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We present a 3D shape retrieval methodology based on the theory of spherical harmonics. Using properties of spherical harmonics, scaling and axial flipping invariance is achieved. Rotation normalization is performed by employing the continuous principal component analysis along with a novel approach which applies PCA on the face normals of the model. The 3D model is decomposed into a set of spherical functions which represents not only the intersections of the corresponding surface with rays emanating from the origin but also points in the direction of each ray which are closer to the origin than the furthest intersection point. The superior performance of the proposed methodology is demonstrated through a comparison against state-of-the-art approaches on standard databases. ᭧

We present two highly efficient second-order algorithms for the training of multilayer feedforward neural networks. The algorithms are based on iterations of the form employed in the Levenberg-Marquardt (LM) method for nonlinear least squares problems with the inclusion of an additional adaptive momentum term arising from the formulation of the training task as a constrained optimization problem. Their implementation requires minimal additional computations compared to a standard LM iteration. Simulations of large scale classical neural-network benchmarks are presented which reveal the power of the two methods to obtain solutions in difficult problems, whereas other standard second-order techniques (including LM) fail to converge.