Consensus Maximization Tree Search Revisited

Tat-Jun Chin; Vladlen Koltun; Zhipeng Cai

REVIEW 2 major objections 7 minor 28 references

Consensus Maximization Tree Search Revisited

T0 review · 2 major / 7 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read This paper claims that two new techniques, NAPA and DIBP, accelerate A* tree search for consensus maximization by avoiding redundant paths and dimension-sensitive pruning, preserving global optimality and producing speedups of over 1000x…

desk verdict Clean algorithmic improvements to exact consensus maximization that deliver real speedups on linear problems, but the homography results rest on a local inner solver and so do not certify global optimality. read the letter →

arxiv 1908.02021 v3 pith:BTP6UC7Q submitted 2019-08-06 cs.CV

Zhipeng Cai , Tat-Jun Chin , Vladlen Koltun This is my paper · ORCID

classification cs.CV

keywords consensusmaximizationrobustfittingA*treesearchLP-typeproblemsbranchpruningglobaloptimizationoutlierdetectionfixed-parametertractability

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper claims that exact A* tree search for consensus maximization—finding the model consistent with the largest number of measurements despite outliers—can be made orders of magnitude faster without giving up global optimality. It identifies two sources of wasted work in the previous algorithm: tree paths connecting nodes at non-adjacent levels, which are redundant but were previously traversed, and a branch-pruning test whose reliability collapses as the model dimension grows. The proposed NAPA strategy skips any generated child basis whose level is not strictly larger than its parent's, while DIBP prunes by certifying that a small subset of the current basis must contain at least one true outlier. On real KITTI fundamental-matrix instances, the combined method finds the globally optimal solution in under 10 seconds where earlier A* variants often failed to finish in 2 hours.

What carries the argument

The object that carries the argument is the basis tree of an LP-type problem. A basis is a minimal subset whose minimax residual equals that of its superset; each node has a violation set $V(B)$ of points whose residual exceeds the minimax value, and its level is $\ell(B)=|V(B)|$. Two bases are adjacent when their violation sets differ by exactly one point, and the earlier algorithm expanded nodes by computing $\tau(C(B)\setminus\{s\})$ for each $s$ in the current basis, which can produce a non-adjacent node whose level is not larger than the parent's. NAPA restores the intended search graph with the simple level test $\ell(B')>\ell(B)$. DIBP replaces the single-point test with a growing subset $S_B$: it adds points with the largest residual under a cheap upper-bound solution and uses the admissible heuristic bound $h_{\mathrm{ins}}(B|S_B)>g(B)$ to certify that $S_B$ contains a true outlier, so all branches not removing a point of $S_B$ can be pruned. The level test is what makes DIBP cheap, because the elements added to $S_B$ are often exactly the ones that generated repeated or non-adjacent nodes.

What would settle it

Take a small homography instance whose inner constrained minimax problems have known lower residuals than the local optimizer returns; if the search then prunes the branch containing the true optimum or returns a feasible basis with suboptimal consensus, the central claim fails. Concretely, run A*-NAPA-DIBP on a benchmark with a known optimal consensus, once with the local inner solver and once with a certified global inner solver, and check whether both return the same consensus value.

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Extended reading notes

Core claim

Consensus maximization is NP-hard, but exact A* tree search is fixed-parameter tractable and can be made practical on moderate inputs by removing two inefficiencies. In the basis tree of the LP-type formulation, a child basis generated by removing one point from the current basis and solving a minimax problem is not always an adjacent child: its violation set can coincide with a basis at the same or lower level. Since tree search only needs adjacent paths, every generated basis $B'$ with level $\ell(B') \le \ell(B)$ can be discarded without changing the optimal solution. The existing True Outlier Detection (TOD) branch pruning decides whether a single point is a true outlier by comparing heuristic bounds, but this decision is systematically unreliable when the outlier rate or dimension is high; DIBP instead greedily accumulates points into a set $S_B$ certified to contain at least one true outlier, a weaker and more frequently satisfiable demand. The paper reports that A*-NAPA-DIBP returns the globally optimal solution on all tested KITTI and homography benchmarks, with speedups of hundreds to more than a thousand times over prior A* variants.

Load-bearing premise

Every minimax subproblem and its constrained version must be solved to global optimality, but the paper's non-linear experiments use a local numerical optimizer with no global optimality guarantee, so a non-global solution anywhere along the search would invalidate the level test, the heuristic bounds, and the optimality certificate.

Editorial extensions

If this is right

A*-NAPA-DIBP solves linearized fundamental matrix estimation on KITTI frames with 13 to 22 outliers in 2 to 8 seconds, whereas A* and A*-TOD often exceed 2 hours; if correct, exact robust fitting becomes usable on realistic two-view geometry problems.
The speedups preserve the fixed-parameter tractability guarantee of tree search, so the returned solution carries a certificate of global optimality rather than an approximation guarantee.
NAPA reduces the number of unique nodes generated by large factors, and DIBP further collapses branching; the two gains are separate and combine, making the full method faster than either technique alone on every reported benchmark.
Because the level test and DIBP are stated for any LP-type problem with pseudo-convex residuals, the same acceleration should transfer to other consensus maximization tasks beyond linear regression and fundamental matrix estimation, and the paper demonstrates the transfer to homography estimation.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

NAPA's insight that generated children with non-increasing levels are redundant generalizes to any tree search over LP-type bases: any expansion violating strict level increase is outside the adjacency graph and can be pruned in other LP-type solvers, not just consensus maximization.
DIBP suggests a general pruning principle: instead of certifying a single required object, certify any subset that contains at least one required object, because the larger the subset the weaker the certificate needed; this trade-off is exactly what DIBP exploits by growing $S_B$ greedily.
A testable extension is to replace the residual-based ordering of additions to $S_B$ with data-dependent priorities; if DIBP's gains depend on reaching a certified $S_B$ early, better ordering could reduce the number of constrained minimax solves further.
Since the paper's runtime is dominated by inner minimax solves, substituting a faster certified global solver for the local optimizer used in the non-linear experiments could extend the same acceleration to residual models where inner solves are currently the bottleneck.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Two things you should know. First, this paper has two genuinely new algorithmic tricks for exact consensus maximization: NAPA, which avoids redundant non-adjacent paths in the LP-type tree, and DIBP, which generalizes the TOD pruning to subsets. Both are clean, the safety arguments are sound, and the speedups on the fundamental matrix experiments are real and large (hundreds to over a thousand times). Second, the homography experiment does not actually establish global optimality, because the inner minimax problems are solved by fminimax, a local optimizer. That doesn't sink NAPA/DIBP as algorithmic ideas, but it means Table 2 should be read as 'A* with a local inner solver,' not as a certificate of optimality.

What's good: The NAPA observation is simple and correct: a generated child satisfies V(B') ⊆ V(B) ∪ {s}, so non-adjacent children have level ≤ l(B) and can be discarded. The DIBP extension is a natural generalization of TOD with decent theoretical motivation, including Lemma 2 for linear residuals. The implementation is released. The KITTI fundamental matrix results are the strong part: the vertex-to-vertex solver is exact, and the time comparisons are striking. The comparison against MIP on synthetic data is also useful and fair (MIP parallelized, tree search sequential).

Soft spots: The fminimax issue is the main one. In Sec 6.3 the paper says the non-linear problems (4) and (14) were solved by MATLAB's fminimax. fminimax is local and gives no global certificate. If the returned solution isn't the global minimizer, the basis, violation set, and level are wrong, which breaks both NAPA's level check and DIBP's pruning. The paper doesn't describe initialization, multi-start, or verification. So Table 2's runtimes may be plausible, but the 'globally optimal' label is not supported there. I'd also note the synthetic timing plots have no error bars, and the choice of homography data isn't justified. Minor: the paper leans on [6] for hins admissibility and the g(B) upper bound; that's a self-citation dependency, but a reasonable one since [6] is published and the authors are extending it.

Bottom line: for readers working on globally optimal geometric fitting, this is worth a serious look. The linear-experiment speedups are credible and the new ideas should transfer. The nonlinear experiment needs to be redone with a certified global inner solver, or at minimum multi-start plus reporting of consensus values, before the global-optimality claim covers homography. I'd send this to a serious referee who can check the LP-type arguments and maybe run the code. It deserves peer review, not a desk reject.

Referee Report

2 major / 7 minor

Summary. This paper revisits A* tree search for exact consensus maximization and proposes two accelerations. The first, NAPA (Non-Adjacent Path Avoidance), observes that when a child B' is generated from B by solving on C(B)\setminus{s}, its violation set satisfies V(B')⊆V(B)∪{s}; if B' is not adjacent to B then l(B')≤l(B), so the generated node can be discarded without losing the adjacent path needed for optimality. The second, DIBP (Dimension-Insensitive Branch Pruning), replaces TOD's search for a single true outlier with a search for a subset S_B of the current basis that must contain at least one true outlier; if condition hins(B|S_B)>g(B) is met, all child branches except those corresponding to points in S_B can be pruned. The authors provide Lemmas 1 and 2 on when TOD is weak and when DIBP can safely start from a larger candidate set, and they evaluate the resulting A*-NAPA-DIBP algorithm on synthetic robust linear regression, linearized fundamental matrix estimation on KITTI, and homography estimation. They report speedups of several orders of magnitude over previous A* and A*-TOD variants, with all KITTI fundamental-matrix instances solved in under 10 seconds.

Significance. If the issues below are addressed, the paper is a meaningful contribution. NAPA is a clean, apparently sound observation about the consensus maximization tree structure, and the reported empirical gains are large. DIBP is a natural and promising extension of TOD that is experimentally much more effective on challenging instances. The release of demo code is a strength, and the synthetic and KITTI fundamental-matrix experiments provide convincing evidence for the linear-residual setting. The theoretical novelty is modest — both techniques build directly on the authors' earlier TPAMI tree search — but the practical acceleration is substantial and the paper is clearly written. The main risk is that the homography experiments, which are the only nonlinear demonstration, currently do not support the global-optimality claim because the inner problems are solved with a local optimizer. Fixed within the manuscript's scope, the paper would be a solid step toward practical exact consensus maximization.

major comments (2)

[Sec. 6.3, Table 2; Sec. 2.2, Eqs. (4), (14)] The homography experiments are load-bearing for the claim that NAPA and DIBP work beyond linear residuals, but the inner minimax problems (4) and (14) are solved with MATLAB fminimax, a local optimizer that provides no global optimality certificate. Section 2.2 asserts that problem (4) has a unique optimal solution and can be solved efficiently with standard solvers, and the A* optimality argument, the NAPA discard rule (Algorithm 3, line 11), and the DIBP pruning test (18) all depend on the computed basis, violation set, and level being the exact LP-type quantities. If fminimax returns a non-global solution, the violation set V(B), the level l(B), the heuristic hins, and the upper bound g(B) are all incorrect, so the 'globally optimal' homography results in Table 2 are not supported by the evidence presented. The linearized fundamental-matrix experiments in Section 6.2 use an exact vertex-to-vertex solver and are not affected. Please either use an exact global solver for the non-linear minimax subproblems or explicitly restrict the global-optimality claims to the linear-residual experiments and present Section 6.3 as a heuristic demonstration.
[Sec. 4.2, Eq. (18); Algorithm 3, line 14] The correctness of DIBP is asserted but not formally established. The paper defines hins(B|S_B) by analogy with hins(B|s) and claims that condition (18) identifies a subset S_B containing at least one true outlier, but it never states or proves the subset analogue of the TOD equivalence (11) — namely that h*(B|S_B)>h*(B) holds exactly when S_B contains a point outside the largest feasible subset of C(B) — nor does it prove that hins(B|S_B) is an admissible lower bound on h*(B|S_B). Because DIBP prunes |B|-|S_B| branches on the basis of (18), this missing argument is load-bearing. Please add a formal lemma with proof, or an explicit reduction to the TOD proof in [6].

minor comments (7)

[Sec. 3, paragraph after Eq. (10)] The sentence 'the repeated basis check heuristic in Algorithm 1 assumes that the level of the child node B' is always lower than the parent B by 1' appears to be a typo: along an adjacent edge the child's level is l(B)+1, not lower. Please correct this, as it obscures the NAPA argument.
[Sec. 6.1, Fig. 5] Please state how many random instances each curve in Figure 5 averages over and include error bars or variance information; it is currently unclear whether each point is a single run.
[Sec. 6.2, Table 1 caption] The speedup row uses '>6400' for timed-out baselines; since the exact termination time is unknown, these are lower bounds. Please state this explicitly in the caption or text.
[Sec. 6.3] The claim that 'the value of φ in the non-linear case was usually also much smaller' is not supported by any measurement in the paper. Please provide the actual φ values or a reference.
[Sec. 4.2, Lemma 1] The quantity φ is described as the 'average size of all Brem during Algorithm 2,' but the average is not specified precisely (over what set of bases or runs). Please define it formally before Lemma 1.
[Algorithm 3, lines 8–18] When l(B')≤l(B), the generated B' is discarded but s is not added to S_B, whereas Section 5 says s can be added to S_B 'even though it leads to repeated bases.' Please clarify whether the non-adjacent case is intentionally treated differently from the repeated-basis case and why.
[General] There are several typos, including 'non-adjacenct' in the algorithm list, 'seach' in Section 6.2, and 'algebaric' in Section 6.2. Please proofread.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the new NAPA and DIBP techniques are algorithmic extensions backed by prior proven lemmas, not by fitted inputs or self-defined predictions.

full rationale

The paper's central claims are two algorithmic accelerations for A* consensus-maximization tree search. NAPA is justified as a graph-theoretic observation: in the basis tree, any basis reachable from the root has an adjacent path, so non-adjacent generated bases are redundant. This is supported by the cited external result of Matousek on the basis tree, not by restating the conclusion as a premise. DIBP extends the TOD pruning argument to subsets: condition (18) is a logical consequence of admissibility of hins and the upper-bound property of g, which are prior theorems from the authors' TPAMI work [6]. Those theorems are parameter-free mathematical statements with stated assumptions (pseudo-convex residuals, non-degeneracy) that do not include the target DIBP result; the paper even sketches the admissibility argument. This is legitimate independent support rather than circular self-citation. No parameter is fitted to the experimental data and then renamed as a prediction; the reported speedups are direct runtime comparisons. The one substantive concern is that in the nonlinear homography experiments the inner minimax problems (4)/(14) are solved with MATLAB fminimax, a local optimizer, so the claimed global optimality of those results is not fully verified. That is a correctness or verification risk, not a circularity: it does not reduce the paper's conclusion to its inputs by construction. Therefore the derivation chain is not circular, and the appropriate score is 0.

Assumptions & free parameters 0 free parameters · 4 assumptions · 0 invented entities

No free parameters are fitted to data; the inlier threshold epsilon is a user input. The central method depends on four prior results, two from the authors' own TPAMI paper [6], whose proofs are cited rather than reproduced. The non-linear experimental implementation adds an unstated exactness assumption on fminimax, which is logged as a red flag.

assumptions (4)

domain assumption Residual r is pseudo-convex and data S is non-degenerate.
Stated in Sec. 2.2; ensures (4) has a unique optimum and satisfies LP-type properties, which both NAPA and DIBP build upon.
standard math Bases of the LP-type problem form a tree and every basis is reachable by a path of adjacent bases (Matousek).
Used in Sec. 3 to justify discarding non-adjacent paths; cited to [18].
domain assumption hins is an admissible heuristic and g(B) is an upper bound of h*(B).
Taken from [6] (Theorem 4); DIBP's pruning condition (18) is only sound if this holds.
domain assumption Constrained minimax problems (14) are LP-type and are solved exactly by standard solvers.
Required for the constrained hins and for Lemma 2; stated in Sec. 4.1 but not proved in this paper.

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Cite this review

Pith. "Pith review of Consensus Maximization Tree Search Revisited." pith.science (2026). https://pith.science/paper/BTP6UC7Q

@misc{pith2026190802021,
  author       = {Pith},
  title        = {Pith review of: Consensus Maximization Tree Search Revisited},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/BTP6UC7Q}},
  note         = {Machine review of arXiv:1908.02021}
}

read the original abstract

Consensus maximization is widely used for robust fitting in computer vision. However, solving it exactly, i.e., finding the globally optimal solution, is intractable. A* tree search, which has been shown to be fixed-parameter tractable, is one of the most efficient exact methods, though it is still limited to small inputs. We make two key contributions towards improving A* tree search. First, we show that the consensus maximization tree structure used previously actually contains paths that connect nodes at both adjacent and non-adjacent levels. Crucially, paths connecting non-adjacent levels are redundant for tree search, but they were not avoided previously. We propose a new acceleration strategy that avoids such redundant paths. In the second contribution, we show that the existing branch pruning technique also deteriorates quickly with the problem dimension. We then propose a new branch pruning technique that is less dimension-sensitive to address this issue. Experiments show that both new techniques can significantly accelerate A* tree search, making it reasonably efficient on inputs that were previously out of reach.

Figures

Figures reproduced from arXiv: 1908.02021 by the authors.

**Figure 1.** (a–c) Path between non-adjacent bases (B → B0 ). B 0 can be generated from both B and Broot, but it is not adjacent to B since l(B 0 ) = l(B). Note that Line 10 in Algorithm 1 cannot avoid this non-adjacent path since V(B 0 ) ∪ {s2} = {s1, s2} 6= V(B 0 ) = {s1}. Panel (d) shows the relationship between the three bases during tree search. In the proposed Non-Adjacent Path Avoidance (NAPA) strategy, the path drawn in … view at source ↗

**Figure 2.** (a) In TOD, on current node B, if s2 is identified as the true outlier, then the shortest path towards a feasible basis B ∗ must pass through s2 (path rendered in red). All the the other |B| − 1 branches (leading from s1 and s3 in this example) can be skipped. (b) In DIBP, instead of attempting to identify a single true outlier, a group SB that contains at least one true outlier (SB = {s1, s2} in this example) is id… view at source ↗

**Figure 3.** Effectiveness of TOD as a function of d. All problem instances are generated randomly and each solid curve contains data with true outlier rates h ∗(B) C(B) from 0 to 90%. Note that (15) is true for a d when the solid curve for the d is below the dashed line. 2 3 4 5 6 7 50 100 150 aaa aaa aaa aaaaaaaaaaaaaaaaaaaaaa aaa [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗

Figures from the paper (2 more)

**Figure 4.** Figure 4: Effectiveness of DIBP when d = 8. |C(B)| = 200. hins(B|SB) increases stably along with |SB| and is effective even when the true outlier rate is 90%. Though only the 50% case is shown, changing the outlier rate in practice merely affects the values of hins(B|SB) as long…

**Figure 6.** Figure 6: (Top) Fundamental matrix estimation result [PITH_FULL_IMAGE:figures/full_fig_p008_6.png]

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Reference graph

Works this paper leans on

28 extracted references · 27 canonical work pages

[6]

Efﬁcient globally optimal consensus maximisation with tree search

Tat-Jun Chin, Pulak Purkait, Anders Eriksson, and David Suter. Efﬁcient globally optimal consensus maximisation with tree search. IEEE Transactions on Pattern Analysis and Machine Intelligence (TPAMI), 39(4):758–772, 2017

work page 2017
[1]

Optimal point placement for mesh smoothing

Nina Amenta, Marshall Bern, and David Eppstein. Optimal point placement for mesh smoothing. Journal of Algorithms, 30(2):302–322, 1999

work page 1999
[2]

De- terministic consensus maximization with biconvex program- ming

Zhipeng Cai, Tat-Jun Chin, Huu Le, and David Suter. De- terministic consensus maximization with biconvex program- ming. In European Conference on Computer Vision (ECCV), 2018

work page 2018
[3]

E. W. Cheney. Introduction to Approximation Theory . McGraw-Hill, 1966

work page 1966
[4]

Robust ﬁtting in computer vision: Easy or hard? In European Con- ference on Computer Vision (ECCV), 2018

Tat-Jun Chin, Zhipeng Cai, and Frank Neumann. Robust ﬁtting in computer vision: Easy or hard? In European Con- ference on Computer Vision (ECCV), 2018

work page 2018
[5]

Efﬁcient globally optimal consensus maximisation with tree search

Tat-Jun Chin, Pulak Purkait, Anders Eriksson, and David Suter. Efﬁcient globally optimal consensus maximisation with tree search. In Computer Vision and Pattern Recognition (CVPR), 2015

work page 2015
[7]

Matching with prosac- progressive sample consensus

Ondrej Chum and Jiri Matas. Matching with prosac- progressive sample consensus. In Computer Vision and Pat- tern Recognition (CVPR), 2005

work page 2005
[8]

Locally optimized RANSAC

Ondˇrej Chum, Jiˇr´ı Matas, and Josef Kittler. Locally optimized RANSAC. In Joint Pattern Recognition Symposium, 2003

work page 2003

Show all 28 references

[9]

Robust ﬁtting for multiple view geometry

Olof Enqvist, Erik Ask, Fredrik Kahl, and Kalle ˚Astr¨om. Robust ﬁtting for multiple view geometry. In European Con- ference on Computer Vision (ECCV), 2012

2012
[10]

Quasiconvex programming

David Eppstein. Quasiconvex programming. Combinatorial and Computational Geometry, 52(3):287–331, 2005

2005
[11]

Fischler and Robert C

Martin A. Fischler and Robert C. Bolles. Random sample consensus: a paradigm for model ﬁtting with applications to image analysis and automated cartography. Communications of the ACM, 24(6):381–395, 1981

1981
[12]

Are we ready for autonomous driving? the kitti vision benchmark suite

Andreas Geiger, Philip Lenz, and Raquel Urtasun. Are we ready for autonomous driving? the kitti vision benchmark suite. In Computer Vision and Pattern Recognition (CVPR), 2012

2012
[13]

Multiple View Ge- ometry in Computer Vision

Richard Hartley and Andrew Zisserman. Multiple View Ge- ometry in Computer Vision . Cambridge University Press, 2003

2003
[14]

An exact penalty method for locally convergent maximum consensus

Huu Le, Tat-Jun Chin, and David Suter. An exact penalty method for locally convergent maximum consensus. In Com- puter Vision and Pattern Recognition (CVPR), 2017

2017
[15]

A practical algorithm for L∞ triangulation with outliers

Hongdong Li. A practical algorithm for L∞ triangulation with outliers. In Computer Vision and Pattern Recognition (CVPR), 2007

2007
[16]

Consensus set maximization with guaranteed global optimality for robust geometry estimation

Hongdong Li. Consensus set maximization with guaranteed global optimality for robust geometry estimation. In Interna- tional Conference on Computer Vision (ICCV), 2009

2009
[17]

Object recognition from local scale-invariant features

David G Lowe. Object recognition from local scale-invariant features. In International Conference on Computer Vision (ICCV), 1999

1999
[18]

Matouˇsek

Jiˇr´ı. Matouˇsek. On geometric optimization with few vio- lated constraints. Discrete and Computational Geometry , 14(4):365–384, 1995

1995
[19]

Numerical Optimization

Jorge Nocedal and Stephen Wright. Numerical Optimization. Springer Science & Business Media, 2006

2006
[20]

A polynomial- time bound for matching and registration with outliers

Carl Olsson, Olof Enqvist, and Fredrik Kahl. A polynomial- time bound for matching and registration with outliers. In Computer Vision and Pattern Recognition (CVPR), 2008

2008
[21]

Efﬁcient optimization for L∞-problems using pseudoconvexity

Carl Olsson, Anders P Eriksson, and Fredrik Kahl. Efﬁcient optimization for L∞-problems using pseudoconvexity. In International Conference on Computer Vision (ICCV), 2007

2007
[22]

Guaranteed outlier removal for rotation search

Alvaro Parra Bustos and Tat-Jun Chin. Guaranteed outlier removal for rotation search. In International Conference on Computer Vision (ICCV), 2015

2015
[23]

Maxi- mum consensus parameter estimation by reweighted L1 meth- ods

Pulak Purkait, Christopher Zach, and Anders Eriksson. Maxi- mum consensus parameter estimation by reweighted L1 meth- ods. In Energy Minimization Methods in Computer Vision and Pattern Recognition (EMMCVPR), 2017

2017
[24]

USAC: a universal framework for random sample consensus

Rahul Raguram, Ondrej Chum, Marc Pollefeys, Jiri Matas, and Jan-Michael Frahm. USAC: a universal framework for random sample consensus. IEEE Transactions on Pattern Analysis and Machine Intelligence (TPAMI) , 35(8):2022– 2038, 2013

2022
[25]

A combinatorial bound for lin- ear programming and related problems

Micha Sharir and Emo Welzl. A combinatorial bound for lin- ear programming and related problems. InAnnual Symposium on Theoretical Aspects of Computer Science, 1992

1992
[26]

Guided-MLESAC: Faster image transform estimation by using matching priors

Ben J Tordoff and David W Murray. Guided-MLESAC: Faster image transform estimation by using matching priors. IEEE Transactions on Pattern Analysis and Machine Intelligence (TPAMI), 27(10):1523–1535, 2005

2005
[27]

VLFeat: An open and portable library of computer vision algorithms

Andrea Vedaldi and Brian Fulkerson. VLFeat: An open and portable library of computer vision algorithms. In ACM International Conference on Multimedia, 2010

2010
[28]

Deterministically maximizing feasible subsystems for robust model ﬁtting with unit norm constraints

Yinqiang Zheng, Shigeki Sugimoto, and Masatoshi Okutomi. Deterministically maximizing feasible subsystems for robust model ﬁtting with unit norm constraints. In Computer Vision and Pattern Recognition (CVPR), 2011

2011

Pith tools

Reviewed August 14, 2026 · model on record in the stance chip above.

[1] [6]

Efﬁcient globally optimal consensus maximisation with tree search

Tat-Jun Chin, Pulak Purkait, Anders Eriksson, and David Suter. Efﬁcient globally optimal consensus maximisation with tree search. IEEE Transactions on Pattern Analysis and Machine Intelligence (TPAMI), 39(4):758–772, 2017

work page 2017

[2] [1]

Optimal point placement for mesh smoothing

Nina Amenta, Marshall Bern, and David Eppstein. Optimal point placement for mesh smoothing. Journal of Algorithms, 30(2):302–322, 1999

work page 1999

[3] [2]

De- terministic consensus maximization with biconvex program- ming

Zhipeng Cai, Tat-Jun Chin, Huu Le, and David Suter. De- terministic consensus maximization with biconvex program- ming. In European Conference on Computer Vision (ECCV), 2018

work page 2018

[4] [3]

E. W. Cheney. Introduction to Approximation Theory . McGraw-Hill, 1966

work page 1966

[5] [4]

Robust ﬁtting in computer vision: Easy or hard? In European Con- ference on Computer Vision (ECCV), 2018

Tat-Jun Chin, Zhipeng Cai, and Frank Neumann. Robust ﬁtting in computer vision: Easy or hard? In European Con- ference on Computer Vision (ECCV), 2018

work page 2018

[6] [5]

Efﬁcient globally optimal consensus maximisation with tree search

Tat-Jun Chin, Pulak Purkait, Anders Eriksson, and David Suter. Efﬁcient globally optimal consensus maximisation with tree search. In Computer Vision and Pattern Recognition (CVPR), 2015

work page 2015

[7] [7]

Matching with prosac- progressive sample consensus

Ondrej Chum and Jiri Matas. Matching with prosac- progressive sample consensus. In Computer Vision and Pat- tern Recognition (CVPR), 2005

work page 2005

[8] [8]

Locally optimized RANSAC

Ondˇrej Chum, Jiˇr´ı Matas, and Josef Kittler. Locally optimized RANSAC. In Joint Pattern Recognition Symposium, 2003

work page 2003