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On the existence of affine connections with recurrent projective curvature

100%

Olszak Z. , Słuka K.

tom Vol. 33, nr 1

171-179

We find new examples of locally equiaffine connections with parallel or recurrent projective curvature tensor. Certain applications in the theory of totally geodesic affine immersions are also discussed.

A Curvature-Tensor-Based Perceptual Quality Metric for 3D Triangular Meshes

75%

Torkhani F. , Wang K. , Chassery J. M.

Machine Graphics and Vision

2014

tom Vol. 23, No. 1/2

59--82

Perceptual quality assessment of 3D triangular meshes is crucial for a variety of applications. In this paper, we present a new objective metric for assessing the visual difference between a reference triangular mesh and its distorted version produced by lossy operations, such as noise addition, simplification, compression and watermarking. The proposed metric is based on the measurement of the distance between curvature tensors of the two meshes under comparison. Our algorithm uses not only tensor eigenvalues (i.e., curvature amplitudes) but also tensor eigenvectors (i.e., principal curvature directions) to derive a perceptually-oriented tensor distance. The proposed metric also accounts for the visual masking effect of the human visual system, through a roughness-based weighting of the local tensor distance. A final score that reflects the visual difference between two meshes is obtained via a Minkowski pooling of the weighted local tensor distances over the mesh surface. We validate the performance of our algorithm on four subjectively-rated visual mesh quality databases, and compare the proposed method with state-of-the-art objective metrics. Experimental results show that our approach achieves high correlation between objective scores and subjective assessments.

Multi-scale curvature tensor analysis of machined surfaces

63%

Bartkowiak T. , Brown C.

tom Vol. 36

44--50

This paper demonstrates the use of multi-scale curvature analysis, an areal new surface characterization technique for better understanding topographies, for analyzing surfaces created by conventional machining and grinding. Curvature, like slope and area, changes with scale of observation, or calculation, on irregular surfaces, therefore it can be used for multi-scale geometric analysis. Curvatures on a surface should be indicative of topographically dependent behavior of a surface and curvatures are, in turn, influenced by the processing and use of the surface. Curvatures have not been well characterized previously. Curvature has been used for calculations in contact mechanics and for the evaluation of cutting edges. In the current work two parts were machined and then one of them was ground. The surface topographies were measured with a scanning laser confocal microscope. Plots of curvatures as a function of position and scale are presented, and the means and standard deviations of principal curvatures are plotted as a function of scale. Statistical analyses show the relations between curvature and these two manufacturing processes at multiple scales.