Extended grassfire transform on medial axes of 2D shapes

Abstract

The medial axis is an important shape descriptor first introduced by Blum [2] via a grassfire burning analogy. However, the medial axes are sensitive to boundary perturbations, which calls for global shape measures to identify meaningful parts of a medial axis. On the other hand, a more compact shape representation than the medial axis, such as a "center point", is needed in various applications ranging from shape alignment to geography. In this paper, we present a uniform approach to define a global shape measure (called extended distance function, or EDF) along the 2D medial axis as well as the center of a 2D shape (called extended medial axis, or EMA). We reveal a number of properties of the EDF and EMA that resemble those of the boundary distance function and the medial axis, and show that EDF and EMA can be generated using a fire propagation process similar to Blum's grassfire analogy, which we call the extended grassfire transform. The EDF and EMA are demonstrated on many 2D examples, and are related to and compared with existing formulations. Finally, we demonstrate the utility of EDF and EMA in pruning medial axes, aligning shapes, and shape description.

Identifying Perceptually Salient Features on 2D Shapes

“…At each junction, we choose the maximum previous WEDF value to proceed. This algorithm is analogous to the scheme for computing EDF [10]. The discrete algorithm is summarized below: …”

“…The definition of WEDF above was made under this assumption of no loops. The measure EDF is defined in a similar way, but allows EDF to become infinite if there are loops in the medial axis [10]. We do not pursue this extension because computationally, we require that WEDF be finite-the area of the shape is finite even when there are holes.…”

“…In [10], the authors propose to compute at each point of the medial axis a quantity EDF (the Extended Distance Function), which measures the distance to the closest extremity of the shape corresponding to a degree-1 node on the longest path of the medial axis containing a given medial point. The set of medial balls corresponding to this longest path is called a tube, and EDF is the distance to the closest extremity of the tube.…”

“…To be robust to such cases, our insight is to use the length of each medial branch to weight the SAT scaling. In order to characterize the length of a medial axis branch, we use the Extended Distance Function (EDF) proposed by Lui et al [10].…”

A Survey of Thinning Techniques on Two Dimensional Binary Images

“…To get rid of this problem in 2011 Lu Liu, Erin W. Chambers, David Letscher, and Tao Ju proposed extended distance function (EDF) and extended medial axis (EMA) [29]. It is based on Blum's grassfire methodology.…”