Histogram partition and interval thresholding for volumetric breast tissue segmentation

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Abstract

It is possible to automatically decompose a volume into subvolumes based on histogram partition and interval thresholding. In practice, a histogram may assume unimodal or multimodal distributions. In this paper, we implement an automatic volumetric segmentation scheme by partitioning a histogram into intervals followed by interval thresholding. Based on its distribution shape, the histogram is partitioned by either a valley-seeking algorithm (for multimodal) or a five-subinterval algorithm (for unimodal). Applied to volumetric breast analysis, this technique decomposes a breast volume into five subvolumes corresponding to five intensity subintervals: lower (air bubble), low (fat), middle (normal tissue, or parenchyma), high (glandular duct), higher (calcification), in the order of X-ray attenuation value. With the assumption that each subvolume resulting from interval thresholding corresponds to a tissue type, the spatial structure of each breast tissue type can be individually visualized and analyzed in a subvolume in an ample space (as big as the whole volume) in the absence of other tissue types. We demonstrate this histogram-partitioned interval thresholding segmentation method with one breast phantom and one breast surgical specimen that are volumetrically reconstructed by cone-beam tomography.

Introduction

Conventional two-dimensional (2D) mammography suffers from unavoidable spatial superimposition of lesion and its surrounding structures in projection images, which may prevent the detection of small lesions, especially for low-contrast tumor masses and small calcification spots. Cone-beam computed tomography (CBCT) can totally eliminate the spatial superposition effect associated with mammography by volumetric tomographic reconstruction [1]. In particular, a cone-beam breast CT system can reproduce a breast object in a three-dimensional (3D) array [1], [2], [3], conforming the natural 3D breast shape. The isotropic gridding and super-gridded resolution reconstruction [2] allow the accurate measurement of 3D local lesions in a breast [4].

With a 3D breast array reconstructed from cone-beam breast tomography, the immediate tasks are to scrutinize the volume contents and to quantitatively measure the constituent subvolumes. Volumetric segmentation serves as the first as well as the most important step in 3D breast analysis. As a result of spatial exclusive occupation (or the elimination of spatial superposition in tomographic reconstruction), the breast volume segmentation is eased [1]. Therefore tomographic images can be segmented by a simple global thresholding operation. A breast is a small soft tissue object, which can be finely classified into different tissue types [5], with each tissue type occupying a subvolume in the breast space. Assuming that breast tissue types correspond to different intensities or intensity intervals in the reconstructed volume, we can decompose a breast into subvolumes by multithresholding [6], [7] or interval thresholding techniques. The interval volume has been proposed for volumetric data exploration and geometrical modeling [8], and we have applied it to breast volumetric segmentation and 3D tumor measurement [4]. In practice, the voxel-value statistics of a breast volume, in terms of histogram, may produce a unimodal or a multimodal distribution. The multimodal histogram (with one or more valleys) can be easily partitioned by multiple subintervals based on the valley points, which can be recognized using a valley-seeking algorithm [8], [9], [10]. A unimodal histogram (one hill without valleys) can always be partitioned by five bins by a triangle algorithm, thus decomposing a breast volume into five subvolumes. Each subvolume is represented in a 3D binary array (consists of 0-voxels and 1-voxles), allowing 3D spatial connectedness study [11] and 3D iso-value volume measurement. As a result, the subvolume decomposition technique provides a way for isolating tissue types, thereby facilitating the characterization for each tissue pattern in terms of 3D geometry, topology, and textures [12], [13], [14]. In this paper, we report the histogram-partition-based volumetric segmentation technique and its application to the volumetric tissue segmentation in a breast volume reconstructed from cone-beam volume tomography.

This paper is organized as follows. In Section 2, we briefly introduce the isotropic grid resolution reconstruction provided by cone-beam breast computed tomography. In Section 3, we present the histogram partition and interval thresholding method. Section 4 demonstrates the implementations with one breast phantom and one breast specimen, which is followed by a discussion in Section 5. Finally, in Section 6 is a summary.

Section snippets

Isotropic grid reconstruction of a breast volume

A CBCT system based on a flat-panel detector (FPD) is applicable to volume reconstruction of small objects, such as a breast that can be totally covered during cone-beam scanning. Fig. 1 illustrates the cone-beam scanning geometry of a cone-beam CT scanner built in the University of Rochester [3]. The volume dataset were reconstructed from a sequence of cone-beam X-ray projection images (∼300 projections) acquired during gantry rotation. The breast object is positioned at the center of the

Spatial partition and intensity interval partition

The essential task for breast volume analysis is to separate a breast into different constituent tissues. Due to the spatial exclusive occupancy, the volumetric segmentation can be expressed by a spatial partition [1]:V=kVkwithVk=V(x,y,z)ifμ(x,y,z)=μk0otherwiseandVk1Vk2={0},k1k2

In Eq. (3), a constituent tissue is characterized by a single voxel value. In computer community, the “equal” condition on float points is always represented by a bounded range, e.g., the equality a = b is

Experiment

In this section, we demonstrate the histogram-partition-based interval thresholding segmentation techniques through the use of a phantom (for Algorithm 2), which produces a unimodal histogram in the reconstructed volume, and a breast surgical part (for Algorithm 1), which produces a multimodal histogram. The details of experimental configuration and 3D reconstruction algorithms have been reported in other places [3], [4]. The experimental settings are summarized in Table 1.

The volume data was

Discussion

Based on the experimental demonstration, we discuss the following aspects.

  • (1)

    The essential step in the multi-interval thresholding technique lies in intensity interval partition. The histogram provides a statistical representation of voxel values. For unimodal histogram, we can forcibly carry out a five-subinterval partition scheme for the sake of automation. In practice, the histogram-based image segmentation may produce suboptimal or meaningless results, which are likely encountered in the

Summary

Based on assumption that the breast tissues are differentiable in terms of X-ray attenuation, it is possible to decompose a breast volume into tissue subvolumes. We have reported in this paper an automatic implementation of volumetric segmentation by partitioning the voxel-value histogram and demonstrated by two cases. A histogram may assume a unimodal or multimodal distribution. The valley-seeking algorithm is proposed to partition multimodal histogram, while the “five-subinterval algorithm”

Acknowledgements

This work was in part supported by National Natural Science Foundation of China, with the project number 30770591. The author acknowledges the use of phantom data acquired in the University of Rochester.

Zikuan Chen received his BS (in 1985) and MS (in 1998) in physics from Yunnan University and his DrEng (in 1993) in optical information processing from Nankai University. From 1993 to 1997 he was an Assistant Professor and an Associate Professor with the Institute of Modern Optics, Nankai University, working on fast fingerprint identification and biometrics applications in security access control. From 1998 to 2000, he was a Postdoctoral Fellow at the University of Tennessee and the University

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Zikuan Chen received his BS (in 1985) and MS (in 1998) in physics from Yunnan University and his DrEng (in 1993) in optical information processing from Nankai University. From 1993 to 1997 he was an Assistant Professor and an Associate Professor with the Institute of Modern Optics, Nankai University, working on fast fingerprint identification and biometrics applications in security access control. From 1998 to 2000, he was a Postdoctoral Fellow at the University of Tennessee and the University of Arkansas, working on multiresolution image processing and fast pattern recognition techniques. From 2001 to 2002, he joined the University of California-Irvine as a Research Associate, working on medical image analysis (blood vessel tracking and measurement in X-ray angiographic images). During the period of 2002 and 2006, he worked as a Senior Research Associate and a Research Assistant Professor at the Department of Imaging Sciences, University of Rochester. Currently, he is a Professor and serves vice dean leading researches in the Sino-Dutch Biomedical and Information Engineering School, Northeastern University, China. His research interests include fast pattern recognition, tomography, stereo reconstruction, medical imaging and medical image analysis, in particular cone-beam tomography and its applications to breast imaging, volumetric angiography and blood flow measurement.

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