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Chapter 10

Hessian-Based Multiscale Enhancement,

Description, and Quantification

of Second-Order 3-D Local Structures from Medical Volume Data

Yoshinobu Sato1

10.1 Introduction

With high-resolution three-dimensional (3-D) imaging modalities becoming commonly available in medical imaging, a strong need has arisen for a means of accurate extraction and 3D quantification of the anatomical structures of interest from acquired volume data. Three-dimensional local structures have been shown to be useful for 3-D modeling of anatomical structures to improve their extraction and quantification [1–16]. In this chapter, we describe an approach to enhancement, description, and quantification of the anatomical structures characterized by second-order 3D local structures, that is, line, sheet, and blob structures.

The human body contains various types of line, sheet, and blob structures. For example, blood vessels, bone cortices, and nodules are characterized by line, sheet, and blob structures, respectively. We present a theoretical framework for systematic analysis of second-order local structures in volume data. A set of volume data is typically represented as a discrete set of samples on a regular grid. The basic approach is to analyze the continuous volume intensity function

1 Division of Interdisciplinary Image Analysis, Osaka University Graduate School of

Medicine, 2-2-D11 Yamada-oka, Suita, Osaka 565-0871, Japan

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