Evolving estimators of the pointwise Holder exponent with Genetic Programming

Published in Journal Articles


The regularity of a signal can be numerically expressed using Hölder exponents, which characterize the singular structures a signal contains. In particular, within the domains of image processing and image understanding, regularity-based analysis can be used to describe local image shape and appearance. However, estimating the Hölder exponent is not a trivial task, and current methods tend to be computationally slow and complex. This work presents an approach to automatically synthesize estimators of the pointwise Hölder exponent for digital images. This task is formulated as an optimization problem and Genetic Programming (GP) is used to search for operators that can approximate a traditional estimator, the oscillations method. Experimental results show that GP can generate estimators that achieve a low error and a high correlation with the ground truth estimation. Furthermore, most of the GP estimators are faster than traditional approaches, in some cases their runtime is orders of magnitude smaller. This result allowed us to implement a real-time estimation of the Hölder exponent on a live video signal, the first such implementation in current literature. Moreover, the evolved estimators are used to generate local descriptors of salient image regions, a task for which a stable and robust matching is achieved, comparable with state-of-the-art methods. In conclusion, the evolved estimators produced by GP could help expand the application domain of Hölder regularity within the fields of image analysis and signal processing.

  1. Leonardo Trujillo, Pierrick Legrand, Gustavo Olague and Jacques Lévy Véhel. Evolving estimators of the pointwise Hölder exponent with Genetic Programming. Inf. Sci. 209:61-79, 2012. BibTeX

    	author = "Leonardo Trujillo and Pierrick Legrand and Gustavo Olague and Jacques L{\'e}vy V{\'e}hel",
    	title = {Evolving estimators of the pointwise H{\"o}lder exponent with Genetic Programming},
    	journal = "Inf. Sci.",
    	volume = 209,
    	year = 2012,
    	pages = "61-79",
    	ee = "http://dx.doi.org/10.1016/j.ins.2012.04.043",
    	bibsource = "DBLP, http://dblp.uni-trier.de"


Regularity based descriptor computed from local image oscillations

Published in Journal Articles


This work presents a novel local image descriptor based on the concept of pointwise signal regularity. Local image regions are extracted using either an interest point or an interest region detector, and discriminative feature vectors are constructed by uniformly sampling the pointwise Hölderian regularity around each region center. Regularity estimation is performed using local image oscillations, the most straightforward method directly derived from the definition of the Hölder exponent. Furthermore, estimating the Hölder exponent in this manner has proven to be superior, in most cases, when compared to wavelet based estimation as was shown in previous work. Our detector shows invariance to illumination change, JPEG compression, image rotation and scale change. Results show that the proposed descriptor is stable with respect to variations in imaging conditions, and reliable performance metrics prove it to be comparable and in some instances better than SIFT, the state-of-the-art in local descriptors.

  1. Leonardo Trujillo, Gustavo Olague, Pierrick Legrand, Evelyne Lutton and others. A new regularity based descriptor computed from local image oscillations.. Optics Express 15(10):6140–6145, 2007. BibTeX

    	title = "A new regularity based descriptor computed from local image oscillations.",
    	author = "Trujillo, Leonardo and Olague, Gustavo and Legrand, Pierrick and Lutton, Evelyne and others",
    	journal = "Optics Express",
    	volume = 15,
    	number = 10,
    	pages = "6140--6145",
    	year = 2007

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