Segmentation given partial grouping constraints

Abstract

We consider data clustering problems where partial grouping is known a priori. We formulate such biased grouping problems as a constrained optimization problem, where structural properties of the data define the goodness of a grouping and partial grouping cues define the feasibility of a grouping. We enforce grouping smoothness and fairness on labeled data points so that sparse partial grouping information can be effectively propagated to the unlabeled data. Considering the normalized cuts criterion in particular, our formulation leads to a constrained eigenvalue problem. By generalizing the Rayleigh-Ritz theorem to projected matrices, we find the global optimum in the relaxed continuous domain by eigendecomposition, from which a nearglobal optimum to the discrete labeling problem can be obtained effectively. We apply our method to real image segmentation problems, where partial grouping priors can often be derived based on a crude spatial attentional map that binds places with common salient features or focuses on expected object locations. We demonstrate not only that it is possible to integrate both image structures and priors in a single grouping process, but also that objects can be segregated from the background without specific object knowledge. KeywordsGrouping, image segmentation, graph partitioning, bias, spatial attention, semisupervised clustering, partially labeled classification This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of the University of Pennsylvania's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to pubs-permissions@ieee.org. By choosing to view this document, you agree to all provisions of the copyright laws protecting it. Abstract-We consider data clustering problems where partial grouping is known a priori. We formulate such biased grouping problems as a constrained optimization problem, where structural properties of the data define the goodness of a grouping and partial grouping cues define the feasibility of a grouping. We enforce grouping smoothness and fairness on labeled data points so that sparse partial grouping information can be effectively propagated to the unlabeled data. Considering the normalized cuts criterion in particular, our formulation leads to a constrained eigenvalue problem. By generalizing the Rayleigh-Ritz theorem to projected matrices, we find the global optimum in the relaxed continuous domain by eigendecomposition, from which a near-global optimum to the discrete labeling problem can be obtained effectively. We apply our method to real image segmentation problems, where partial grouping priors can often be derived based on a crude spatial attentional map that binds places with common salient features or focuses on expected object loc...

Fast normalized cut with linear constraints

“…Often in graph partitioning, prior knowledge about the cluster assignment is encoded as pairwise constraints, like "mustlink" or "cannot-link". One example is [18], where pairwise grouping information is included as linear equality constraints. However these constraints have to be homogeneous, which can only handle the information that a pair of examples are from the same cluster.…”

“…Generally, incorporating this prior knowledge will help to improve the performance of the algorithm. A natural way to incorporate prior information is with explicit constraints [7,18], and solve the augmented optimization problem correspondingly.…”

Bayesian Feedback in Data Clustering

“…The answer of the query leads to a constraint on z u and z v . However, this will lead to the "non-smooth" cluster label problem mentioned in [9]: objects that are similar can have different cluster labels. To overcome this, we adopt the solution in [9] and consider the "average" label X u , which can be viewed as the smoothed version of the cluster labels of the objects that are similar to the u-th object.…”

Semi-supervised statistical region refinement for color image segmentation

“…An essential difference between these algorithms is the locality of the grouping process. Shi and Malik [3] and Yu and Shi [1,7] solve it from a global standpoint, whereas Felzenszwalb and Huttenlocher [4], Nock [2] and Nielsen and Nock [5] make greedy local decisions to merge the connex components of induced subgraphs. Since segmentation is a global optimization process, the former approach is a priori a good candidate to tackle the problem, even when it faces computational complexity issues [3].…”

“…1, is based on a segmentation framework previously studied by Yu and Shi [1,7]: grouping with bias. It is particularly useful for domains in which the user may interact with the segmentation, by inputting constraints to bias its result: sensor models in MRF [8], Human-computer interaction, spatial attention and others [1].…”