Template-Matching Approach to Edge Detection of Volume Data
Lisheng Wang
Tien-Tsin Wong
Pheng Ann Heng
Jack Chun Yiu Cheng*
Department of Computer Science & Engineering, *Department of Orthopaedics & Traumatology The Chinese University of Hong Kong, {lswang, ttwong, pheng} @cse.cuhk.edu.hk
developed a multidimensional edge detection technique by hypersurface fitting, which extends the Prewitt approach. Monga et al. [4] proposed a 3D edge detection technique based on the 3D extension of the 2D Deriche optimal edge detector, which in turn is derived using Canny's criteria. Bomans et al. [5] described the '3D extension of the Man-Hildretch operator and showed that its zero-crossings are related to anatomical surface of MRI data. Zhan [6] obtained an optimal step edge detector by optimizing a penalty function that combines some optimality criteria. Luo et al. [7] presented a 3D moment-based detector as the generalization of 2D moment-based detecting approach. Thus many existing 3D edge detectors developed are the generalization of 2D edge detectors. Many of them are gradient-based edge detectors, which enhance the volume data by estimating its gradient function and then signal that an edge is present if the gradient value is greater than some defined threshold. It is known that template-matching operators are another class of important edge detector for 2D image, including Prewitt operator and Kirsch operator [SI. They detect edge from 2D image by matching the templates of ideal edge in various orientations. In this paper, we propose a template-matching approach to detect edges from the volume data. We give all possible templates of ideal step-like edge in the 3 x 3 ~ 3neighborhood of volume data, and detect step-like edge from volume data by matching these templates. The template producing the highest correlation determines the edge magnitude and the edge orientation at a 3D point. Edge detection can be accomplished through thresholding, in the same manner as other 3D gradient based approaches. This is a simple and straightforward approach to edge detection of volume data, generalizing well-known Kirsch operator [9]. It can detect intensity in every direction and has the property of rotational invariance in 18-neighbourhood. The proposed approach has been applied to various medical volume data.
Abstract This paper proposes a template-matching approach to the edge detection of volume data. Twenty-six templates of ideal step-like edge in the 3 x 3 ~ 3 neighborhood of volume data are given, and step-like edge of volume data is detected by matching such pattems in various orientations. The approach is a simple and straightforward one to edge detection of volume data. It generalizes the well-known Kirsch operator for 2 0 image. It can detect change of intensity in every direction, and has the property of rotation invariance in 18neighborhood. Implementation of proposed approach is given for biological and medical volume data, including MRI and CT volume data.
1. Introduction . Modem scanning techniques and methodologies used in scientific computing provide us many volume data containing intemal structures, such as 3D medical data (CT, MFU, SAT), regular Computer Fluid Dynamic (CFD) data, oceanographic data and so on. Identifying these internal structures from volume data has become an important research topic in the analysis of volume data. The first stage toward identifying and modeling these intemal structures is to search the surfaces that form their boundary. Since different structures within volume data usually give rise to different intensities, therefore the points of boundary surface are located where gradient value is high. This leads to the classical problem of edge detection in volume data. Edge detection of volume data has received much attention. Liu [ 2 ] reported the first 3D edge detection technique based on the 3D generalization of the Roberts operator. Zucker and Hummel [2] proposed a 3D extension of the Hueckel operator by determining a best fit step function. Morgenthaler and Rosenfeld [3]
0-7695-1113-9\01$10.00 0 2001 IEEE
286
a = sin @. sin cp
2. Method
b =
[email protected]
In volume data, step-like edge is a surface or plane in the local neighbourhood of the volume data, the intensities on either side of the edge has great difference. In many cases, the boundaries of structures within volume data are step-like edge, such as bone in CT, eddy in oceanographic data [lo], shock in the compressible flow of fluid or gas [ll]. To segment CT and MRI image, assume constant intensity plus additive noise within a given anatomical structure is often a reasonable assumption in the regions with low texture [12]. In fact, the boundaries of such anatomical structures are just steplike edges. In volume data, ideal step-like edge is essentially a step-like pattern, it is oriented such that the neighbourhood of edge point is separated into two distinct parts. Therefore, instead of estimating the gradient at every 3D point, we can detect step-like edge from volume data by matching such patterns in various orientations. The template (pattern) producing the highest correlation determines the edge magnitude at the point and the edge orientation is assumed to be that of the corresponding template. Edges are extracted by thresholding in the same manner as 3D gradient approaches. We will give all patterns of ideal step-like edge in the 3 x 3 ~ 3 neighbourhood of volume data and their corresponding templates. In the 3 x 3x 3 neighbourhood of volume data, there are 26 pattems all together. Hence, 26 templates are used for matching. Each template represents an ideal steplike edge at a different orientation in 3D space.
c =cos@, 0 I@ < 360, -90 I < 9 0 Therefore, edge target patterns are the function of (@,cp) , expressed as Pattem(@l,@2 ,...9"). This is a set of planes. In 3D polar coordinate, (@,cp) actually represents a ray from the origin. Writing the ray as l($,cp), then Z(@, cp) and (a,b, c) represent the same direction in R 3 . Therefore, l(@,cp) is the perpendicular of plane Pattern(@,cp) . It concludes that, for any given (9, cp) or l(@,cp), its corresponding edge target pattern is a plane perpendicular to the ray Z(@,q) and separating the neighbourhood of edge point into two distinct parts having different values. Based on the above analysis, it is easy to obtain the templates of ideal step-like edge for 2D image. Eight pattems along eight orientations (0", 45",
go", 135",
18@, 225" 27@, 315") will be obtained. In fact, these are edge detectors proposed by of Kirsch [8]. 2.2. Templates and patterns of step-like edge in volume data Suppose volume data is represented as a N x M x L matrix F(i, j , k ) :
2.1. Model of pattern of step-like edge in volume data
F(i, j , k ) ={ijk :1li I N,l I j
