2018 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works
All documents in ORBi are protected by a user license.
image edge detection; range image; probability density function; surface; probabilistic framework; time-of-flight camera; kinect
Abstract :
[en] We develop a powerful probabilistic framework for the local characterization of surfaces and edges in range images, which is useful in many applications of computer vision, such as filtering, edge detection, feature extraction, and classification. We use the geometrical nature of the data to derive an analytic expression for the joint probability density function (pdf) for the random variables used to model the ranges of a set of pixels in a local neighborhood of an image. We decompose this joint pdf by considering independently the cases where two real world points corresponding to two neighboring pixels are locally on the same real world surface or not. In particular, we show that this joint pdf is linked to the Voigt pdf and not to the Gaussian pdf as it is assumed in some applications. We apply our framework to edge detection and develop a locally adaptive algorithm that is based on a probabilistic decision rule. We show in an objective evaluation that this new edge detector performs better than prior art edge detectors. This proves the benefits of the probabilistic characterization of the local neighborhood as a tool to improve applications that involve range images.
Research center :
Montefiore Institute - Montefiore Institute of Electrical Engineering and Computer Science - ULiège Telim
Disciplines :
Computer science
Author, co-author :
Lejeune, Antoine ; Université de Liège > Dép. d'électric., électron. et informat. (Inst.Montefiore) > Exploitation des signaux et images
Verly, Jacques ; Université de Liège > Dép. d'électric., électron. et informat. (Inst.Montefiore) > Exploitation des signaux et images
Van Droogenbroeck, Marc ; Université de Liège > Dép. d'électric., électron. et informat. (Inst.Montefiore) > Télécommunications
Language :
English
Title :
Probabilistic Framework for the Characterization of Surfaces and Edges in Range Images, with Application to Edge Detection
Publication date :
September 2018
Journal title :
IEEE Transactions on Pattern Analysis and Machine Intelligence
M. Abramowitz and I. Stegun, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. New York, NY. USA: Dover Publications, 1964.
M. Adams, "Amplitude modulated optical range data analysis in mobile robotics," in Proc. IEEE Int. Conf. Robot. Autom., 1993, vol. 2, pp. 8-13.
P. Arbelaez, M. Maire, C. Fowlkes, and J. Malik, "Contour detection and hierarchical image segmentation," IEEE Trans. Pattern Anal. Mach. Intell., vol. 33, no. 5, pp. 898-916, May 2011.
F. Blais, "Review of 20 years of range sensor development," J. Electron. Imaging, vol. 13, no. 1, pp. 231-243, Jan. 2004.
P. Boulanger, F. Blais, and P. Cohen, "Detection of depth and orientation discontinuities in range images using mathematical morphology," in Proc. IEEE Int. Conf. Comput. Vis. Pattern Recognit., Jun. 1990, vol. 1, pp. 729-732.
A. Buch, J. Jessen, D. Kraft, T. Savarimuthu, and N. Kruger, "Extended 3D line segments from RGB-D data for pose estimation," in Proc. Scandinavian Conf. Image Anal., Jun. 2013, vol. 7944, pp. 54-65.
J. Canny, "A computational approach to edge detection," IEEE Trans. Pattern Anal.Mach. Intell., vol. 8, no. 6, pp. 679-698, Nov. 1986.
S. Coleman, B. Scotney, and S. Suganthan, "Edge detecting for range data using Laplacian operators," IEEE Trans. Image Process., vol. 19, no. 11, pp. 2814-2824, Nov. 2010.
P. Dollar and L. Zitnick, "Fast edge detection using structured forests," IEEE Trans. Pattern Anal. Mach. Intell., vol. 37, no. 8, pp. 1558-1570, Aug. 2015.
B. Freedman, A. Shpunt, M. Machline, and Y. Arieli, "Depth mapping using projected patterns," U.S. Patent 20 100 118 123, 2010.
B. Gunsel, A. Jain, and E. Panayirci, "Reconstruction and boundary detection of range and intensity images using multiscale MRF representations," Comput. Vis. Image Understanding, vol. 63, no. 2, pp. 353-366, Mar. 1996.
S. Gupta, P. Arbelaez, and J. Malik, "Perceptual organization and recognition of indoor scenes from RGB-D images," in Proc. IEEE Int. Conf. Comput. Vis. Pattern Recognit., Jun. 2013, pp. 564-571.
S. Gupta, R. Girshick, P. Arbelaez, and J. Malik, "Learning rich features from RGB-D images for object detection and segmentation," in Proc. Eur. Conf. Comput. Vis., Sep. 2014, pp. 345-360.
R. Hartley and A. Zisserman, Multiple View Geometry in Computer Vision. Cambridge, U.K.: Cambridge University Press, 2004.
J. Huang, A. Lee, and D. Mumford, "Statistics of range images," in Proc. IEEE Int. Conf. Comput. Vis. Pattern Recognit., Jun. 2000, vol. 1, pp. 324-331.
T. Ida, M. Ando, and H. Toraya, "Extended pseudo-Voigt function for approximating the Voigt profile," J. Appl. Crystallography, vol. 33, no. 6, pp. 1311-1316, Dec. 2000.
X. Jiang and H. Bunke, "Edge detection in range images based on scan line approximation," Comp. Vis. Image Understanding, vol. 73, no. 2, pp. 183-199, Feb. 1999.
T. Kanade, A. Yoshida, K. Oda, H. Kano, and M. Tanaka, "A stereo machine for video-rate dense depth mapping and its new applications," in Proc. IEEE Int. Conf. Comput. Vis. Pattern Recognit., Jun. 1996, pp. 196-202.
C. Kerl, M. Souiai, J. Sturm, and D. Cremers, "Towards illumination-invariant 3D reconstruction using ToF RGB-D cameras," in Proc. Int. Conf. 3D Vis., Dec. 2014, vol. 1, pp. 39-46.
K. Khoshelham, "Accuracy analysis of Kinect depth data," Int. Archives Photogrammetry Remote Sens. Spatial Inform. Sci., vol. XXXVIII-5/W12, pp. 133-138, 2011.
S. Konishi, A. Yuille, J. Coughlan, and S. Zhu, "Statistical edge detection: Learning and evaluating edge cues," IEEE Trans. Pattern Anal. Mach. Intell., vol. 25, no. 1, pp. 57-74, Jan. 2003.
R. Krishnapuram and S. Gupta, "Morphological methods for detection and classification of edges in range images," J. Math. Imaging Vis., vol. 2, no. 4, pp. 351-375, Nov. 1992.
R. Lange and P. Seitz, "Solid-state time-of-flight range camera," IEEE J. Quantum Electron., vol. 37, no. 3, pp. 390-397, Mar. 2001.
A. Lee, D. Mumford, and J. Huang, "Occlusion models for natural images: A statistical study of a scale-invariant dead leaves model," Int. J. Comp. Vision, vol. 41, no. 1-2, pp. 35-59, Jan. 2001.
A. Lejeune, S. Pierard, M. Van Droogenbroeck, and J. Verly, "A new jump edge detection method for 3D cameras," in Proc. IEEE Int. Conf. 3D Imaging, Dec. 2011, pp. 1-7.
M. Lindner, I. Schiller, A. Kolb, and R. Koch, "Time-of-Flight sensor calibration for accurate range sensing," Comput. Vis. Image Understanding, vol. 114, no. 12, pp. 1318-1328, Dec. 2010.
F. Mufti and R. Mahony, "Statistical analysis of signal measurement in time-of-flight cameras," ISPRS J. Photogrammetry Remote Sensing., vol. 66, no. 5, pp. 720-731, Sep. 2011.
A. Papoulis, Probability, Random Variables, and Stochastic Processes. New York, NY, USA: McGraw-Hill, 1991.
B. Parvin and G. Medioni, "Adaptive multiscale feature extraction from range data," Comput. Vis. Graph. Image Process., vol. 45, no. 3, pp. 346-356, Mar. 1989.
H. Rapp, M. Frank, F. Hamprecht, and B. Jahne, "A theoretical and experimental investigation of the systematic errors and statistical uncertainties of time-of-flight-cameras," Int. J. Intell. Syst. Technol. Appl., vol. 5, no. 3/4, pp. 402-413, Nov. 2008.
X. Ren and L. Bo, "Discriminatively trained sparse code gradients for contour detection," in Proc. Int. Conf. Advances Neural Inform. Process. Syst., Dec. 2012, pp. 584-592.
H. Schafer, F. Lenzen, and C. Garbe, "Depth and intensity based edge detection in time-of-flight images," in Prof. Int. Conf. 3D Vis., Jun. 2013, pp. 111-118.
J. Shotton, et al., "Real-time human pose recognition in parts from single depth images," in Proc. IEEE Int. Conf. Comput. Vis. Pattern Recognit., Jun. 2011, pp. 1297-1304.
N. Silberman, D. Hoiem, P. Kohli, and R. Fergus, "Indoor segmentation and support inference from RGBD images," in Proc. Eur. Conf. Comput. Vis., Oct. 2012, vol. 7576, pp. 746-760.
B. Steder, R. Rusu, K. Konolige, and W. Burgard, "Point feature extraction on 3D range scans taking into account object boundaries," in Proc. IEEE Int. Conf. Robot. Autom.,May. 2011, pp. 2601-2608.
J. Sturm, N. Engelhard, F. Endres, W. Burgard, and D. Cremers, "A benchmark for the evaluation of RGB-D SLAM systems," in Proc. IEEE/RSJ Int. Conf. Intell. Robots Syst., Oct. 2012, pp. 573-580.
T. Tang, W. Lui, and W. Li, "A lightweight approach to 6-DOF plane-based egomotion estimation using inverse depth," in Proc. Australasian Conf. Robot. Autom., Dec. 2011, pp. 1-10.
S. Xie and Z. Tu, "Holistically-nested edge detection," in Proc. IEEE Int. Conf. Comput. Vis., Dec. 2015, pp. 1395-1403.
C. Ye and G. Hegde, "Robust edge extraction for SwissRanger SR-3000 range images," in Proc. IEEE Int. Conf. Robot. Autom., May 2009, pp. 2437-2442.
