Delineating Elliptical Objects with an Application to Cardiac Scintigrams

Abstract

To delineate the myocardium in planar thallium-201 scintigrams of the left ventricle, a method, based on the Hough transformation, is presented. The method maps feature points (X, Y, Y')-where Y' reflects the direction of the tangent in edge point (X,Y)-into the two-dimensional space of the axis lengths of the ellipse. Within this space, a probability density function (pdf) can be estimated. When the center of the ellipse or its orientation are unknown, the 2-D pdf of the lengths of the axes is extended to a 5-D pdf of all parameters of the ellipse (lengths of the axes, coordinates of the center, and the orientation). It is shown that the variance of the edge-point-based estimates of the axis lengths increases when the location error of the center of the supposed ellipse or its orientation error increases. The likelihood of the estimates is expected to decrease with increasing variance. Therefore, local search algorithms can be applied to find the maximum likelihood estimate of the parameters of the ellipse. Curves describing the convergency of the algorithm are presented, as well as an example of the application of the algorithm to real scintigrams. The method is able to detect contours even if they are only partly visualized, as in thallium scintigrams of the myocardium of patients with ischemic heart disease. As long as the number of parameters describing the contour is relatively low, such an algorithm is also suitable for application to differently curved contours.

Snakes With an Ellipse-Reproducing Property

“…If we now convolve both sides of (18) (20) where Note that sequences and are -periodic and that the summations in (19) and (20) can be reduced to finite ones if we make use of the periodized basis functions.…”

“…We have expressed in (19) and (20) how to compute the vector coefficients for reproducing sinusoids of unit period and the initial phase of . The appropriate linear combination of and then allows one to reproduce sinusoids of arbitrary shape.…”

“…1 how our snake can adopt the shape of a perfect ellipse (i.e., reproduces the ellipse) as well as more refined shapes. Segmenting circles and ellipses in images is a problem that arises in many fields, such as biomedical engineering [19]- [22] or computer graphics [23], [24]. In medical imaging in particular, it is usually necessary to segment arteries and veins within tomographic slices [25].…”

Semi-Automatic Lymph Node Segmentation in LN-MRI

“…Specifically, an ellipse is a powerful parametric form used in many computer vision tasks [4,5]. A parametric maximum likelihood fit to the medical data, particularly cardiac scintigrams, using an ellipse parameterization was developed in [6]. Other parametric approaches to segmentation include Fourier descriptors in [7], and spherical harmonics in [8].…”

Reconstructing Ellipsoids from Projections

“…In [1] an ellipse is used as a simple parameterized model in an attempt to recover object eccentricity and orientation from low signal-to-noise ratio tomographic data. In other medical areas ellipsoids are used to model both the shape and volume or area of anatomical parts, such as the heart, spine, and blood vessels [2][3][4][5]. In [6,7] the state of a system is assumed confined to an unknown ndimensional ellipsoid and the goal is essentially to reconstruct this ellipsoid from observations of its lower-dimensional projections.…”