Research Article Edge Detection in Digital Images Using Dispersive Phase Stretch Transform Mohammad H. Asghari 1 and Bahram Jalali 1,2,3 1 Department of Electrical Engineering, University of California, Los Angeles, Los Angeles, CA 90095, USA 2 Department of Bioengineering, University of California, Los Angeles, Los Angeles, CA 90095, USA 3 Department of Surgery, David Gefen School of Medicine, University of California, Los Angeles, Los Angeles, CA 90095, USA Correspondence should be addressed to Mohammad H. Asghari; asghari@ucla.edu Received 25 December 2014; Revised 20 February 2015; Accepted 6 March 2015 Academic Editor: Tiange Zhuang Copyright © 2015 M. H. Asghari and B. Jalali. Tis is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. We describe a new computational approach to edge detection and its application to biomedical images. Our digital algorithm transforms the image by emulating the propagation of light through a physical medium with specifc warped difractive property. We show that the output phase of the transform reveals transitions in image intensity and can be used for edge detection. 1. Introduction Edge detection is the name for a set of mathematical methods for identifying patterns in digital images where brightness or color changes abruptly [1–3]. Applying an edge detection algorithm to an image can be used for object detection and classifcation. It also reduces the digital fle size while preserving important information, albeit data compression is not the main objective in edge detection. Many methods for edge detection have been proposed, but most of them can be grouped into two main categories: zero-crossing based and search-based. Te zero-crossing based methods search for zero crossings in a Laplacian or second-order derivative computed from the image [1]. Te search-based methods compute the edge strength, usually with a frst-order derivative, and then search for local direc- tional maxima of the gradient amplitude [2]. Detailed survey of available techniques for edge detection can be found in [3]. We employ a physics-inspired digital image transfor- mation that emulates propagation of electromagnetic waves through a difractive medium with a dielectric function that has warped dispersive (frequency dependent) property. We show that the phase of the transform has properties conducive for detection of edges and sharp transitions in the image. Our method emulates difraction using an all-pass phase flter with specifc frequency dispersion dependencies. Te output phase profle in spatial domain reveals variations in image intensity and when followed by thresholding and morphological postprocessing provides edge detection. We show how flters with linear and nonlinear phase derivatives can be used for edge detection and how the shape and magnitude of the phase function infuence the edge image. Earlier it was shown that the magnitude of the complex amplitude for a similarly transformed image exhibits reduc- tion in space-bandwidth product and may be useful for data compression [4]. Te present paper employs the phase of the transform for application to edge detection. Also, the details of the flter kernel are diferent in the two cases. Going further back, the concept of difraction based image processing has its roots in the Photonic Time Stretch, a temporal signal processing technique that employs temporal dispersion to slow down, capture, and digitally process fast waveforms in real time [5]. Known as the time-stretch dispersive Fourier transform, this technique has led to the discovery of optical rogue waves and detection of cancer cells in blood with record sensitivity [6], as well as highest performance analog- to-digital conversion [7]. In this paper, we also demonstrate application of the proposed edge detection algorithm to some biomedical images. Hindawi Publishing Corporation International Journal of Biomedical Imaging Volume 2015, Article ID 687819, 6 pages http://dx.doi.org/10.1155/2015/687819