolution of its level curves and extract a probabilistic representation of shape decomposition hierarchy. Then, in the context of a groupwise shape analysis task, we demonstrate how such a probabilistic structure enables us to select the task-dependent optimum from the set of possible hierarchies. Finally, we devise an unsupervised mesh segmentation algorithm which utilizes SAP after projecting it to the surface mesh. Benchmark evaluation shows that the algorithm performs the best among the unsupervised algorithms and even performs comparable to supervised and groupwise segmentation methods.

Subject Keywords

Poisson's equation., Differential equations, Elliptic.

URI

http://etd.lib.metu.edu.tr/upload/12622784/index.pdf
https://hdl.handle.net/11511/27783

Collections

Graduate School of Natural and Applied Sciences, Thesis

Suggestions

OpenMETU
Core

Inverse problems for a semilinear heat equation with memory Kaya, Müjdat; Çelebi, Okay; Department of Mathematics (2005) In this thesis, we study the existence and uniqueness of the solutions of the inverse problems to identify the memory kernel k and the source term h, derived from First, we obtain the structural stability for k, when p=1 and the coefficient p, when g( )= . To identify the memory kernel, we find an operator equation after employing the half Fourier transformation. For the source term identification, we make use of the direct application of the final overdetermination conditions.
Differential - Operator solutions for complex partial differential equations Celebi, O; Sengul, S (1998-07-10) The solutions of complex partial differential equations of order four are obtained by using polynomial differential operators. A correspondence principle is also derived for the solutions of two different differential equations, imposing conditions on the coefficients.
On the consistency of the solutions of the space fractional Schroumldinger equation (vol 53, 042105, 2012) Bayin, Selcuk S. (2012-08-01) Recently we have reanalyzed the consistency of the solutions of the space fractional Schroumldinger equation found in a piecewise manner, and showed that an exact and a proper treatment of the relevant integrals prove that they are consistent. In this comment, for clarity, we present additional information about the critical integrals and describe how their analytic continuation is accomplished.
Boundary value problems for higher order linear impulsive differential equations Uğur, Ömür; Akhmet, Marat (2006-07-01) In this paper higher order linear impulsive differential equations with fixed moments of impulses subject to linear boundary conditions are studied. Green's formula is defined for piecewise differentiable functions. Properties of Green's functions for higher order impulsive boundary value problems are introduced. An appropriate example of the Green's function for a boundary value problem is provided. Furthermore, eigenvalue problems and basic properties of eigensolutions are considered. (c) 2006 Elsevier In...
Periodic solutions and stability of differential equations with piecewise constant argument of generalized type Büyükadalı, Cemil; Akhmet, Marat; Department of Mathematics (2009) In this thesis, we study periodic solutions and stability of differential equations with piecewise constant argument of generalized type. These equations can be divided into three main classes: differential equations with retarded, alternately advanced-retarded, and state-dependent piecewise constant argument of generalized type. First, using the method of small parameter due to Poincaré, the existence and stability of periodic solutions of quasilinear differential equations with retarded piecewise constant...

Citation Formats

M. Gençtav, “Source-aggregated-poisson with applications to groupwise shape analysis and mesh segmentation,” Ph.D. - Doctoral Program, Middle East Technical University, 2018.