Structure-From-Motion in Spherical Video Using the von Mises-Fisher Distribution

Guan, Hao; Smith, William A. P.

doi:10.1109/tip.2016.2621662

Cited by 37 publications

(24 citation statements)

References 31 publications

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“…This is perhaps most easily seen when the data consist of measures of directions in three-dimensional space, such as the directions of radiation beams used for treatment (Bangert, Hennig, & Oelfke, 2010), directions from the earth to stars (Mardia & Jupp, 2009), locating emergency transmitters (Guttorp & Lockhart, 1988), microphone beamforming (Anderson, Teal, & Poletti, 2015), and modeling structure from spherical cameras (Guan & Smith, 2017). One of the most frequently used directional distributions is the von Mises-Fisher distribution (vMF) (Fisher, 1953;Mardia & El-Atoum, 1976).…”

Section: Introductionmentioning

confidence: 99%

Infinite von Mises–Fisher Mixture Modeling of Whole Brain fMRI Data

et al. 2017

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Cluster analysis of functional magnetic resonance imaging (fMRI) data is often performed using gaussian mixture models, but when the time series are standardized such that the data reside on a hypersphere, this modeling assumption is questionable. The consequences of ignoring the underlying spherical manifold are rarely analyzed, in part due to the computational challenges imposed by directional statistics. In this letter, we discuss a Bayesian von Mises-Fisher (vMF) mixture model for data on the unit hypersphere and present an efficient inference procedure based on collapsed Markov chain Monte Carlo sampling. Comparing the vMF and gaussian mixture models on synthetic data, we demonstrate that the vMF model has a slight advantage inferring the true underlying clustering when compared to gaussian-based models on data generated from both a mixture of vMFs and a mixture of gaussians subsequently normalized. Thus, when performing model selection, the two models are not in agreement. Analyzing multisubject whole brain resting-state fMRI data from healthy adult subjects, we find that the vMF mixture model is considerably more reliable than the gaussian mixture model when comparing solutions across models trained on different groups of subjects, and again we find that the two models disagree on the optimal number of components. The analysis indicates that the fMRI data support more than a thousand clusters, and we confirm this is not a result of overfitting by demonstrating better prediction on data from held-out subjects. Our results highlight the utility of using directional statistics to model standardized fMRI data and demonstrate that whole brain segmentation of fMRI data requires a very large number of functional units in order to adequately account for the discernible statistical patterns in the data.

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Section: Introductionmentioning

confidence: 99%

Infinite von Mises–Fisher Mixture Modeling of Whole Brain fMRI Data

et al. 2017

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“…Another possible limitation is the need of video sequences for estimating the 3D geometry. The methods from [1], [8], [28], [29] use traditional approaches -8-PA and direct linear transform (DLT) [15] -for initial pose and 3D geometry estimation based on sparse keypoint matching. After linearly extracting the extrinsic parameters of the cameras -using either the 8-PA or the "spherical n-point problem" (SnP) [29] it is common to apply a non-linear refinement technique to the pose estimates [1], [28], [29].…”

Section: Related Workmentioning

confidence: 99%

Dense 3D Indoor Scene Reconstruction from Spherical Images

Silveira¹,

Jung

2020

Anais Estendidos Da Conference on Graphics, Patterns and Images (SIBRAPI Estendido 2020)

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Techniques for 3D reconstruction of scenes based on images are popular and support a number of secondary applications. Traditional approaches require several captures for covering whole environments due to the narrow field of view (FoV) of the pinhole-based/perspective cameras. This paper summarizes the main contributions of the homonym Ph.D. Thesis, which addresses the 3D scene reconstruction problem by considering omnidirectional (spherical or 360◦ ) cameras that present a 360◦ × 180◦ FoV. Although spherical imagery have the benefit of the full-FoV, they are also challenging due to the inherent distortions involved in the capture and representation of such images, which might compromise the use of many wellestablished algorithms for image processing and computer vision. The referred Ph.D. Thesis introduces novel methodologies for estimating dense depth maps from two or more uncalibrated and temporally unordered 360◦ images. It also presents a framework for inferring depth from a single spherical image. We validate our approaches using both synthetic data and computer-generated imagery, showing competitive results concerning other state-ofthe-art methods.

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“…Several distributions exist for random unit vectors and some are presented in this section. Applications of such distributions include RGB-D image segmentation [5] and structure from motion in 360 video [18] amongst others [1], [2], [3].…”

Section: B Directional Datamentioning

confidence: 99%

Shape registration with directional data

Grogan

Dahyot

2018

Pattern Recognition

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We propose several cost functions for registration of shapes encoded with Euclidean and/or non-Euclidean information (unit vectors). Our framework is assessed for estimation of both rigid and non-rigid transformations between the target and model shapes corresponding to 2D contours and 3D surfaces. The experimental results obtained confirm that using the combination of a point's position and unit normal vector in a cost function can enhance the registration results compared to state of the art methods.

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Structure-From-Motion in Spherical Video Using the von Mises-Fisher Distribution

Cited by 37 publications

References 31 publications

Infinite von Mises–Fisher Mixture Modeling of Whole Brain fMRI Data

Infinite von Mises–Fisher Mixture Modeling of Whole Brain fMRI Data

Dense 3D Indoor Scene Reconstruction from Spherical Images

Shape registration with directional data

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