Dimah Dera

Date Approved

7-29-2015

Embargo Period

1-25-2016

Document Type

Thesis

Degree Name

M.S. Electrical and Computer Engineering

Department

Electrical and Computer Engineering

College

Henry M. Rowan College of Engineering

Advisor

Bouaynaya, Nidhal

Subject(s)

Image segmentation; Magnetic resonance imaging

Disciplines

Electrical and Computer Engineering

Abstract

We address the problem of image segmentation using a new deformable model based on the level set method (LSM) and non-negative matrix factorization (NMF). We describe the use of NMF to reduce the dimension of large images from thousands of pixels to a handful of "metapixels" or regions. In addition, the exact number of regions is discovered using the nuclear norm of the NMF factors. The proposed NMF-LSM characterizes the histogram of the image, calculated over the image blocks, as nonnegative combinations of basic histograms computed using NMF (V ~ W H). The matrix W represents the histograms of the image regions, whereas the matrix H provides the spatial clustering of the regions. NMF-LSM takes into account the bias field present particularly in medical images. We define two local clustering criteria in terms of the NMF factors. The first criterion defines a local intensity clustering property based on the matrix W by computing the average intensity and standard deviation of every region. The second criterion defines a local spatial clustering using the matrix H. The local clustering is then summed over all regions to give a global criterion of image segmentation. In LSM, these criteria define an energy minimized w.r.t. LSFs and the bias field to achieve the segmentation. The proposed method is validated on synthetic binary and gray-scale images, and then applied to real brain MRI images. NMF-LSM provides a general approach for robust region discovery and segmentation in heterogeneous images.

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