Globally optimal hand-eye calibration

Ruland, Thomas; Pajdla, Tomáš; Krüger, Lars

doi:10.1109/cvpr.2012.6247781

Cited by 27 publications

(14 citation statements)

References 13 publications

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“…While there are globally optimal branchand-bound (BnB) algorithms that can guarantee a solution to point cloud registration up to a desired accuracy [14], these techniques can be extremely slow. Similarly, the global optimum of a hand-eye calibration problem is found in [15] and [16] using BnB, but the runtime is orders of magnitude larger than for convex methods.…”

Section: A Globally Optimal Calibrationmentioning

confidence: 99%

Certifiably Globally Optimal Extrinsic Calibration From Per-Sensor Egomotion

Giamou

Peretroukhin

et al. 2019

IEEE Robot. Autom. Lett.

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We present a certifiably globally optimal algorithm for determining the extrinsic calibration between two sensors that are capable of producing independent egomotion estimates. This problem has been previously solved using a variety of techniques, including local optimization approaches that have no formal global optimality guarantees. We use a quadratic objective function to formulate calibration as a quadratically constrained quadratic program (QCQP). By leveraging recent advances in the optimization of QCQPs, we are able to use existing semidefinite program (SDP) solvers to obtain a certifiably global optimum via the Lagrangian dual problem. Our problem formulation can be globally optimized by existing general-purpose solvers in less than a second, regardless of the number of measurements available and the noise level. This enables a variety of robotic platforms to rapidly and robustly compute and certify a globally optimal set of calibration parameters without a prior estimate or operator intervention. We compare the performance of our approach with a local solver on extensive simulations and multiple real datasets. Finally, we present necessary observability conditions that connect our approach to recent theoretical results and analytically support the empirical performance of our system. Global Optimum minimize R,t JR + Jt, subject to R 2 SO(3) < l a t e x i t s h a 1 _ b a s e 6 4 = " j v M n N v m u H A y R x q A 6 N L e F c X m 9 j 2 c = " > A A A C r H i c b V F d b 9 M w F H X C x 7 b w s T I e e b G o Q E O s U Q L V y t 4 m 8 Y K Q E A P W b l J d V Y 7 j r G a O k 9 n X a C X y j + F n 8 T / 4 A b h p x D b g S J a O z 7 3 n 2 j o 3 q 6 U w k C Q / g / D W 7 T t 3 N z a 3 o n v 3 H z z c 7 j 3 a m Z j K a s b H r J K V P s 2 o 4 V I o P g Y B k p / W m t M y k / w k O 3 + 7 q p 9 8 4 9 q I S h 3 D s u a z k p 4 pz 7 3 n 2 j o 3 q 6 U w k C Q / g / D W 7 T t 3 N z a 3 o n v 3 H z z c 7 j 3 a m Z j K a s b H r J K V P s 2 o 4 V I o P g Y B k p / W m t M y k / w k O 3 + 7 q p 9 8 4 9 q I S h 3 D s u a z k p 4 p U Q h G w U v z 3 o 8 t j D G x K v c 9 H B r y g Y I W l 8 1 n t 0 c m n E G l G 3 C u I c A v o S m F E q X 4 z p 2 L v O s 5 J h e W 5 v j 9 / J r L 4 Z e t c O X d w 4 R E 7 S P t D G O z r 7 6 G o b o x 5 G o C J k J 1 v V 8 + u t 3 X L + a 9 f h I n L f C / J O 1 I H 3 U 4 m v d + k b x i t u Q K m K T G T N O k h l l D N Q g m u Y u I N b y m 7 J y e 8 a m n i p b c z J o 2 S o e f e S X H R a X 9 U Y B b 9 b q j o a U x y z L z n S W F h f m 7 t h L / V 5 t a K N 7 M G q F q C 1 y x 9 U O F l T 4 I v N o L z o X 2 u c i l J 5 R p 4 f + K 2 Y J q y s B v J i K t s b m w w i 9 z I K n P Z 2 A W l Q Z m w c T + 5 t q U Q L V y t 4 m 8 Y K Q E A P W b l J d V Y 7 j r G a O k 9 n X a C X y j + F n 8 T / 4 A b h p x D b g S J a O z 7 3 n 2 j o 3 q 6 U w k C Q / g / D W 7 T t 3 N z a 3 o n v 3 H z z c 7 j 3 a m Z j K a s b H r J K V P s 2 o 4 V I o P g Y B k p / W m t M y k / w k O 3 + 7 q p 9 8 4 9 q I S h 3 D s u a z k p 4 p U Q h G w U v z 3 o 8 t j D G x K v c 9 H B r y g Y I W l 8 1 n t 0 ...

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Section: A Globally Optimal Calibrationmentioning

confidence: 99%

Certifiably Globally Optimal Extrinsic Calibration From Per-Sensor Egomotion

Giamou

Peretroukhin

et al. 2019

IEEE Robot. Autom. Lett.

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“…Our method is related to the idea of SO(3) space search, as proposed in [15,16] and extended in (e.g. [30,3]). Most of the existing work along this line are based on the L ∞ -norm minimization.…”

Section: Related Workmentioning

confidence: 99%

Go-ICP: Solving 3D Registration Efficiently and Globally Optimally

Yang

Jia

2013

2013 IEEE International Conference on Computer Vision

386

282

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Registration is a fundamental task in computer vision. The Iterative Closest Point (ICP) algorithm is one of the widely-used methods for solving the registration problem. Based on local iteration, ICP is however well-known to suffer from local minima. Its performance critically relies on the quality of initialization, and only local optimality is guaranteed. This paper provides the very first globally optimal solution to Euclidean registration of two 3D pointsets or two 3D surfaces under the L 2 error. Our method is built upon ICP, but combines it with a branch-and-bound (BnB) scheme which searches the 3D motion space SE(3) efficiently. By exploiting the special structure of the underlying geometry, we derive novel upper and lower bounds for the ICP error function. The integration of local ICP and global BnB enables the new method to run efficiently in practice, and its optimality is exactly guaranteed. We also discuss extensions, addressing the issue of outlier robustness.

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“…Unlike RANSAC, BnB is guaranteed to find the globally optimal result. The solution of many computer vision problems have benefited from BnB rotation search as a subroutine [5,7,15,9,13]; such as essential matrix and camera pose estimation, hand-eye calibration, panoramic image stitching, and point cloud registration.…”

Section: Introductionmentioning

confidence: 99%

Guaranteed Outlier Removal for Rotation Search

Parra

Chin

2015

2015 IEEE International Conference on Computer Vision (ICCV)

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Rotation search has become a core routine for solving many computer vision problems. The aim is to rotationally align two input point sets with correspondences. Recently, there is significant interest in developing globally optimal rotation search algorithms. A notable weakness of global algorithms, however, is their relatively high computational cost, especially on large problem sizes and data with a high proportion of outliers. In this paper, we propose a novel outlier removal technique for rotation search. Our method guarantees that any correspondence it discards as an outlier does not exist in the inlier set of the globally optimal rotation for the original data. Based on simple geometric operations, our algorithm is deterministic and fast. Used as a preprocessor to prune a large portion of the outliers from the input data, our method enables substantial speed-up of rotation search algorithms without compromising global optimality. We demonstrate the efficacy of our method in various synthetic and real data experiments 1 .

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Globally optimal hand-eye calibration

Cited by 27 publications

References 13 publications

Certifiably Globally Optimal Extrinsic Calibration From Per-Sensor Egomotion

Certifiably Globally Optimal Extrinsic Calibration From Per-Sensor Egomotion

Go-ICP: Solving 3D Registration Efficiently and Globally Optimally

Guaranteed Outlier Removal for Rotation Search

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