Aditya Tatu har opnået phd-graden i datalogi på DIKU – Københavns Universitet

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28. april 2010

Aditya Tatu har opnået phd-graden i datalogi på DIKU

Med sin afhandling om

Curve Evolution in Subspaces and Exploring the Metameric Class of Histogram of Gradient Orientation based Features using Nonlinear Projection Methods

har Aditya Tatu den 28. april 2010 opnået phd-graden i Datalogi

En enig bedømmelseskomite bestående af

Formand: Lektor Jon Sporring, DIKU
Professor Nikos Paragios, Ecole Centrale de Paris
Professor Kaleem Siddiqi, McGill University, Montreal, Quebec, Canada

har indstillet Aditya til phd-graden.
DIKU ønsker tillykke med præstationen.

En kopi af phd-rapporten kan bestilles hos Dina Riis Johannessen, tlf 35 32 14 23,


This thesis deals with two unrelated issues, restricting curve evolution to subspaces and computing image patches in the equivalence class of Histogram of Gradient orientation based features using nonlinear projection methods.

Curve evolution is a well known method used in various applications like tracking interfaces, active contour based segmentation methods and others. It can also be used to study shape spaces, as deforming a shape can be thought of as evolving its boundary curve. During curve evolution a curve traces out a path in the infinite dimensional space of curves. Due to application specific requirements like shape priors or a given data model, and due to limitations of the computer, the computed curve evolution forms a path in some finite dimensional subspace of the space of curves. We give methods to restrict the curve evolution to a finite dimensional linear or implicitly defined nonlinear subspace of curves. We also deal with cases where a non-Euclidean metric is induced on such a subspace. We build differential geometric tools like the Exponential map and Log map which are essential for the study of such nonlinear spaces.

We demonstrate these tools on a particular implicitly defined subspace, the N-links bicycle chain space, i.e. the space of curves with equidistant neighboring landmark points. This in itself is a useful shape space for medical image analysis applications.

The Histogram of Gradient orientation based features are many in number and are widely used in applications like object recognition which is a vital component of any computer vision system. In order to get some intuition behind their success, we attempt to explore the metameric class of a basic version of such features. We characterize such an equivalence class using implicitly defined constraints over the statistical moments of the gradient orientations. This is another case for use of nonlinear projection methods since such an equivalence class is nonlinear. We use an approximation of the Exponential map developed in the first part of the thesis to evolve a given patch in the equivalence class. Specifically, given two initial visually different patches, we evolve one patch into another patch that visually looks like the other given patch, while still preserving its Histogram of Gradient orientation features.