Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 0803.0146

Polynomial time algorithms for bi-criteria, multi-objective and ratio problems in clustering and imaging. Part I: Normalized cut and ratio regions

Dorit S. Hochbaum
View original source ↗Read source document ↗Export metadata ↓

Abstract

Partitioning and grouping of similar objects plays a fundamental role in image segmentation and in clustering problems. In such problems a typical goal is to group together similar objects, or pixels in the case of image processing. At the same time another goal is to have each group distinctly dissimilar from the rest and possibly to have the group size fairly large. These goals are often combined as a ratio optimization problem. One example of such problem is the normalized cut problem, another is the ratio regions problem. We devise here the first polynomial time algorithms solving these problems optimally. The algorithms are efficient and combinatorial. This contrasts with the heuristic approaches used in the image segmentation literature that formulate those problems as nonlinear optimization problems, which are then relaxed and solved with spectral techniques in real numbers. These approaches not only fail to deliver an optimal solution, but they are also computationally expensive. The algorithms presented here use as a subroutine a minimum $s,t-cut procedure on a related graph which is of polynomial size. The output consists of the optimal solution to the respective ratio problem, as well as a sequence of nested solution with respect to any relative weighting of the objectives of the numerator and denominator. An extension of the results here to bi-criteria and multi-criteria objective functions is presented in part II.

Explore related subjects

cs.CVcs.DM

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Dorit S. Hochbaum. 2008-03-02. Polynomial time algorithms for bi-criteria, multi-objective and ratio problems in clustering and imaging. Part I: Normalized cut and ratio regions. https://arxiv.org/abs/0803.0146

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

SAMReg: SAM-enabled Image Registration with ROI-based Correspondence

This paper describes a new spatial correspondence representation based on paired regions-of-interest (ROIs), for medical image registration. The distinct properties of the proposed ROI-based correspondence are discussed, in the context of potential benefits in clinical applications following image registration, compared with alternative correspondence-representing approaches, such as those based on sampled displacements and spatial transformation functions. These benefits include a clear connection between learning-based image registration and segmentation, which in turn motivates two cases of image registration approaches using (pre-)trained segmentation networks. Based on the segment anything model (SAM), a vision foundation model for segmentation, we develop a new registration algorithm SAMReg, which does not require any training (or training data), gradient-based fine-tuning or prompt engineering. The proposed SAMReg models are evaluated across five real-world applications, including intra-subject registration tasks with cardiac MR and lung CT, challenging inter-subject registration scenarios with prostate MR and retinal imaging, and an additional evaluation with a non-clinical example with aerial image registration. The proposed methods outperform both intensity-based iterative algorithms and DDF-predicting learning-based networks across tested metrics including Dice and target registration errors on anatomical structures, and further demonstrates competitive performance compared to weakly-supervised registration approaches that rely on fully-segmented training data. Open source code and examples are available at: https://github.com/sqhuang0103/SAMReg.git.

cs.CV↗
arXiv2026

Q-SiT: Teaching LMMs for Image Quality Scoring and Interpreting

Image quality scoring and interpreting are two fundamental components of Image Quality Assessment (IQA). The former quantifies image quality, while the latter enables descriptive question answering about image quality. Traditionally, these two tasks have been addressed independently. However, image-quality-specific psychophysical studies suggest that these two tasks are conceptually interconnected: interpreting explicitly represents perceived quality attributes whereas scoring summarizes such evidence into an overall quality judgment. Thus, unifying these capabilities within a single model is both intuitive and logically coherent. In this paper, we propose Q-SiT (Quality Scoring and Interpreting joint Teaching), a unified framework that enables large multimodal models (LMMs) to learn both image quality scoring and interpreting simultaneously. We achieve this by transforming conventional IQA datasets into learnable question-answering datasets and incorporating human-annotated quality interpreting data for training. Furthermore, we introduce an efficient scoring \& interpreting balance strategy, which first determines the optimal data mix ratio on lightweight LMMs and then maps this ratio to primary LMMs for fine-tuning adjustment. This strategy not only mitigates task interference and enhances cross-task knowledge transfer but also significantly reduces computational costs compared to direct optimization on full-scale LMMs. With this joint learning framework and corresponding training strategy, we develop Q-SiT, the first model capable of simultaneously performing image quality scoring and interpreting tasks, along with its lightweight variant, Q-SiT-mini. Experimental results demonstrate that Q-SiT achieves strong performance in both tasks with superior generalization IQA abilities, while Q-SiT-mini significantly reduces computational overhead while maintaining competitive performance.

cs.CV↗
arXiv2026

Preserving Guidance in Cost-Volume Retrieval under Extreme LiDAR Sparsity in Iterative Stereo

While accurate LiDAR depth has been shown to improve stereo matching, high-end LiDAR remains costly and difficult to deploy at scale, motivating guidance from sparse LiDAR measurements. In this paper, we revisit how extremely sparse LiDAR can guide iterative stereo by examining its cost-volume retrieval mechanism. Our analysis shows that LiDAR guidance degrades sharply when only a few hundred points are available, and we provide a signal-processing explanation for why iterative stereo fails to fully exploit such sparse input. This insight leads to a simple yet highly effective remedy: pre-filling the initial disparity map so that cost-volume retrieval becomes more reliable under extremely sparse LiDAR. We find that pre-filling is also effective when injecting LiDAR depth into image features via early fusion, but for a fundamentally different reason, necessitating a distinct pre-filling approach. Combining both forms of guidance, our proposed Guided RAFT-Stereo (GRAFT-Stereo) achieves substantial improvements over existing LiDAR-guided stereo methods across multiple datasets.

cs.CV↗