Removal of translation bias when using subspace methods

MacLean, W. James

doi:10.1109/iccv.1999.790297

Cited by 24 publications

(30 citation statements)

References 15 publications

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“…It can be viewed as one of advantageous effects of data normalization. The establishment of the property parallels similar findings related to other methods [10,14,18].…”

Section: Extended Statistical Modelsupporting

confidence: 73%

A Consistency Result for the Normalized Eight-Point Algorithm

Chojnacki¹,

Brooks²

2007

14th International Conference on Image Analysis and Processing (ICIAP 2007)

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A recently proposed argument to explain the improved performance of the eight-point algorithm that results from using normalized data [IEEE Trans. Pattern Anal. Mach. Intell., 25(9):1172-1177, 2003] relies upon adoption of a certain model for statistical data distribution. Under this model, the cost function that underlies the algorithm operating on the normalized data is statistically more advantageous than the cost function that underpins the algorithm using unnormalized data. Here we extend this explanation by introducing a more refined, structured model for data distribution. Under the extended model, the normalized eight-point algorithm turns out to be approximately consistent in a statistical sense. The proposed extension provides a link between the existing statistical rationalization of the normalized eight-point algorithm and the approach of Mühlich and Mester for enhancing total least squares estimation methods via equilibration. Our contribution forms part of a wider effort to rationalize and interrelate foundational methods in vision parameter estimation.

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“…It can be viewed as one of advantageous effects of data normalization. The establishment of the property parallels similar findings related to other methods [10,14,18].…”

Section: Extended Statistical Modelsupporting

confidence: 73%

A Consistency Result for the Normalized Eight-Point Algorithm

Chojnacki¹,

Brooks²

2007

14th International Conference on Image Analysis and Processing (ICIAP 2007)

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“…Resorting to some approximations, we both analytically and experimentally demonstrate that the errors in calibration introduce an additional bias term in motion estimation, which reduces the previously observed translation bias reported in [8]. The overall translation bias distorts the resulting structure proportionally to the distance of the measurements from the optical axis.…”

Section: Introductionmentioning

confidence: 67%

Motion bias and structure distortion induced by calibration errors

Zucchelli¹,

Košecká²

2001

Procedings of the British Machine Vision Conference 2001

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This article provides an account of sensitivity and robustness of structure and motion recovery with respect to the errors in intrinsic parameters of the camera. We demonstrate both analytically and in simulation, the interplay between measurement and calibration errors and their effect on motion and structure estimates. In particular we show that the calibration errors introduce an additional bias towards the optical axis, which has opposite sign to the bias typically observed by egomotion algorithms. The overall bias causes a distortion of the resulting 3D structure, which we express in a parametric form. The analysis and experiments are carried out in the differential setting for motion and structure estimation from image velocities. While the analytical explanations are derived in the context of linear techniques for motion estimation, we verify our observations experimentally on a variety of optimal and suboptimal motion and structure estimation algorithms. The obtained results illuminate and explain the performance and sensitivity of the differential structure and motion recovery techniques in the presence of calibration errors.

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“…whose bilinear nature has been noted by various authors (Heeger and Jepson, 1992;Ma et al, 2000;MacLean, 1999;Vieville and Faugeras, 1995).…”

Section: Motion and Flow Representationmentioning

confidence: 87%

Quasi-Parallax for Nearly Parallel Frontal Eyes

Cheong

Gao

2012

Int J Comput Vis

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In this paper, we explore how a visual system equipped with a pair of frontally-placed eyes/cameras can rapidly estimate egomotion and depths for the task of locomotion by exploiting the eye topography. We eschew the traditional approach of motion-stereo integration, as finding stereo correspondence is a computationally expensive operation. Instead, we propose a quasi-parallax scheme by pairing appropriate visual rays together, thus obviating the need for stereo correspondence and yet being able to leverage on the redundant information present in the binocular overlap. Our model covers realistic visual systems where the two eyes might deviate from the strictly frontal-parallel configuration, and yet the results show that the advantages of the parallax-based approach are retained. In particular, it offers better disambiguation of translation and rotation over conventional two-frame structure from motion approaches, despite not having views covering diametrically opposing directions like that of spherical eyes or laterally-placed eyes. The rapid processing that such scheme entails seems to offer a more realizable and useful alternative for depth recovery during locomotion.

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Removal of translation bias when using subspace methods

Cited by 24 publications

References 15 publications

A Consistency Result for the Normalized Eight-Point Algorithm

A Consistency Result for the Normalized Eight-Point Algorithm

Motion bias and structure distortion induced by calibration errors

Quasi-Parallax for Nearly Parallel Frontal Eyes

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