Kluwer - Handbook of Biomedical Image Analysis Vol

θ and φ and the plots of the simulated thickness representing the dependences

on sheet normal orientation θ and φ. Figures 10.22(a) and 10.22(b) show the

√

plots of the dependences of θ and φ with σ = 22 xy, respectively. Good agreement between the simulated and the in vitro thicknesses was observed in both cases although the in vitro thicknesses was slightly greater than the simulated thickness. The biases, i.e., the difference between the simulated thickness and the average of in vitro thickness, were predominantly around 0.1 mm or less (except for θ = 75◦ of τ = 3 mm), and the SDs of the in vitro thickness were mostly within 0.1 mm (except for θ = 45◦ of τ = 2 mm and θ ≥ 35◦ of τ = 3 mm). It should be noted that the dependence on φ is theoretically equivalent to

the dependence on θ when the anisotropy is z = 1.

xy

10.6 Concluding Remarks

We have presented a framework for multiscale analysis of the second-order local structures in medical volume data based on the analysis of the Hessian matrix. Multiscale filtering methods for enhancement of sheet, line, and blob structures were formulated. The guidelines for the filter design were clarified based on detailed analyses of singleand multiscale filter responses using mathematical local structure models. Further, formal approaches to description and quantification of sheet and line structures were presented. The accuracy of width quantification of sheet structures were theoretically analyzed and its inherent limits due to imaging resolution and postprocessing parameters were derived. In this chapter, we purely focus on local structures. Future work will include grouping these local structures to obtain higher-level descriptions incorporating global structures.

10.7 Acknowledgments

The author thanks Dr. Ron Kikinis and Dr. Shin Nakajima at Harvard Medical School and Brigham and Women’s Hospital for providing MR data of a brain, Dr. Hironobu Ohmatsu of the National Cancer Center, Japan, for providing CT data of a chest, Dr. Nobuyuki Shiraga at Keio University for providing abdominal CT data, Dr. Shigeyuki Yoshida at Osaka University for providing a CT data of a

chest, and Dr. Katsuyuki Nakanishi, Dr. Hisashi Tanaka, Dr. Nobuhiko Sugano, and Dr. Takashi Nishii at Osaka University for providing hip joint MR data and phantom MR data. The author also thanks all the above researchers and Prof. Shinicni Tamura at Osaka University for fruitful discussion.

Questions

1.Summarize a series of procedures for multiscale enhancement filtering described in this chapter from input original images to output final filterenhanced images.

2.Explain the parameters involved in the procedures and discuss how to select these parameters.

3.Derive the mathematical formula of the width response curves shown in Fig. 10.3.

4.Discuss the effect of the anisotropic resolution (voxel shape) of input volume data on multiscale enhancement filtering.

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based on the properties of the image under consideration, predict the single best algorithm to be applied at each layer from this set. We demonstrate that this scheme of work has significant advantages over a nonadaptive structure (where only one algorithm is available per layer and it is fixed for all images in the dataset).

We aim to answer the following questions: (a) What is a knowledge-based framework? We discuss the components of this framework in section 11.2 putting it in the context of previous research. (b) How does the image enhancement layer work in this framework? This is detailed in section 11.3 where we discuss measures of image viewability based on enhancement, and demonstrate the role of good enhancement in image segmentation. We also propose two new mapping schemes that can map the image features to chosen enhancement methods. (c) How does the image segmentation layer work within the knowledgebased framework? In section 11.4 we detail the implementation of sophisticated Gaussian mixture models in both supervised and unsupervised modes, with an expert combination framework and compare them on overlap measures.

(d) What are the different strategies for reducing false positives? In section 11.5 we discuss several postprocessing steps that are aimed at reducing the number of false positives per image. (e) Is the adaptive knowledgebased framework superior to a nonadaptive scheme that uses the same algorithms across all images uniformly? We discuss our results on this issue in section 11.6 where we show the relative superiority of the adaptive framework.

11.2 Knowledge-Based Framework

The CAD scheme detailed in this chapter is based on an adaptive framework. An adaptive framework is capable of modifying itself such that it is more suitable to the environment within which it operates. Within the context of CAD, an adaptable component or a framework, attempts to automatically optimize the lesion detection process for a given mammogram. Broadly speaking, an adaptive characteristic can be built into CAD in three different ways: (1) Using a deterministic component; (2) knowledge-based component; (3) with a knowledge-based framework. Each approach may be used in combination with the others. These approaches are summarized below.