Image segmentation is a process used in computer vision to partition an image into regions with similar characteristics. One category of image segmentation algorithms is graph-based, where pixels in an image are represented by vertices in a graph and the similarity between pixels is represented by weighted edges. A segmentation of the image can be found by cutting edges between dissimilar groups of pixels in the graph, leaving different clusters or partitions of the data.

A popular graph-based method for segmenting images is the Normalized Cuts (NCuts) algorithm, which quantifies the cost for graph partitioning in a way that biases clusters or segments that are balanced towards having lower values than unbalanced partitionings. This bias is so strong, however, that the NCuts algorithm avoids any singleton partitions, even when vertices are weakly connected to the rest of the graph. For this reason, we propose the Compassionately Conservative Normalized Cut (CCNCut) objective function, which strikes a better compromise between the desire to avoid too many singleton partitions and the notion that all partitions should be balanced.

We demonstrate how CCNCut minimization can be relaxed into the problem of computing Piecewise Flat Embeddings (PFE) and provide an overview of, as well as two efficiency improvements to, the Splitting Orthogonality Constraint (SOC) algorithm previously used to approximate PFE. We then present a new algorithm for computing PFE based on iteratively minimizing a sequence of reweighted Rayleigh quotients (IRRQ) and run a series of experiments to compare CCNCut-based image segmentation via SOC and IRRQ to NCut-based image segmentation on the BSDS500 dataset. Our results indicate that CCNCut-based image segmentation yields more accurate results with respect to ground truth than NCut-based segmentation, and IRRQ is less sensitive to initialization than SOC.

Library of Congress Subject Headings

Image processing--Digital techniques; Computer vision; Graph theory; Optical pattern recognition

Publication Date


Document Type


Student Type


Degree Name

Applied and Computational Mathematics (MS)

Department, Program, or Center

School of Mathematical Sciences (COS)


Nathan Cahill

Advisor/Committee Member

Elizabeth Cherry

Advisor/Committee Member

John Hamilton Jr.


RIT – Main Campus

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