Multiple Structure Recovery via Probabilistic Biclustering

Denitto, Matteo; Magri, Luca; Farinelli, Alessandro; Fusiello, Andrea; Bicego, Manuele

doi:10.1007/978-3-319-49055-7_25

Cited by 5 publications

(8 citation statements)

References 30 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…3 as RS-NMU. We clarify that RPA [11] and FABIA [3] achieve good results; however, to yield these performances, they use the ground truth number of models as an input. The remaining methods, as well as the method here proposed, automatically estimate this number.…”

Section: Resultsmentioning

confidence: 99%

“…We next estimate multiple fundamental matrices (moving camera and moving objects) and multiple homographies (moving planar objects) on the images in the AdelaideRMF dataset [22]. This is a standard dataset in the literature (e.g., [3,10,11,15,18,22]), but as pointed out in [18] it contains a non-negligible quantity of errors in its ground truth. This implies that, beyond some point, an improvement in the actual performance might not necessarily reflect itself as an improvement compared to the ground truth.…”

Section: Resultsmentioning

confidence: 99%

“…As standard in the literature [3,10,11,15,18] we use the misclassification error (ratio of misclassified points) to measure performance. While the ground truth assigns elements to groups in a hard fashion, the values sm µ (x i ,θ t ) are continuous in [0, 1].…”

Section: Resultsmentioning

confidence: 99%

See 2 more Smart Citations

Nonnegative Matrix Underapproximation for Robust Multiple Model Fitting

Tepper

Sapiro

2017

2017 IEEE Conference on Computer Vision and Pattern Recognition (CVPR)

View full text Add to dashboard Cite

In this work, we introduce a highly efficient algorithm to address the nonnegative matrix underapproximation (NMU) problem, i.e., nonnegative matrix factorization (NMF) with an additional underapproximation constraint. NMU results are interesting as, compared to traditional NMF, they present additional sparsity and part-based behavior, explaining unique data features. To show these features in practice, we first present an application to the analysis of climate data. We then present an NMU-based algorithm to robustly fit multiple parametric models to a dataset. The proposed approach delivers state-of-the-art results for the estimation of multiple fundamental matrices and homographies, outperforming other alternatives in the literature and exemplifying the use of efficient NMU computations.

show abstract

Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

See 1 more Smart Citation

Nonnegative Matrix Underapproximation for Robust Multiple Model Fitting

Tepper

Sapiro

2017

2017 IEEE Conference on Computer Vision and Pattern Recognition (CVPR)

View full text Add to dashboard Cite

show abstract

“…Their method gains robustness via a t-test that efficiently filters out statistically insignificant hypotheses. Denitto et al [36] propose an approach to compute a sparse low-rank representation of the preference matrix using FABIA [37] and obtain bi-clusters, i.e. clustering in rows and columns of the matrix, that allows points to belong to different geometric models simultaneously.…”

Section: Related Workmentioning

confidence: 99%

“…5. Here we also compare against Random Cluster Models Simulated Annealing (RCMSA) [92], Robust Preference Analysis (RPA) [34], FABIA [36], Multi-X [41], Mode-Seeking on Hypergraphs Fitting (MSHF) [46], and Convex Relaxation Algorithm (CORAL) [40]. Our model yields competitive performance with a particularly low error for motion model estimation.…”

Section: Geometric Model Fittingmentioning

confidence: 99%

Higher-Order Multicuts for Geometric Model Fitting and Motion Segmentation

Levinkov

Kardoost

Andres

et al. 2023

IEEE Trans. Pattern Anal. Mach. Intell.

View full text Add to dashboard Cite

The minimum cost lifted multicut problem is a generalization of the multicut problem (also known as correlation clustering) and is a means to optimizing a decomposition of a graph w.r.t. both positive and negative edge costs. It has been shown to be useful in a large variety of applications in computer vision thanks to the fact that multicut-based formulations do not require the number of components given a priori; instead, it is deduced from the solution. However, the standard multicut cost function is limited to pairwise relationships between nodes, while several important applications either require or can benefit from a higher-order cost function, i.e. hyper-edges. In this paper, we propose a pseudo-boolean formulation for a multiple model fitting problem. It is based on a formulation of any-order minimum cost lifted multicuts, which allows to partition an undirected graph with pairwise connectivity such as to minimize costs defined over any set of hyper-edges. As the proposed formulation is NP-hard and the branch-and-bound algorithm (as well as obtaining lower bounds) is too slow in practice, we propose an efficient local search algorithm for inference into resulting problems. We demonstrate versatility and effectiveness of our approach in several applications: 1) We define a geometric multiple model fitting, more specifically, a line fitting problem on all triplets of points and group points, that belong to the same line, together. 2) We formulate homography and motion estimation as a geometric model fitting problem where the task is to find groups of points that can be explained by the same geometrical transformation. 3) In motion segmentation our model allows to go from modeling translational motion to Euclidean or affine transformations, which improves the segmentation quality in terms of F-measure.

show abstract