Correspondence to: <firstname.lastname@example.org>
Recommended for acceptance by Dr. Sporring
ELCVIA ISSN: 1577-5097
Published by Computer Vision Center / Universitat Autonoma de Barcelona, Barcelona, Spain
Electronic Letters on Computer Vision and Image Analysis 6(2):9-21, 2007
A PDE Method to Segment Image Linear Objects with Application
to Lens Distortion Removal
Moumen T. El-Melegy and Nagi H. Al-Ashwal
Electrical Engineering Department,
Assiut University, Assiut 71516, Egypt
Received 23 October 2006; accepted 3 October 2007
In this paper, we propose a partial differential equation based method to segment image objects, which have a
given parametric shape based on energy functional. The energy functional is composed of a term that detects
object boundaries and a term that constrains the contour to find a shape compatible with the parametric shape.
While the shape constraints guiding the PDE may be determined from object's shape statistical models, we
demonstrate the proposed approach on the extraction of objects with explicit shape parameterization, such as
linear image segments. Several experiments are reported on synthetic and real images to evaluate our approach.
We also demonstrate the successful application of the proposed method to the problem of removing camera lens
distortion, which can be significant in medium to wide-angle lenses.
Key Words: Variational Methods, Partial Differential Equations, Level Sets, Image Segmentation, Hough
Transform, Fuzzy Memberships, Radial Distortion, Lens Distortion Calibration.
Variational methods and partial differential equations (PDEs) are more and more being used to analyze,
understand and exploit properties of images in order to design powerful application techniques, see for
example [15, 16, 17]. Variational methods formulate an image processing or computer vision problem as an
optimization problem depending on the unknown variables (which are functions) of the problem. When the