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Students research projects

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  • Fall 2011: Modeling vector fields with discrete exterior calculus by George Chappell, senior capstone project
  • Image-to-image search

Summer 2011: Evaluating the quality of image-to-image search by Misha Dowd

It is the exact opposite of the text-to-image search we are familiar with. Given an image, visual image search engines find images in a given collection that are similar, in some way, to the query image. So far, these engines exist mostly as experimental prototypes. Most of these demo programs work with small collections of images and, frequently, without an upload feature, which makes testing impossible. Meanwhile, when testing is possible, the results are questionable.

The approach is based on the methods related to the digital image analysis project: the distribution of the sizes of the objects in the image is compared to those of other images.

Possible projects, software PxSearch (Windows):

  • creating datasets for various, medium-size image collections;
  • developing a comprehensive review of the literature on the subject;
  • evaluating the quality of the matching;
  • modifying the matching criteria (bins for the distributions, thresholds for noise, etc);
  • analyzing the topology of the datasets (project below).


Summer 2011: Modeling Heat Transfer on Various Grids with Discrete Exterior Calculus by Julie Lang

Conway's Game of Life and other cellular automata produce fascinating pictures, but, to the best of my knowledge, can't be used to model such a simple thing as a circular wave... We will be using discrete exterior calculus to model elementary ODE's and PDE's in dimension 2 with C++, MATLAB, and/or Excel.

Possible projects:


  • Digital image analysis in 3D

Summer 2010: 3D image analysis by James Molchanoff

Image analysis and computer vision is the extraction of meaningful information from digital images. Some of the most prominent application is in cell analysis, medical image processing, and industrial machine vision. There exists an abundance of methods for solving various well-defined computer vision tasks, where the methods are very task specific and seldom can be reused in a wide range of applications. Our long term goal is to design a computer vision system “from first principles”. These principles will come initially from algebraic topology.

Possible projects:


  • Topological data analysis

Summer 2010: The topology of data by Joseph Snyder

Suppose we have conducted 1000 experiments with a set of 100 various measurements in each. Then each experiment is a string of 100 numbers, or simply a vector of dimension 100. The result is a collection of disconnected 1000 points, called the point cloud, in a 100-dimensional vector space. It is impossible to visualize this data as any representation that one can see is limited to dimension 3. Yet we still need to answer a few simple topological questions about the object behind the point cloud:

  • Is it one piece or more?
  • Is there a tunnel?
  • Or a void?
  • And what about possible 100-dimensional topological features?

Through clustering (and related approaches) statistics answers the first question. This is a common topological approach to the problem. For a point cloud in a euclidean space, suppose we are given a threshold r so that any two points within r from each other are to be considered "close". Then each pair of such points is connected by an edge. If three points are “close”, we add a face, etc. The result is a simplicial complex that approximates the manifold M behind the point cloud. More: Topological data analysis.

Possible projects, software jPlex (Java):

  • applying jPlex to various datasets,
  • applying jPlex to the dataset from the image-to-image search project
  • local analysis and dimensionality reduction


  • Using MATLAB to process images for the analysis of plant organ growth and curvature, Harrison, Marcia; Silver, Donald; Saveliev, Peter; Sarra, Scott, 19th International Conference on Arabidopsis Research, Montreal, July 2008.
  • 2007: HON 396 Problem Solving in Sciences and Engineering. This is a project oriented course focused firstly on image/signal processing. There will be also other types of computational problems in the sciences and engineering.

During the first half of semester each class will start with a lecture. The homework will consist primarily of small projects. The lecture will be followed by discussions and individual consultations intended to help the student to choose and start the main project. Later on, the former part will become shorter and may consist also of guest lectures. The students will start to submit weekly progress reports and give presentations to the class. Semester will complete with a formal ½ hour presentation/demonstration of a research paper and/or an operational software program.

  • May-July 2007. Research on grant for the US Navy - Autonomous maritime navigation.

Covered by Huntington Herald Dispatch. Marshall U Team Works on Computer Vision Navigation. Three Marshall University computer science students and faculty are working on a project to build a sensor suite for the United States Navy to be used on autonomous marine vehicles.

  • 2006: HON 396 Problem Solving in Sciences and Engineering
  1. Lindsay Dale, Kevin Forget, Amber Lilly, Virtual Stock Broker
  2. John Stonestreet, Charlie Lowe, Geometric Study of the Pattern of Microscopic Hair Development on the Wings of the Mutated Fruitfly
  3. Jared Marsh, Camden Clutter, Effects of Ethylene on Stem Gravitropic Curvature
  4. Shane Gillies; Richard Kuykendall, Blended Learning Model And Implementation of An Individual Diagnosis Tool


  • Spring 2005 Math 491/591 Senior Seminar/Masters Essay. Applications of Algebraic Topology in Sciences and Engineering

Nathan Cantrell, Investigation of Human Brain Structures through MRI and Cubical Homology Abstract: Employing magnetic resonance (MR) data sets, I will investigate the advantages of cubical homology in the examination of two dimensional and three dimensional grey-scale density maps of the human brain. The ability of MR to section the brain into sliced images of the sagittal, coronal, and transverse planes presents non-intrusive methods by which to study the brain. The digital format of the data is perfectly suited for cubical computational homology. Some brain characteristics, such as folds, do not have interesting topological features, but the ventricles do. Furthermore, three dimensional computer modeling of the brain is an extremely active area of study, but little, if any, cubical homology is in use. Several currently occurring model errors can be corrected by utilizing cubical homology. Also, I will work to acquire a cubical method that parallels simplicial homology’s “alpha shape” technique. This will allow topological study of certain non-topological features. Finally, I will continue to research the relation between the brain’s topological characteristics and their functions seeking a role for cubical homology and further study.

Bonnie Shook, Topological Approaches to Fingerprint Identification. Abstract: In this project, I will analyze the topology of different types of fingerprints in order to find a new tool to assist in computer identification. My project will focus on the homology groups of the main types of fingerprints – loops, whorls, and arches – and their variations. The dimensions of the homology groups of fingerprints will represent the number of ridges and the number of valleys. I will examine if there are fundamental differences between these types. Then I will explore how the number and types of minutiae points affect the homology groups of fingerprints. I will research the identification methods that are currently in place and examine how looking at the topological aspects of fingerprints could further this field.

Gustavo Sa, Homological Fingerprint Matching. Abstract: Homology is a mathematical algorithm that studies the structure of a space by examining its local proprieties. This project explores the applications of homology in two dimensional identical fingerprint images with the goal of accurately match these prints. In other words, the matching of fingerprints will be done by transforming the unique image of a fingerprint into homological data. Moreover, this homological data will permit us to accurately match fingerprints when there is only a partial print of one of the fingers.

Tue Ngoc Ly, Graph Topology: Chessboard and Matching Complexes. Abstract: Networking Graphs (or combinatorial graphs) are widely used to model various problems in networks (such as electric network, water flow network, Internet, and so on), relations and other fields. Many graph problems are hard, especially when the graph is large. Most of them are non-polynomial. Therefore, reducing the size of a graph means that we can save much time to get the result. We will talk about the role of topology in graph theory. To every finite collection of graphs that is closed under removal of edges, we can associate an abstract simplicial complex whose faces are the edge sets of the graphs in the collection. A bounded degree graph complex is a simplicial complex associated with the collection of subgraphs of a graph G whose maximum vertex degree is at most b. In this project, I will focus on two important special cases, matching complex (G is a complete graph and b=1) and chessboard complex (G is a complete bipartite graph and b=1).

Introduction to CHomP by Nathan Cantrell

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