title: Spherical nonlinear correlations for global invariant three-dimensional object recognition.
abstract: We define a nonlinear filtering based on correlations on unit spheres to obtain both rotation- and scale-invariant three-dimensional (3D) object detection. Tridimensionality is expressed in terms of range images. The phase Fourier transform (PhFT) of a range image provides information about the orientations of the 3D object surfaces. When the object is sequentially rotated, the amplitudes of the different PhFTs form a unit radius sphere. On the other hand, a scale change is equivalent to a multiplication of the amplitude of the PhFT by a constant factor. The effect of both rotation and scale changes for 3D objects means a change in the intensity of the unit radius sphere. We define a 3D filtering based on nonlinear operations between spherical correlations to achieve both scale- and rotation-invariant 3D object recognition.
authors.affiliation: Departament d'Optica, Universitat de València, c/o Dr. Moliner, 50 46100-Burjassot, València, Spain.
authors.forename: José J
authors.initials: JJ
authors.lastname: Vallés
authors.forename: Pascuala
authors.initials: P
authors.lastname: García-Martínez
authors.forename: Carlos
authors.initials: C
authors.lastname: Ferreira
mesh_terms: D000465:Algorithms; D001185:Artificial Intelligence; D007089:Image Enhancement / Q000379:methods; D007090:Image Interpretation, Computer-Assisted / Q000379:methods*; D021621:Imaging, Three-Dimensional / Q000379:methods*; D016247:Information Storage and Retrieval / Q000379:methods*; D017711:Nonlinear Dynamics; D010363:Pattern Recognition, Automated / Q000379:methods*; D015203:Reproducibility of Results; D012399:Rotation; D012680:Sensitivity and Specificity; D013223:Statistics as Topic