In recent years, topology based techniques have begun to emerge as a general framework in visualization with the increase of scientific data in size and complexity. Topology could be used to capture significant features of the data at an abstract level, enabling and facilitating data understanding in visualization. This book focuses on investigating effective uses of the contour tree, one of topological abstractions of the scalar field, in improving efficiency of volumetric data analysis. It achieves the goals by increasing the presentation of topology information in order to explore various relationships of geometrical structures. In particular, the book plays emphasis on a novel approach for automating transfer function generations in volume visualization using topology-controlled residue flow model and harmonic colors. The generated transfer functions reveal structural relationships automatically. To make this work practical, this book also deals with topology simplification. The analysis should help shed some light on the research of topology-controlled visualization. It should be especially useful to professionals in volumetric visualization and medical image analysis.