INDUSTRIAL AND COMMERCIAL APPLICATION A new radial symmetry measure applied to photogrammetry Raquel Dosil • Xose ´ M. Pardo • Xose ´ R. Fdez-Vidal • Anto ´n Garcı ´a-Dı ´az • Vı ´ctor Lebora ´n Received: 22 March 2011 / Accepted: 25 June 2012 Ó Springer-Verlag London Limited 2012 Abstract This work presents a new measure for radial symmetry and an algorithm for its computation. This measure identifies radially symmetric blobs as locations with contributions from all orientations at some scale. Hence, at a given scale, radial symmetry is computed as the product of the responses of a set of even symmetric feature detectors, with different orientations. This operator presents low sensitivity to shapes lacking radial symmetry, is robust to noise, contrast changes and strong perspective distor- tions, and shows a narrow point spread function. A multi- resolution measure is provided, computed as the maximum of the symmetry measure evaluated over a set of scales. We have applied this measure in the field of photogrammetry for the detection of circular coded fiducial targets. The detection of local maxima of multi-resolution radial sym- metry is combined with a step of false-positive rejection, based on elliptical model fitting. In our experiments, the efficiency of target detection with this method is improved regarding a well-known commercial system, which is expected to improve the performance of bundle adjustment techniques. In order to fulfill all steps previous to bundle adjustment, we have also developed our own method for recognition of coded targets. This is accomplished by a standard procedure of segmentation and decoding of the ring sequence. Nevertheless, we have included a step for the verification of false positives of decoding based on corre- lation with reference targets. As far as we know, this approach cannot be found in literature. Keywords Circular coded targets  Radial symmetry  Filter banks  Log Gabor  Target identification  Correlation 1 Originality and contribution We have developed a new measure for radial symmetry and an algorithm for its computation. Our measure identifies radially symmetric blobs as locations with contributions from all orientations at some scale. Hence, at a given scale, radial symmetry is computed as the product of the responses of a set of even symmetric feature detectors, with different orientations. In this way, the response of this detector will vanish at locations with contributions from a subset of oriented features, thus avoiding weak responses from non- radially symmetric shapes. This operator presents low sensitivity to shapes lacking radial symmetry, is robust to noise, contrast changes and strong perspective distortions, and shows a narrow point spread function. A multiresolu- tion measure is provided, computed as the maximum of the symmetry measure evaluated over a set of scales. We have applied this measure in the field of photogram- metry, for the detection of circular coded fiducial targets. Research in photogrammetry is usually focused on the development of robust bundle adjustment methods, while previous steps for location and identification of targets receive little attention. Here, we propose to facilitate bundle R. Dosil (&)  X. M. Pardo  X. R. Fdez-Vidal  A. Garcı ´a-Dı ´az  V. Lebora ´n Centro de Investigacio ´n en Tecnoloxı ´as da Informacio ´n (CITIUS), Universidade de Santiago de Compostela, Campus Vida s/n, 15782 Santiago de Compostela, Spain e-mail: raquel.dosil@usc.es Present Address: R. Dosil Multimodal Information Area, Galician Research and Development Center in Advanced Telecommunications (GRADIANT), Ed. CITEXVI, local 14, Fonte das Abelleiras, 4, Campus Universitario de Vigo, 36310 Vigo, Spain e-mail: rdosil@gradiant.org 123 Pattern Anal Applic DOI 10.1007/s10044-012-0281-y