PLMP - Point-Line Minimal Problems in Complete Multi-View Visibility

Duff, Timothy; Kohn, Kathlén; Leykin, Anton; Pajdla, Tomáš

doi:10.1109/iccv.2019.00176

Cited by 34 publications

(42 citation statements)

References 51 publications

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“…A sizeable literature has also emerged on solving other minimal problems in real-time with specialized solvers based on Gröbner bases and resultants (see, e.g., [143,149]). Recently, homotopy continuation methods have played a complementary role, enabling the study of a much wider class of minimal problems than before [133,86,80].…”

Section: Algebraic Vision By Timothy Duffmentioning

confidence: 99%

Nonlinear algebra and applications

Breiding¹,

Çelik²,

Duff³

et al. 2023

NACO

Self Cite

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<p style='text-indent:20px;'>We showcase applications of nonlinear algebra in the sciences and engineering. Our review is organized into eight themes: polynomial optimization, partial differential equations, algebraic statistics, integrable systems, configuration spaces of frameworks, biochemical reaction networks, algebraic vision, and tensor decompositions. Conversely, developments on these topics inspire new questions and algorithms for algebraic geometry.</p>

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Section: Algebraic Vision By Timothy Duffmentioning

confidence: 99%

Nonlinear algebra and applications

Breiding¹,

Çelik²,

Duff³

et al. 2023

NACO

Self Cite

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“…Second, the exploited geometric primitives can be points [5], [11], oriented points [15], [16], hybrid of point and line structures [24], [25], [26], etc. Recently, oriented points (or an infinitesimal patch equivalently) have drawn much attention.…”

Section: Related Workmentioning

confidence: 99%

On Relative Pose Recovery for Multi-Camera Systems

Zhao¹,

Guan²

2021

Preprint

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The point correspondence (PC) and affine correspondence (AC) are widely used for relative pose estimation. An AC consists of a PC across two views and an affine transformation between the small patches around this PC. Previous work demonstrates that one AC generally provides three independent constraints for relative pose estimation. For multi-camera systems, there is still not any AC-based minimal solver for general relative pose estimation. To deal with this problem, we propose a complete solution to relative pose estimation from two ACs for multi-camera systems, consisting of a series of minimal solvers. The solver generation in our solution is based on Cayley or quaternion parameterization for rotation and hidden variable technique to eliminate translation. This solver generation method is also naturally applied to relative pose estimation from PCs, resulting in a new six-point method for multi-camera systems. A few extensions are made, including relative pose estimation with known rotation angle and/or with unknown focal lengths. Extensive experiments demonstrate that the proposed AC-based solvers and PC-based solvers are effective and efficient on synthetic and real-world datasets.

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“…Our retrained L-CNN obtained slightly better performance than the original one. † means that the post-processing scheme proposed in L-CNN [40] 10 and AP H for DWP [14], AFM [33], L-CNN [40] and HAWP (ours) on the wireframe benchmark (the left two plots) and the YorkUrban benchmark (the right two plots). Best viewed in color and magnification.…”

Section: Evaluation Metricmentioning

confidence: 99%

“…Line segments and junctions are prominent visual patterns in the low-level vision, and thus often used as important cues/features to facilitate many downstream vision tasks such as camera pose estimation [23,24,10], image matching [35], image rectification [36], structure from motion (SfM) [4,21], visual SLAM [18,38,41], and surface reconstruction [16]. Both line segment detection and junction detection remain Figure 1.…”

Section: Introduction 1motivations and Objectivesmentioning

confidence: 99%

Holistically-Attracted Wireframe Parsing

Xue

Bai

et al. 2020

Preprint

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This paper presents a fast and parsimonious parsing method to accurately and robustly detect a vectorized wireframe in an input image with a single forward pass. The proposed method is end-to-end trainable, consisting of three components: (i) line segment and junction proposal generation, (ii) line segment and junction matching, and (iii) line segment and junction verification. For computing line segment proposals, a novel exact dual representation is proposed which exploits a parsimonious geometric reparameterization for line segments and forms a holistic 4-dimensional attraction field map for an input image. Junctions can be treated as the "basins" in the attraction field. The proposed method is thus called Holistically-Attracted Wireframe Parser (HAWP). In experiments, the proposed method is tested on two benchmarks, the Wireframe dataset [14] and the YorkUrban dataset [8]. On both benchmarks, it obtains state-of-the-art performance in terms of accuracy and efficiency. For example, on the Wireframe dataset, compared to the previous state-of-the-art method L-CNN [40], it improves the challenging mean structural average precision (msAP) by a large margin (2.8% absolute improvements), and achieves 29.5 FPS on single GPU (89% relative improvement). A systematic ablation study is performed to further justify the proposed method. * Corresponding author (a) Image (b) Learned Lines (c) HAWP (score>0.9) (d) Junction Proposals (e) Enumerated Lines (f) L-CNN (score>0.9)

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PLMP - Point-Line Minimal Problems in Complete Multi-View Visibility

Cited by 34 publications

References 51 publications

Nonlinear algebra and applications

Nonlinear algebra and applications

On Relative Pose Recovery for Multi-Camera Systems

Holistically-Attracted Wireframe Parsing

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