Abstract
This chapter discusses the use of decision forests for the probabilistic estimation of continuous variables. Regression forests are used for the non-linear regression of dependent variables given independent input, where both input and output may be multi-dimensional. As with the other chapters we start with a brief literature survey of linear and non-linear regression techniques. We then describe the regression forest model, and finally we demonstrate its properties with a number of illustrative examples. Exercises are presented in the final section.
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Notes
- 1.
The smoothness of the mean curve is a function of T. In general, the larger the forest size the smoother the mean prediction curve.
References
Bishop CM (2006) Pattern recognition and machine learning. Springer, New York
Bjoerck A (1996) Numerical methods for least squares problems. Society for Industrial and Applied Mathematics (SIAM), Philadelphia
Breiman L (2001) Random forests. Mach Learn 45(1)
Breiman L, Friedman J, Stone CJ, Olshen RA (1984) Classification and regression trees. Chapman and Hall/CRC, London
Cootes TF, Ionita MC, Lindner C, Sauer P (2012) Robust and accurate shape model fitting using random forest regression voting. In: Proc European conf on computer vision (ECCV)
Criminisi A, Shotton J, Robertson D, Konukoglu E (2010) Regression forests for efficient anatomy detection and localization in CT studies. In: MICCAI workshop on medical computer vision: recognition techniques and applications in medical imaging, Beijing. Springer, Berlin
Criminisi A, Shotton J, Konukoglu E (2011) Online tutorial on decision forests. http://research.microsoft.com/projects/decisionforests
Criminisi A, Shotton J, Konukoglu E (2012) Decision forests: a unified framework for classification, regression, density estimation, manifold learning and semi-supervised learning. Found Trends Comput Graph Vis 7(2–3)
Cuingnet R, Prevost R, Lesage D, Cohen L, Mory B, Ardon R (2012) Automatic detection and segmentation of kidneys in 3D CT images using random forests. In: Proc medical image computing and computer assisted intervention (MICCAI)
Dantone M, Gall J, Fanelli G, van Gool L (2012) Real-time facial feature detection using conditional regression forests. In: Proc IEEE conf computer vision and pattern recognition (CVPR)
Fanelli G, Gall J (2011) Real time head pose estimation with random regression forests. In: Proc IEEE conf computer vision and pattern recognition (CVPR)
Fischler MA, Bolles RC (1981) Random sample consensus: a paradigm for model fitting with applications to image analysis and automated cartography. Commun ACM 24
Girshick R, Shotton J, Kohli P, Criminisi A, Fitzgibbon A (2011) Efficient regression of general-activity human poses from depth images. In: Proc IEEE intl conf on computer vision (ICCV)
Glocker B, Feulner J, Criminisi A, Haynor DR, Konukoglu E (2012) Automatic localization and identification of vertebrae in arbitrary field-of-view CT scans. In: Proc medical image computing and computer assisted intervention (MICCAI)
Glocker B, Pauly O, Konukoglu E, Criminisi A (2012) Joint classification-regression forests for spatially structured multi-object segmentation. In: Proc European conf on computer vision (ECCV). Springer, Berlin
Hartley R, Zisserman A (2003) Multiple view geometry in computer vision, 2nd edn. Cambridge University Press, Cambridge
Kelm BM, Mittal S, Zheng Y, Tsymbal A, Bernhardt D, Vega-Higuera F, Zhou KS, Meer P, Comaniciu D (2011) Detection, grading and classification of coronary stenoses in computed tomography angiography. In: Proc medical image computing and computer assisted intervention (MICCAI)
Lampert CH (2008) Kernel methods in computer vision. Found Trends Comput Graph Vis 4(3)
Lindner C, Thiagarajah S, Wilkinson JM, arcOGEN Consortium, Wallis GA, Cootes TF (2012) Accurate fully automatic femur segmentation in pelvic radiographs using regression voting. In: Proc medical image computing and computer assisted intervention (MICCAI)
Montillo A, Ling H (2009) Age regression from faces using random forests. In: Proc intl conf on image processing (ICIP)
Rasmussen CE, Williams C (2006) Gaussian processes for machine learning. MIT Press, Cambridge
Roberts MG, Cootes TF, Adams JE (2012) Automatic location of vertebrae on DXA images using random forest regression. In: Proc medical image computing and computer assisted intervention (MICCAI)
Seber GAF, Wild CJ (1989) Non linear regression. Wiley, New York
Smola AJ, Scholkopf B (2003) A tutorial on support vector regression. Technical report, Statistics and Computing
Sun M, Kohli P, Shotton J (2012) Conditional regression forests for human pose estimation. In: Proc IEEE conf computer vision and pattern recognition (CVPR)
Wang Y, Fan Y, Bhatt P, Davatzikos C (2010) High-dimensional pattern regression using machine learning: from medical images to continuous clinical variables. NeuroImage
Zhou SK, Comaniciu D (2010) Shape regression machine and efficient segmentation of left ventricle endocardium from 2D B-mode echocardiogram. Med Image Anal
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Criminisi, A., Shotton, J. (2013). Regression Forests. In: Criminisi, A., Shotton, J. (eds) Decision Forests for Computer Vision and Medical Image Analysis. Advances in Computer Vision and Pattern Recognition. Springer, London. https://doi.org/10.1007/978-1-4471-4929-3_5
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DOI: https://doi.org/10.1007/978-1-4471-4929-3_5
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