On the accuracy of point localisation in a circular camera-array

Although many advances have been made in light-field and camera-array image processing, there is still a lack of thorough analysis of the localisation accuracy of different multi-camera systems. By considering the problem from a frame-quantisation perspective, we are able to quantify the point localisation error of circular camera configurations. Specifically, we obtain closed form expressions bounding the localisation error in terms of the parameters describing the acquisition setup. These theoretical results are independent of the localisation algorithm and thus provide fundamental limits on performance. Furthermore, the new frame-quantisation perspective is general enough to be extended to more complex camera configurations.

[1]  Sundeep Rangan,et al.  Recursive consistent estimation with bounded noise , 2001, IEEE Trans. Inf. Theory.

[2]  Vivek K. Goyal,et al.  Quantized Overcomplete Expansions in IRN: Analysis, Synthesis, and Algorithms , 1998, IEEE Trans. Inf. Theory.

[3]  Andrea Cavallaro,et al.  Multi-Camera Networks: Principles and Applications , 2009 .

[4]  G. Westheimer,et al.  Light distribution in the image formed by the living human eye. , 1962, Journal of the Optical Society of America.

[5]  Martin Vetterli,et al.  Detecting planar surface using a light-field camera with application to distinguishing real scenes from printed photos , 2014, 2014 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP).

[6]  Martin Vetterli,et al.  Reduction of the MSE in R-times oversampled A/D conversion O(1/R) to O(1/R2) , 1994, IEEE Trans. Signal Process..

[7]  Tsuhan Chen,et al.  Spectral analysis for sampling image-based rendering data , 2003, IEEE Trans. Circuits Syst. Video Technol..

[8]  Vladimir Kolmogorov,et al.  Multi-camera Scene Reconstruction via Graph Cuts , 2002, ECCV.

[9]  Minh N. Do,et al.  Ieee Transactions on Image Processing on the Bandwidth of the Plenoptic Function , 2022 .

[10]  Harry Shum,et al.  Plenoptic sampling , 2000, SIGGRAPH.

[11]  Jake K. Aggarwal,et al.  Stochastic Analysis of Stereo Quantization Error , 1990, IEEE Trans. Pattern Anal. Mach. Intell..

[12]  Harit P. Trivedi.  Can multiple views make up for lack of camera registration? , 1988, Image Vis. Comput..

[13]  Martin Vetterli,et al.  Scale-invariant representation of light field images for object recognition and tracking , 2013, Electronic Imaging.

[14]  Hamid R. Rabiee,et al.  A Bayesian Approach to the Data Description Problem , 2012, AAAI.

[15]  Shahin Sirouspour,et al.  Active multi-camera object recognition in presence of occlusion , 2005, 2005 IEEE/RSJ International Conference on Intelligent Robots and Systems.

[16]  Mike Brookes,et al.  On the Spectrum of the Plenoptic Function , 2014, IEEE Transactions on Image Processing.

[17]  Martin Vetterli,et al.  LCAV-31: a dataset for light field object recognition , 2013, Electronic Imaging.

[18]  E. Adelson,et al.  The Plenoptic Function and the Elements of Early Vision , 1991 .

[19]  Antonio Ortega,et al.  Efficient quantization for overcomplete expansions in RN , 2003, IEEE Trans. Inf. Theory.

[20]  S. Pizer,et al.  The Image Processing Handbook , 1994 .

[21]  Karl C. Walli,et al.  Plenoptic camera range finding , 2013, 2013 IEEE Applied Imagery Pattern Recognition Workshop (AIPR).

[22]  Zhan Yu,et al.  Lytro camera technology: theory, algorithms, performance analysis , 2013, Electronic Imaging.

[23]  Marc Levoy,et al.  High performance imaging using large camera arrays , 2005, ACM Trans. Graph..

[24]  Antonio Ortega,et al.  EFFICIENT QUANTIZATION FOR OVERCOMPLETE EXPANSIONS IN , 2000 .

[25]  D BlosteinSteven,et al.  Error Analysis in Stereo Determination of 3-D Point Positions , 1987 .

[26]  Antonio Ortega,et al.  Efficient quantization for overcomplete expansions in R/sup N/ , 2001, 2001 IEEE International Conference on Acoustics, Speech, and Signal Processing. Proceedings (Cat. No.01CH37221).

[27]  Ajay Divakaran,et al.  Multi-camera calibration, object tracking and query generation , 2003, 2003 International Conference on Multimedia and Expo. ICME '03. Proceedings (Cat. No.03TH8698).

[28]  Zoran Cvetkovic.  Source coding with quantized redundant expansions: accuracy and reconstruction , 1999, Proceedings DCC'99 Data Compression Conference (Cat. No. PR00096).

[29]  Steven D. Blostein,et al.  Error Analysis in Stereo Determination of 3-D Point Positions , 1987, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[30]  Shree K. Nayar,et al.  PiCam , 2013, ACM Trans. Graph..

[31]  G. Healey,et al.  Face recognition in hyperspectral images - Pattern Analysis and Machine Intelligence, IEEE Transactions on , 2001 .

[32]  J. Y. S. Luh,et al.  A Three-Dimensional Vision by Off-Shelf System with Multi-Cameras , 1985, IEEE Transactions on Pattern Analysis and Machine Intelligence.