In recent years, projection-based no-reference point cloud quality metrics have shown remarkable performance on public datasets. These metrics involve projecting the point cloud onto a 2D space from multiple viewpoints and applying traditional image quality metrics to the resulting projected images. However, these existing methods suffer from a measurable projection strategy, which would induce information loss or redundancy leading to training bias and reduced generalizability. To overcome these limitations, we propose AKSNet, a novel no-reference point cloud quality metric that utilizes an adaptive keyframe selection strategy. In particular, we treat the process of point cloud projection as video sequences captured from successive viewpoints and design a keyframe selection module to pick the most representative frames. Based on the selected frames, we can subsequently predict the quality score of the point cloud. Experimental results demonstrate that our method achieves competitive performance in comparison with state-of-the-art methods. While the proposed adaptive keyframe selecting strategy can effectively promote the generalization performance.

In this paper, a new type of hybrid method that hybridizes PCA and EBGM as a two-stage procedure is presented to improve recognition performance in large-scale face recognition. Among various methods in face recognition, PCA is considered to identify human faces by holistic views, while EBGM is supposed to distinguish one face from another by details, but they are both excellent representative methods due to their respective advantages. However, when the size of gallery gets large, the recognition performance of both PCA and EBGM degrades severely. To improve recognition performance with large-scale gallery, we propose a hybrid method, which preprocesses the gallery images with PCA at first stage, and produces the final result with EBGM based on the preliminary result generated by PCA. Since the hybrid method combines the advantages of PCA and EBGM, the recognition performance with large-scale gallery has been improved greatly. Experimental result shows that the hybrid method has a remarkably better recognition accuracy than either PCA or EBGM. Moreover, it seems that the larger the gallery size, the better the improvement. On the other hand, the hybrid method brings no additional computational cost, even less than EBGM.

The sensitivity of a neural network's output to its parameter variation is an important issue in both theoretical researches and practical applications of neural networks. This paper proposes a quantified sensitivity measure of the Radial Basis Function Neural Networks (RBFNNs) to input variation. The sensitivity is defined as the mathematical expectation of squared output deviations caused by input variations. In order to quantify the sensitivity, the input is treated as a statistical variable and a numerical integral technique is employed to approximately compute the expectation. Experimental verifications are run and the results show a very good agreement between the proposed sensitivity computation and computer simulation. The quantified sensitivity measure could be helpful as a general tool for evaluating RBFNNs' performance.

B-spline multiplication, that is, finding the coefficients of the product B-spline of two given B-splines is useful as an end result, in addition to being an important prerequisite component to many other symbolic computation operations on B-splines. Algorithms for B-spline multiplication standardly use indirect approaches such as nodal interpolation or computing the product of each set of polynomial pieces using various bases. The original direct approach is complicated. B-spline blossoming provides another direct approach that can be straightforwardly translated from mathematical equation to implementation; however, the algorithm does not scale well with degree or dimension of the subject tensor product B-splines. To addresses the difficulties mentioned heretofore, we present the Sliding Windows Algorithm (SWA), a new blossoming based algorithm for the multiplication of two B-spline curves, two B-spline surfaces, or any two general multivariate B-splines.

B-spline multiplication, that is, finding the coefficients of the product B-spline of two given B-splines, is useful as an end result, in addition to being an important prerequisite component to many other symbolic computation operations on B-splines. Algorithms for B-spline multiplication standardly use indirect approaches such as nodal interpolation or computing the product of each set of polynomial pieces using various bases. The original direct approach is complicated. B-spline blossoming provides another direct approach that can be straightforwardly translated from mathematical equation to implementation; however, the algorithm does not scale well with degree or dimension of the subject tensor product B-splines. We present the Sliding Windows Algorithm (SWA), a new blossoming based algorithm for B-spline multiplication that addresses the difficulties mentioned heretofore.

Symbolic computation of NURBS plays an important role in many areas of NURBS-based geometric computation and design. However, any nontrivial symbolic computation, especially when rational B-splines are involved, would typically result in B-splines with high degrees. In this paper we develop degree reduction strategies for NURBS symbolic computation on curves. The specific topics we consider include zero curvatures and critical curvatures of plane curves, various ruled surfaces related to space curves, and point/curve bisectors and curve/curve bisectors.

This paper introduces the rational forward difference operator for differential computation on a rational Bezier patch based on its control mesh. With this rational version of the forward difference operator, and by ignoring the appropriate dependent (on lower order derivatives) terms of various derivatives, the derivatives themselves have the same expressions as their polynomial counterparts; the curvature and torsion, and the first and second fundamental forms, all have very similar expressions as those equations from classical differential geometry. This new approach also allows straightforward generalization to higher dimensional rational Bezier patches, the special co-dimension 1 case of which is treated with the result of the first and second fundamental forms.

In manufacturing processes like injection molding or die casting, a 2-piece mold is required to be separable, that is, having both pieces of the molds removed in opposite directions while interfering neither with the mold nor with each other. The fundamental problem is to find a viewing (i.e. separating) direction, from which a valid partition line (i.e. the contact curves of the two mold pieces) exists. While previous research work on this problem exists for polyhedral models, verifying and finding such a partition line for general freeform shapes, represented by NURBS surfaces, is still an open question. This paper shows that such a valid partition exists for a compact surface of genus g, if and only if there is a viewing direction from which the silhouette consists of exactly g + 1 nonsingular disjoint loops. Hence, the 2-piece mold separability problem is essentially reduced to the topological analysis of silhouettes. It follows that the aspect graph, which gives all topologically distinct silhouettes, allows one to determine the existence of a valid partition as well as to find such a partition when it exists. We present an aspect graph computation technique for compact free-form objects represented as NURBS surfaces. All the vision event curves (parabolic curves, flecnodal curves, and bitangency curves) relevant to mold separability are computed by symbolic techniques based on the NURBS representation, combined with numerical processing. An image dilation technique is then used for robust aspect graph cell decomposition on the sphere of viewing directions. Thus, an exact solution to the 2-piece mold separability problem is given for such models.