Evaluation of form data using computational geometric techniques—Part I: Circularity error

The present work deals with evaluation of form error from the measured profiles obtained using a form tester, namely roundness/cylindricity measuring instrument. In Part I, details of circularity evaluation are presented. Due to eccentricity in component setting and radius-suppression inherent in the measurement, circularity error has to be evaluated with reference to a limacon. A computational geometry-based algorithm is proposed for establishing minimum circumscribed, maximum inscribed and minimum zone limacons. A new type of control hull for directly constructing equi-angular diagrams and a new procedure for updating are introduced. Validation has been done with bench-mark data set and corresponding results available in the literature. Being geometry-based algorithm, it is simple to follow and each iteration can be visualized and interpreted geometrically. On comparison with simplex search method, the proposed algorithm is found to be computationally efficient in terms of accuracy and time taken. The proposed methods can be easily implemented in computer-aided roundness measuring instruments. Extension of this work for evaluation of cylindricity error has been dealt in Part II.     

Connectionist Finite State Natural Language Processing

Unless one is prepared to argue that existing, ‘classical’formal language and automata theory, together with the natural language linguistics built on them, are fundamentally mistaken about the nature of language, any viable connectionist natural language processing (NLP) model will have to be characterizable, at least approximately, by some generative grammar or by an automaton of the corresponding class. An obvious way of ensuring that a connectionist NLP device is so characterizable is to specify it in classical terms and then to implement it in an artificial neural network, and that is what this paper does. It adopts the deterministic pushdown transducer (DPDT) as an adequate formal model for general NLP and shows how a simple recurrent network (SRN) can be trained to implement a finite state transducer (FST) which simulates the DPDT. A computer simulation of a parser for a small fragment of English is used to study the properties of the model. The conclusion is that such SRN implementation results in a device which is broadly consistent with its classical specification, but also has emergent properties relative to that specification which are desirable in an NLP device.     

Continuous-time orbit problems are decidable in polynomial-time

We place the continuous-time orbit problem in P$\mathsf{P}$, sharpening the decidability result shown by Hainry [7].     

On hypercube packings,blocking sets and a covering problem

Consider sets S of hypercubes of side 2 in the discrete n-dimensional torus of side 4 with the property that every possible hypercube of side 2 has a nonempty intersection with some hypercube in S. The problem of minimizing the size of S is studied in two settings, depending on whether intersections between hypercubes in S are allowed or not. If intersections are not allowed, then one is asking for the smallest size of a non-extensible packing S  ; this size is denoted by f(n)$f(n)$. If intersections are allowed, then the structure S is called a blocking set. The smallest size of a blocking set S   is denoted by h(n)$h(n)$. By computer-aided techniques, it is shown that f(5)=12$f(5)=12$, f(6)=16$f(6)=16$, h(6)=15$h(6)=15$ and h(7)≤23$h(7)\le 23$. Also, non-extensible packings as well as blocking sets of certain small sizes are classified for n≤6$n\le 6$. There is a direct connection between these problems and a covering problem originating from the football pools.     

Projective Feature Learning for 3D Shapes with Multi‐View Depth Images

Feature learning for 3D shapes is challenging due to the lack of natural paramterization for 3D surface models. We adopt the multi‐view depth image representation and propose Multi‐View Deep Extreme Learning Machine (MVD‐ELM) to achieve fast and quality projective feature learning for 3D shapes. In contrast to existing multi‐view learning approaches, our method ensures the feature maps learned for different views are mutually dependent via shared weights and in each layer, their unprojections together form a valid 3D reconstruction of the input 3D shape through using normalized convolution kernels. These lead to a more accurate 3D feature learning as shown by the encouraging results in several applications. Moreover, the 3D reconstruction property enables clear visualization of the learned features, which further demonstrates the meaningfulness of our feature learning.     

Mesh Denoising using Extended ROF Model with L1 Fidelity

This paper presents a variational algorithm for feature‐preserved mesh denoising. At the heart of the algorithm is a novel variational model composed of three components: fidelity, regularization and fairness, which are specifically designed to have their intuitive roles. In particular, the fidelity is formulated as an L₁ data term, which makes the regularization process be less dependent on the exact value of outliers and noise. The regularization is formulated as the total absolute edge‐lengthed supplementary angle of the dihedral angle, making the model capable of reconstructing meshes with sharp features. In addition, an augmented Lagrange method is provided to efficiently solve the proposed variational model. Compared to the prior art, the new algorithm has crucial advantages in handling large scale noise, noise along random directions, and different kinds of noise, including random impulsive noise, even in the presence of sharp features. Both visual and quantitative evaluation demonstrates the superiority of the new algorithm.     

Semi‐Regular Triangle Remeshing: A Comprehensive Study

Semi‐regular triangle remeshing algorithms convert irregular surface meshes into semi‐regular ones. Especially in the field of computer graphics, semi‐regularity is an interesting property because it makes meshes highly suitable for multi‐resolution analysis. In this paper, we survey the numerous remeshing algorithms that have been developed over the past two decades. We propose different classifications to give new and comprehensible insights into both existing methods and issues. We describe how considerable obstacles have already been overcome, and discuss promising perspectives.