Shape recovery algorithms using level sets in 2-D/3-D medical imagery: a state-of-the-art review

Abstract

The class of geometric deformable models, also known as level sets, has brought tremendous impact to medical imagery due to its capability of topology preservation and fast shape recovery. In an effort to facilitate a clear and full understanding of these powerful state-of-the-art applied mathematical tools, this paper is an attempt to explore these geometric methods, their implementations and integration of regularizers to improve the robustness of these topologically independent propagating curves/surfaces. This paper first presents the origination of level sets, followed by the taxonomy of level sets. We then derive the fundamental equation of curve/surface evolution and zero-level curves/surfaces. The paper then focuses on the first core class of level sets, known as "level sets without regularizers." This class presents five prototypes: gradient, edge, area-minimization, curvature-dependent and application driven. The next section is devoted to second core class of level sets, known as "level sets with regularizers." In this class, we present four kinds: clustering-based, Bayesian bidirectional classifier-based, shape-based and coupled constrained-based. An entire section is dedicated to optimization and quantification techniques for shape recovery when used in the level set framework. Finally, the paper concludes with 22 general merits and four demerits on level sets and the future of level sets in medical image segmentation. We present applications of level sets to complex shapes like the human cortex acquired via MRI for neurological image analysis.

Deformable Models for Segmentation Based on Local Analysis

“…(iii) Pose model is adjusted including translation, rotation, and scaling, aligning the points model to currentf ound in the previous step. (iv) Compute shape adjustment in order to update parameter, according to (6).…”

“…Some of the more popular methods in medical image analysis are those based on deformable models [3][4][5]. They include algorithms, such as Active Shape Models (ASM) and level sets (LS), which are widely documented in the literature [6]. Efficient implementations have been designed aiming at faster methods [7,8].…”

SketchSnakes: Sketch-line initialized Snakes for efficient interactive medical image segmentation

“…Since their inception in the late 1980's, many improvements to Snakes models for medical image applications have been proposed. For example, many Snakes variants have been developed that ameliorate the well-known initialization sensitivity problem, allowing "one-click" initialization and the ability of these active contour models to "flow" into complex shapes [9][10][11] as well as change their connectivity [12,13]. These improvements have proved effective for some segmentation tasks, especially involving very complex-shaped objects (e.g.…”

Shape optimized design of microwave dielectric resonators by level-set and topology gradient methods

“…LS methods have been applied very successfully in many areas of scientific modeling and optimization [12][13][14][15] and more recently, in the design of microwave components [16] but generally in two-dimensional problems.…”