312 IEEE SIGNAL PROCESSING LETTERS, VOL. 17, NO. 3, MARCH 2010 KPAC: A Kernel-Based Parametric Active Contour Method for Fast Image Segmentation Akshaya Mishra and Alexander Wong Abstract—Object boundary detection has been a topic of keen interest to the signal processing and pattern recognition com- munity. A popular approach for object boundary detection is parametric active contours. Existing parametric active contour approaches often suffer from slower convergence rates, diffi- culty dealing with complex high curvature boundaries, and are prone to being trapped in local optima in the presence of noise and background clutter. To address these problems, this paper proposes a novel kernel-based active contour (KPAC) approach, which replaces the conventional internal energy term used in existing approaches by incorporating an adaptive kernel derived for the underlying image characteristics. Experimental results demonstrate that the KPAC approach achieves state-of-the-art performance when compared to two other state-of-the-art para- metric active contour approaches. Index Terms—Boundary extraction, kernel, parametric active contour. I. INTRODUCTION R OBUST identification of object boundaries in the pres- ence of noise and background clutter has many important applications in biomedical engineering [1], [2], visual tracking [3], content based image and video retrieval [4], video seg- mentation [5], and image composition [6]. A popular approach to object boundary detection are those based on active con- tours [7]–[14]. Existing parametric active contour approaches iteratively evolve a deformable model to minimize the sum of internal and external energies of the model to obtain an optimal curve representing the object boundary. The internal energy enforces a penalty on the slope and curvature of the object boundary, while the external energy pulls the deformable model towards the object boundary. Many variations of the tra- ditional active contour approach [7] proposed have focused on increasing the capture range [15]–[19] of the traditional active contour approach. Further, PCA based training [20] has been attempted to avoid initialization and capture range problem. There are three major challenges currently faced by para- metric active contour approaches for object boundary detection. The first major challenge deals with slow convergence rate, par- ticularly when faced with complex imagery. The second major Manuscript received September 09, 2009; revised November 02, 2009. First published November 13, 2009; current version published February 03, 2010. This work was supported in part by the Natural Sciences and Engineering Re- search Council (NSERC) of Canada and Vision and Image Processing Lab, Sys- tems Design Engineering, University of Waterloo. The associate editor coordi- nating the review of this manuscript and approving it for publication was Prof. Dimitrios Androutsas. The authors are with the University of Waterloo, Waterloo, ON Canada N2L 3G1 (e-mail: akmishrau@waterloo.ca ,a28wong@uwaterloo.ca. Digital Object Identifier 10.1109/LSP.2009.2036654 challenge deals with the presence of image noise contamination and background clutter, which can lead to poor boundary de- tection accuracy due to convergence to local optima. Third, ex- isting approaches have difficulty dealing with complex high cur- vature boundaries. To address these issues, this paper proposes a novel kernel-based parametric active contour (KPAC) method, that shares the same underlying theory of traditional deformable models. However, instead of employing penalties on slope and curvature as an internal energy, which are highly sensitive to noise and handles high curvature boundaries poorly, KPAC in- troduces an adaptive non-stationary kernel, derived from the un- derlying image characteristics, as the internal energy of the de- formable model. This approach allows the faster and more ac- curate convergence by adapting to the underlying image char- acteristics, particularly under situations characterized by noise and complex high curvature boundaries. II. PARAMETRIC ACTIVE CONTOUR THEORY The seminal work on parametric active contour [7] defined the active contour as an energy minimizing deformable model , , with normalized arclength . The goal is to evolve the deformable model to minimize the energy functional (1) where and are the first and second derivatives of with respect to arclength , and the parameters , and are the penalties on slope, curvature and the external force, respectively. The internal energy, representing the prior, is a weighted sum of elastic and membrane energies, whereas the external energy is computed from the image in a manner dependant upon the application. Typically, as the object boundaries coincide with image edges, the external energy is made a function of the image gradient ( ) such that the contour could converge to the bound- aries, (2) where is the convolution operator and is the first-order Gaussian derivative. Using the Euler-Lagrange equation, the minimization of (1) in vector and matrix format can be expressed as (3) 1070-9908/$26.00 © 2010 IEEE