DeepAI AI Chat
Log In Sign Up

The Weighted Euler Curve Transform for Shape and Image Analysis

by   Qitong Jiang, et al.
Florida State University
The Ohio State University

The Euler Curve Transform (ECT) of Turner et al. is a complete invariant of an embedded simplicial complex, which is amenable to statistical analysis. We generalize the ECT to provide a similarly convenient representation for weighted simplicial complexes, objects which arise naturally, for example, in certain medical imaging applications. We leverage work of Ghrist et al. on Euler integral calculus to prove that this invariant—dubbed the Weighted Euler Curve Transform (WECT)—is also complete. We explain how to transform a segmented region of interest in a grayscale image into a weighted simplicial complex and then into a WECT representation. This WECT representation is applied to study Glioblastoma Multiforme brain tumor shape and texture data. We show that the WECT representation is effective at clustering tumors based on qualitative shape and texture features and that this clustering correlates with patient survival time.


page 3

page 7

page 8


How Many Directions Determine a Shape and other Sufficiency Results for Two Topological Transforms

In this paper we consider two topological transforms based on Euler calc...

On the invariant region for compressible Euler equations with a general equation of state

The state space for solutions of the compressible Euler equations with a...

Streaming Algorithm for Euler Characteristic Curves of Multidimensional Images

We present an efficient algorithm to compute Euler characteristic curves...

Randomness and Statistical Inference of Shapes via the Smooth Euler Characteristic Transform

In this paper, we provide the mathematical foundations for the randomnes...

Cosine Series Representation

This short paper is based on Chung et al. (2010), where the cosine serie...

Effects of Nonparanormal Transform on PC and GES Search Accuracies

Liu, et al., 2009 developed a transformation of a class of non-Gaussian ...

Sparse and Cosparse Audio Dequantization Using Convex Optimization

The paper shows the potential of sparsity-based methods in restoring qua...