Curve Reconstruction via the Global Statistics of Natural Curves

Reconstructing the missing parts of a curve has been the subject of much computational research, with applications in image inpainting, object synthesis, etc. Different approaches for solving that problem are typically based on processes that seek visually pleasing or perceptually plausible completions. In this work we focus on reconstructing the underlying physically likely shape by utilizing the global statistics of natural curves. More specifically, we develop a reconstruction model that seeks the mean physical curve for a given inducer configuration. This simple model is both straightforward to compute and it is receptive to diverse additional information, but it requires enough samples for all curve configurations, a practical requirement that limits its effective utilization. To address this practical issue we explore and exploit statistical geometrical properties of natural curves, and in particular, we show that in many cases the mean curve is scale invariant and oftentimes it is extensible. This, in turn, allows to boost the number of examples and thus the robustness of the statistics and its applicability. The reconstruction results are not only more physically plausible but they also lead to important insights on the reconstruction problem, including an elegant explanation why certain inducer configurations are more likely to yield consistent perceptual completions than others.Comment: CVPR versio

Recognition of feature curves on 3D shapes using an algebraic approach to Hough transforms

Feature curves are largely adopted to highlight shape features, such as sharp lines, or to divide surfaces into meaningful segments, like convex or concave regions. Extracting these curves is not sufficient to convey prominent and meaningful information about a shape. We have first to separate the curves belonging to features from those caused by noise and then to select the lines, which describe non-trivial portions of a surface. The automatic detection of such features is crucial for the identification and/or annotation of relevant parts of a given shape. To do this, the Hough transform (HT) is a feature extraction technique widely used in image analysis, computer vision and digital image processing, while, for 3D shapes, the extraction of salient feature curves is still an open problem. Thanks to algebraic geometry concepts, the HT technique has been recently extended to include a vast class of algebraic curves, thus proving to be a competitive tool for yielding an explicit representation of the diverse feature lines equations. In the paper, for the first time we apply this novel extension of the HT technique to the realm of 3D shapes in order to identify and localize semantic features like patterns, decorations or anatomical details on 3D objects (both complete and fragments), even in the case of features partially damaged or incomplete. The method recognizes various features, possibly compound, and it selects the most suitable feature profiles among families of algebraic curves

Analytical Method of Modelling the Geometric System of Communication Route

The paper presents a new analytical approach to modelling the curvature of a communication route by making use of differential equations. The method makes it possible to identify both linear and nonlinear curvature. It enables us to join curves of the same or opposite signs of curvature. Solutions of problems for linear change of curvature and selected variants of nonlinear curvature in polynomial and trigonometric form were analyzed. A comparison of determined horizontal transition curves was made and examples of negotiating these curves into a geometric system were given

Association between shell morphology of micro-land snails (genus Plectostoma) and their predator’s predatory behaviour

Predator–prey interactions are among the main ecological interactions that shape the diversity of biological form. In many cases, the evolution of the mollusc shell form is presumably driven by predation. However, the adaptive significance of several uncommon, yet striking, shell traits of land snails are still poorly known. These include the distorted coiled “tuba” and the protruded radial ribs that can be found in micro-landsnails of the genus Plectostoma. Here, we experimentally tested whether these shell traits may act as defensive adaptations against predators. We characterised and quantified the possible anti-predation behaviour and shell traits of Plectostoma snails both in terms of their properties and efficiencies in defending against the Atopos slug predatory strategies, namely, shell-apertural entry and shell-drilling. The results showed that Atopos slugs would first attack the snail by shell-apertural entry, and, should this fail, shift to the energetically more costly shell-drilling strategy. We found that the shell tuba of Plectostoma snails is an effective defensive trait against shell-apertural entry attack. None of the snail traits, such as resting behaviour, shell thickness, shell tuba shape, shell rib density and intensity can fully protect the snail from the slug’s shell-drilling attack. However, these traits could increase the predation costs to the slug. Further analysis on the shell traits revealed that the lack of effectiveness in these anti-predation shell traits may be caused by a functional trade-off between shell traits under selection of two different predatory strategies

On growth and form of irregular coiled-shell of a terrestrial snail: Plectostoma concinnum (Fulton, 1901) (Mollusca: Caenogastropoda: Diplommatinidae)

The molluscan shell can be viewed as a petrified representation of the organism’s ontogeny and thus can be used as a record of changes in form during growth. However, little empirical data is available on the actual growth and form of shells, as these are hard to quantify and examine simultaneously. To address these issues, we studied the growth and form of a land snail that has an irregularly coiled and heavily ornamented shell–Plectostoma concinnum. The growth data were collected in a natural growth experiment and the actual form changes of the aperture during shell ontogeny were quantified. We used an ontogeny axis that allows data of growth and form to be analysed simultaneously. Then, we examined the association between the growth and the form during three different whorl growing phases, namely, the regular coiled spire phase, the transitional constriction phase, and the distortedly-coiled tuba phase. In addition, we also explored the association between growth rate and the switching between whorl growing mode and rib growing mode. As a result, we show how the changes in the aperture ontogeny profiles in terms of aperture shape, size and growth trajectory, and the changes in growth rates, are associated with the different shell forms at different parts of the shell ontogeny. These associations suggest plausible constraints that underlie the three different shell ontogeny phases and the two different growth modes. We found that the mechanism behind the irregularly coiled-shell is the rotational changes of the animal’s body and mantle edge with respect to the previously secreted shell. Overall, we propose that future study should focus on the role of the mantle and the columellar muscular system in the determination of shell form

TEXTILE PATTERNS FOR INTERIOR DESIGN WITH THREE-DIMENSIONAL SPIRALS

Three-dimensional (3D) spirals are fascinating geometric shapes that are used in a variety of applications, such as textile fabric pattern and texture design, architecture, art, and engineering. In this paper, design of patterns using three-dimensional spirals are explored. The work began by discussing the mathematical properties of spirals and their applications. Then, several techniques for designing textile patterns are presented, including the use computer algorithms. Finally, examples of patterns that have been designed using spirals are presented. A comparative analysis was made with available literary sources. Guidelines for applying the obtained results in practice and guidelines for continuing this development are proposed