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This paper addresses the problem of timber board positioning within the log where they were sawn from. The method takes as input log and board end cross-section images. It uses a two-step image matching method based on scale invariant feature transform and normalized correlation coefficient (NCC). In the first step, the scale factor and rotation angle of board end images are estimated from the board images that are correctly identified on the log end image by SIFT. Then, the accurate position of each board within the log end image is achieved by the NCC method. The method has been tested on 70 different log images and the 798 corresponding board images of various visual aspects and coming from three different species (Douglas fir, Norway spruce, and oak). The results fully demonstrate that the proposed method is not only rotation and scale invariant, but also has high accuracy properties. [ABSTRACT FROM AUTHOR]

Topology preservation is a property of affine transformations in R 2 , but not in Z 2 . In this article, given a binary object X ⊂ Z 2 and an affine transformation A , we propose a method for building a binary object X ^ ⊂ Z 2 resulting from the application of A on X . Our purpose is, in particular, to preserve the homotopy type between X and X ^ . To this end, we formulate the construction of X ^ from X as an optimization problem in the space of cellular complexes, and we solve this problem under topological constraints. More precisely, we define a cellular space H by superimposition of two cellular spaces F and G corresponding to the canonical Cartesian grid of Z 2 where X is defined, and a regular grid induced by the affine transformation A , respectively. The object X ^ is then computed by building a homotopic transformation within the space H , starting from the complex in G resulting from the transformation of X with respect to A and ending at a complex fitting X ^ in F that can be embedded back into Z 2 . [ABSTRACT FROM AUTHOR]

Reliable hand gesture recognition is extremely relevant for automatic interpretation of sign languages used by people with hearing and speech disabilities. In this work, we present (i) new benchmark datasets of depth-sensor based, multi-oriented, isolated and static hand gestures of numerals and alphabets following the conventions of American Sign Language (ASL), (ii) an effective strategy for segmentation of hand region from depth data and appropriate preprocessing for feature extraction, and (iii) an effective statistical-geometrical feature set for recognition of multi-oriented hand gestures. Besides setting benchmark performances on the developed datasets, viz. 97.67%, 96.53% and 96.86% on numerals, alphabets and alpha-numerals respectively, the proposed pipeline is also implemented on two related public datasets and is found superior to state-of-the-art methods reported so far. [ABSTRACT FROM AUTHOR]

Rigid motions (i.e. transformations based on translations and rotations) are simple, yet important, transformations in image processing. In Rn, they are both topology and geometry preserving. Unfortunately, these properties are generally lost in Zn. In particular, when applying a rigid motion on a digital object, one generally alters its structure but also the global shape of its boundary. These alterations are mainly caused by digitization during the transformation process. In this specific context, some solutions for the handling of topological issues were proposed in Z2. In this article, we also focus on geometric issues in Z2. Indeed, we propose a rigid motion scheme that preserves geometry and topology properties of the transformed digital object: a connected object will remain connected, and some geometric properties (e.g. convexity, area and perimeter) will be preserved. To reach that goal, our main contributions are twofold. First, from an algorithmic point of view, our scheme relies on (1) a polygonization of the digital object, (2) the transformation of the intermediate piecewise affine object of R2 and (3) a digitization step for recovering a result within Z2. The intermediate modeling of a digital object of Z2 as a piecewise affine object of R2 allows us to avoid the geometric alterations generally induced by standard pointwise rigid motions. However, the final digitization of the polygon back to Z2 has to be carried out cautiously. In particular, our second, theoretical contribution is a notion of quasi-regularity that provides sufficient conditions to be fulfilled by a continuous object for guaranteeing both topology and geometry preservation during its digitization. [ABSTRACT FROM AUTHOR]

We investigate inflation with a class of concave inflaton potentials of the form ∼ ϕ n (0 < n < 1) in the Randall–Sundrum model with an infinite extra spatial dimension. We show that this class of models is much more in good agreement with observations compared to the standard inflation. We also find the range of the five-dimensional Planck scale ( M 5 ) and show that large tensor-to-scalar ratios do not eliminate small-field inflation in braneworld cosmology. [ABSTRACT FROM AUTHOR]

The notion of tangential cover, based on maximal segments, is a well-known tool to study the geometrical characteristics of a discrete curve. However, it is not robust to noise, while extracted contours from digital images typically contain noise, and this makes the geometric analysis tasks on such contours difficult. To tackle this issue, we investigate in this paper a discrete structure, named adaptive tangential cover (ATC), which is based on the notion of tangential cover and on a local noise estimator. More specifically, the ATC is composed of maximal segments with different widths deduced from the local noise values estimated at each point of the contour. Furthermore, a parameter-free algorithm is also presented to compute ATC. This study leads to the proposal of several applications of ATC on noisy digital contours: dominant point detection, contour length estimator, tangent/normal estimator, detection of convex and concave parts. An extension of ATC to 3D curves is also proposed in this paper. The experimental results demonstrate the efficiency of this new notion. [ABSTRACT FROM AUTHOR]

Rigid transformations are involved in a wide range of digital image processing applications. In such a context, they are generally considered as continuous processes, followed by a digitization of the results. Recently, rigid transformations on ℤ have been alternatively formulated as a fully discrete process. Following this paradigm, we investigate - from a combinatorial point of view - the effects of pixel-invariance constraints on such transformations. In particular we describe the impact of these constraints on both the combinatorial structure of the transformation space and the algorithm leading to its generation. [ABSTRACT FROM AUTHOR]

In the continuous domain $\mathbb{R}^{n}$, rigid transformations are topology-preserving operations. Due to digitization, this is not the case when considering digital images, i.e., images defined on $\mathbb{Z}^{n}$. In this article, we begin to investigate this problem by studying conditions for digital images to preserve their topological properties under all rigid transformations on $\mathbb{Z}^{2}$. Based on (i) the recently introduced notion of DRT graph, and (ii) the notion of simple point, we propose an algorithm for evaluating digital images topological invariance. [ABSTRACT FROM AUTHOR]