Abstract：A unified mathematical model and an algorithm are proposed to solve the problems of the estimation of illumination and reflectance images of a natural image and the segmentation and bias field estimation of a magnetic resonance image(MRI). The proposed model only requires a basic assumption that the observed image can be approximated by the product of two intrinsic images with different properties. One of the two intrinsic images is a smooth image, S-image, and the other is a piece-wise approximately constant image, L-image. To fully exploit the properties of the intrinsic images, a scalable local analysis and integration(SLAI) approach is proposed for the problem of intrinsic image estimation. Due to the smoothness of the S-image, a low order Taylor expansion or a linear combination of general smooth basis functions is utilized to locally approximate the S-image. The obtained local smooth approximation of the S-image can be extended to a smooth image on the entire region of interest(ROI) using partition of unity subordinate to a cover of ROI. Meanwhile, the segmentation result and the estimation of the L-image are obtained. The proposed method is based on a weaker assumption than the methods in the literature, and therefore it is applicable to more images. The proposed method produces satisfactory results on MR images and natural images.
石雪, 徐海平, 李纯明. 本征图像分解的可变尺度局部分析与集成方法[J]. 模式识别与人工智能, 2021, 34(4): 322-332.
SHI Xue, XU Haiping, LI Chunming. A Scalable Local Analysis and Integration Approach to Intrinsic Image Decomposition. , 2021, 34(4): 322-332.
[1] BARROW H, TENENBAUM J M. Recovering Intrinsic Scene Cha-racteristics from Images // HANSON A, RISEMAN E, eds. Computer Vision Systems. New York, USA: Academic Press, 1978: 3-26. [2] TAPPEN M F, ADELSON E H, FREEMAN W T. Estimating Intrinsic Component Images Using Non-linear Regression // Proc of the IEEE Computer Society Conference on Computer Vision and Pa-ttern Recognition. Washington, USA: IEEE, 2006, II: 1992-1999. [3] BARRON J T, MALIK J. Shape, Illumination, and Reflectance from Shading. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2015, 37(8): 1670-1687. [4] BELL S, BALA K, SNAVELY N. Intrinsic Images in the Wild. ACM Transactions on Graphic, 2014, 33(4). DOI: 10.1145/2601097.2601206. [5] WEISS Y. Deriving Intrinsic Images from Image Sequences // Proc of the 8th IEEE International Conference on Computer Vision. Washing-ton, USA: IEEE, 2001, II: 68-75. [6] KIMMEL R, ELAD M, SHAKED D, et al. A Variational Framework for Retinex. International Journal of Computer Vision, 2003, 52(1): 7- 23. [7] HORN B K P. Determining Lightness from an Image. Computer Gra-phics and Image Processing, 1974, 3: 277-299. [8] LAND E H, MCCANN J J. Lightness and Retinex Theory. Journal of the Optical Society of America, 1971, 61(1): 1-11. [9] BLAKE A. Boundary Conditions for Lightness Computation in Mondrian World. Computer Vision, Graphics and Image Processing, 1985, 32(3): 314-327. [10] SHEN L, TAN P, LIN S. Intrinsic Image Decomposition with Non-local Texture Cues // Proc of the IEEE Conference on Computer Vision and Pattern Recognition. Washington, USA: IEEE, 2008. DOI: 10.1109/CVPR.2008.4587660. [11] ZHAO Q, TAN P, DAI Q, et al. A Closed-Form Solution to Re-tinex with Nonlocal Texture Constraints. IEEE Transactions on Pa-ttern Analysis and Machine Intelligence, 2012, 34(7): 1437-1444. [12] BOUSSEAU A, PARIS S, DURAND F. User-Assisted Intrinsic Images. ACM Transactions on Graphics, 2009, 28(5). DOI: 10.1145/1618452.1618476. [13] BARRON J T, MALIK J. Shape, Albedo, and Illumination from a Single Image of an Unknown Object // Proc of the IEEE Confe-rence on Computer Vision and Pattern Recognition. Washington, USA: IEEE, 2012: 334-341. [14] CHEN Q F, KOLTUN V. A Simple Model for Intrinsic Image Decomposition with Depth Cues // Proc of the IEEE International Conference on Computer Vision. Washington, USA: IEEE, 2013: 241-248. [15] SHEN L, YEO C H. Intrinsic Images Decomposition Using a Local and Global Sparse Representation of Reflectance // Proc of the IEEE Conference on Computer Vision and Pattern Recognition. Washington, USA: IEEE, 2011: 697-704. [16] LI C M, LI F, KAO C Y, et al. Image Segmentation with Simultaneous Illumination and Reflectance Estimation: An Energy Minimization Approach // Proc of the 12th IEEE International Conference on Computer Vision. Washington, USA: IEEE, 2009: 702-708. [17] YANG Y Y, JIA W J, WU B Y. Simultaneous Segmentation and Correction Model for Color Medical and Natural Images with Intensity Inhomogeneity. The Visual Computer, 2020, 36(4): 717-731. [18] BASLAMISLI A S, GROENESTEGE T T, DAS P, et al. Joint Learning of Intrinsic Images and Semantic Segmentation // Proc of the European Conference on Computer Vision. Berlin, Germany: Springer, 2018: 289-305. [19] FAN Q N, YANG J L, HUA G, et al. Revisiting Deep Intrinsic Image Decompositions // Proc of the IEEE/CVF Conference on Com-puter Vision and Pattern Recognition. Washington, USA: IEEE, 2018: 8944-8952. [20] TAPPEN M F, FREEMAN W T, ADELSON E H. Recovering Intrinsic Images from a Single Image // Proc of the 15th International Conference on Neural Information Processing Systems. Cambridge, USA: The MIT Press, 2002: 1367-1374. [21] JANNER M, WU J J, DULJARNI T D, et al. Self-supervised Intrinsic Image Decomposition // Proc of the 31st International Conference on Neural Information Processing Systems. Cambridge, USA: The MIT Press, 2017: 5936-5946. [22] CHANG J, CABEZAS R, FISHER III J W. Bayesian Nonparame-tric Intrinsic Image Decomposition // Proc of the European Confe-rence on Computer Vision. Berlin, Germany: Springer, 2014: 704-719. [23] MA W C, CHU H, ZHOU B L, et al. Single Image Intrinsic Decomposition without a Single Intrinsic Image // Proc of the Euro-pean Conference on Computer Vision. Berlin, Germany: Springer, 2018: 211-229. [24] LI C M, XU C Y, ANDERSON A W, et al. MRI Tissue Classification and Bias Field Estimation Based on Coherent Local Intensity Clustering: A Unified Energy Minimization Framework // Proc of the International Conference on Information Processing in Medical Imaging. Berlin, Germany: Springer, 2009: 288-299. [25] LI C M, HUANG R, DING Z H, et al. A Level Set Method for Image Segmentation in the Presence of Intensity Inhomogeneities with Application to MRI. IEEE Transactions on Image Processing, 2011, 20(7): 2007-2016. [26] WANG L, ZHU J B, SHENG M, et al. Simultaneous Segmentation and Bias Field Estimation Using Local Fitted Images. Pattern Re-cognition, 2018, 74: 145-155. [27] CAI Q, LIU H Y, ZHOU S P, et al. An Adaptive-Scale Active Contour Model for Inhomogeneous Image Segmentation and Bias Field Estimation. Pattern Recognition, 2018, 82: 79-93. [28] LI C M, GORE J C, DAVATZIKOS C. Multiplicative Intrinsic Component Optimization(MICO) for MRI Bias Field Estimation and Tissue Segmentation. Magnetic Resonance Imaging, 2014, 32(7): 913-923. [29] YANG Y Y, WANG R F, FENG C. A New Method for Simulta-neous Moderate Bias Correction and Image Segmentation. IET Image Processing, 2019, 13(6): 939-945. [30] WAN F K, SMEDBY Ö, WANG C L. Simultaneous MR Knee Image Segmentation and Bias Field Correction Using Deep Learning and Partial Convolution[C/OL]. [2020-06-12]. https://doi.org/10.1117/12.2512950. [31] ZHANG Y, BRADY M, SMITH S. Segmentation of Brain MR Images through a Hidden Markov Random Field Model and the Expectation-Maximization Algorithm. IEEE Transactions on Medical Imaging, 2001, 20(1): 45-57. [32] WELLS III W M, GRIMSON W E L, KIKINIS R, et al. Adaptive Segmentation of MRI Data. IEEE Transactions on Medical Imaging, 1996, 15(4): 429-442. [33] PHAM D L, PRINCE J L. Adaptive Fuzzy Segmentation of Magnetic Resonance Images. IEEE Transactions on Medical Imaging, 1999, 18(9): 737-752. [34] WARNER F W. Foundations of Differentiable Manifolds and Lie Group. Berlin, Germany: Springer-Verlag, 1983. [35] WENDLAND H. Fast Evaluation of Radial Basis Functions: Me-thods Based on Partition of Unity // CHUI C K, SCHUMAKER L L, STÖCKLER J, eds. Approximation Theory X: Wavelets, Splines, and Applications. Nashville, USA: Vanderbilt University Press, 2002: 473-483. [36] POWELL M J D. Approximation Theory and Methods. Cambridge, UK: Cambridge University Press, 1981. [37] GROSSE R, JOHNSON M K, ADELSON E H, et al. Ground Truth Dataset and Baseline Evaluations for Intrinsic Image Algorithms // Proc of the 12th IEEE International Conference on Computer Vision. Washington, USA: IEEE, 2009: 2335-2342.
2021, Vol. 34 
