Decision trees have proven useful for classification and regression, as well as other types of discrimination problems. A collection of decision trees, varying in specific ways related to their training data and/or configuration, is referred to as a decision forest (or random forest). This book is a comprehensive presentation of the theory and use of decision forests in a wide range of applications, centered on computer vision and medical imaging. The book is strikingly well integrated. Early chapters provide an introduction to tree-based methods that is approachable by readers new to the field, followed by the application of these methods to the two common problems of classification and regression. Later chapters discuss application of the methods to the estimation of probability density functions, learning manifolds in higher-dimensioned spaces, and the problem of semi-supervised learning for classifiers.
The foundational chapters are highly readable and complete in their coverage as it relates to the major topics of the book. Space limitations prevent the book from being a comprehensive text on tree methods (for example, one could not understand the widely used C4.5 method based solely on this text), but the references are complete and appropriate for further study.
An especially intriguing topic is the notion of learning manifolds in some space of dimension d that will allow effective representation in a lower-dimension space d′. A random forest is used to deduce an affinity matrix between points in the sample set, which then drives a standard dimensionality reduction technique. The result is to produce a suitable mapping from d to d′ for this data. Results for this application were satisfactory. Given the wide range of needs for effective and accurate dimensionality reduction when a manifold is present, this technique deserves careful attention.
The final and largest section of the book consists of invited chapters on various applications of decision forests. Lepetit and Fua discuss the location of keypoints in imagery by training a multiclass classifier on a set of affine transformed images of the region surrounding the desired keypoint; a random forest is trained on the anticipated transforms and successful classification locates the keypoint and provides information on its appearance. Gall and Lempitsky cover class-specific Hough forests for object detection.
Criminisi et al. present work on anatomy detection in 3D medical images, that is, the segmentation and detection of organs. Results are shown for both CT and MR imaging. Segmentation in both images and video are well treated in papers by Johnson et al. and Badrinarayanan et al. Two chapters address segmentation of brain imagery by decision forests: Geremia et al. show segmentation of brain lesions in MRIs, while Gray and others use multimodal imaging, PET, and MRI to detect Alzheimer’s; both papers are very thorough and accessible.
An important later chapter by Shotton et al. discusses the efficient implementation of decision forests. They compare breadth-first and depth-first training and recommend a strategy using both, address data structure and multiprocessor considerations, and give valuable information on parameter tuning. The inclusion of this chapter shows the practical nature of the entire work.
This is an excellent volume on the concept, theory, and application of decision forests. It is well integrated and as complete as can be expected. I highly recommend it to those currently working in the field, as well as researchers desiring an introduction to the application of random forests for imaging applications.
