JHU Computer Vision Machine Learning

Project Summary

Orientation extraction and tracing of tubular structures in medical images are important quantitative tools for developing models of the heart both at the histological and cytological levels. For instance, the configuration of the myocardial fibers and the Purkinje network are crucial for modeling the mechanical and electrical properties of the heart and understanding structural changes with myocardial infarction or arrhythmias. Likewise, the cytological mechanical properties are related to the spatial orientation of the cytoskeletal filaments. In addition, detection and enhancement of human vasculature is important for giving insight before interventional procedures.

The problems of detecting orientation and tracing tubular structures are closely related to a primal problem in image processing and computer vision: edge detection. Existing approaches to solve those problems are based on the image Hessian H(x) or the structure tensor S(x) at the point of interest x. Consider a grayscale image I:&upsih &rarr &real, &upsih being the image domain. While H(x) possesses 2^nd order derivative information, i.e. H(x) = [I_xx I_xy; I_yx I_yy], the structure tensor S(x) has 1^st order derivative information, S(x) = [I_x² I_xI_y; I_yI_x I_y²]. The eigendecomposition of the matrix H (or S) gives the orientation information: the eigenvector associated with the leading eigenvalue is in the direction of the maximum gradient (perpendicular to the structure) and the remaining eigenvector shows the tangential direction (along the structure). However, in case of intersections or bifurcations, it has the drawback of "averaging" the orientation information built in the true structure. In our problem we have to deal with not only the image noise but also the complexity such as intersection of fibers and bifurcation of the structure, which make the aforementioned approaches useless.

In this project, we consider the problem of extracting spatial orientation and tracing 2-D and 3-D tubular structures in medical images.The problems we try to solve are:

Local orientation extraction in myofiber arrays.
Tracing tubular structures such as fibers, vessels, Purkinje network, etc. in medical images.

Local Orientation Extraction

In [1], we propose a nonlinear template to extract the local orientation at a point of interest using both a directional and an appearance profile. The directional profile is extracted by computing several intensity differences dictated by the template, whereas the appearance profile is formed by examining the intensity coherence along the template. The local orientation of the structure is then detected by locating the mode of the combined profiles. Figure 1 shows the preliminary results of our algorithm.

Figure 1: (a) Template response on a synthetic 2-D image with a bifurcating fiber. Extraction of local orientation in (b) microtubules, and (c) cardiac myofibers.

Tracing Tubular Structures

The same nonlinear template can be used to track tubular structures. In [1], we present an interactive tracing algorithm that locates points on a tubular structure by maximizing a cost function. More specifically, starting from a user-specified seed point, we find the next point in the curve by maximizing a cost function that favors both smoothness of the curve as well as alignment with the locally estimated orientation. Figure 2 shows the preliminary results of our tracing algorithm.

Figure 2: Preliminary results on fiber tracing in 3-D Purkinje network.