A closed formula for the number of convex permutominoes

In this paper we determine a closed formula for the number of convex permutominoes of size n. We reach this goal by providing a recursive generation of all convex permutominoes of size n+1 from the objects of size n, according to the ECO method, and then translating this construction into a system of functional equations satisfied by the generating function of convex permutominoes. As a consequence we easily obtain also the enumeration of some classes of convex polyominoes, including stack and directed convex permutominoes

Rapid Online Analysis of Local Feature Detectors and Their Complementarity

A vision system that can assess its own performance and take appropriate actions online to maximize its effectiveness would be a step towards achieving the long-cherished goal of imitating humans. This paper proposes a method for performing an online performance analysis of local feature detectors, the primary stage of many practical vision systems. It advocates the spatial distribution of local image features as a good performance indicator and presents a metric that can be calculated rapidly, concurs with human visual assessments and is complementary to existing offline measures such as repeatability. The metric is shown to provide a measure of complementarity for combinations of detectors, correctly reflecting the underlying principles of individual detectors. Qualitative results on well-established datasets for several state-of-the-art detectors are presented based on the proposed measure. Using a hypothesis testing approach and a newly-acquired, larger image database, statistically-significant performance differences are identified. Different detector pairs and triplets are examined quantitatively and the results provide a useful guideline for combining detectors in applications that require a reasonable spatial distribution of image features. A principled framework for combining feature detectors in these applications is also presented. Timing results reveal the potential of the metric for online applications. © 2013 by the authors; licensee MDPI, Basel, Switzerland

On the exhaustive generation of convex permutominoes

A permutomino of size n is a polyomino determined by a pair of permutations of size n+1, such that they differ in each position. In this paper, after recalling some enumerative results about permutominoes, we give a first algorithm for the exhaustive generation of a particular class of permutominoes, the convex permutominoes, proving that its cost is proportional to the number of generated objects.Comment: 15 pages, 14 figure

A tension approach to controlling the shape of cubic spline surfaces on FVS triangulations

We propose a parametric tensioned version of the FVS macro-element to control the shape of the composite surface and remove artificial oscillations, bumps and other undesired behaviour. In particular, this approach is applied to C1 cubic spline surfaces over a four-directional mesh produced by two-stage scattered data fitting methods

A Computational Model of the Short-Cut Rule for 2D Shape Decomposition

We propose a new 2D shape decomposition method based on the short-cut rule. The short-cut rule originates from cognition research, and states that the human visual system prefers to partition an object into parts using the shortest possible cuts. We propose and implement a computational model for the short-cut rule and apply it to the problem of shape decomposition. The model we proposed generates a set of cut hypotheses passing through the points on the silhouette which represent the negative minima of curvature. We then show that most part-cut hypotheses can be eliminated by analysis of local properties of each. Finally, the remaining hypotheses are evaluated in ascending length order, which guarantees that of any pair of conflicting cuts only the shortest will be accepted. We demonstrate that, compared with state-of-the-art shape decomposition methods, the proposed approach achieves decomposition results which better correspond to human intuition as revealed in psychological experiments.Comment: 11 page

On the Distribution of Salient Objects in Web Images and its Influence on Salient Object Detection

It has become apparent that a Gaussian center bias can serve as an important prior for visual saliency detection, which has been demonstrated for predicting human eye fixations and salient object detection. Tseng et al. have shown that the photographer's tendency to place interesting objects in the center is a likely cause for the center bias of eye fixations. We investigate the influence of the photographer's center bias on salient object detection, extending our previous work. We show that the centroid locations of salient objects in photographs of Achanta and Liu's data set in fact correlate strongly with a Gaussian model. This is an important insight, because it provides an empirical motivation and justification for the integration of such a center bias in salient object detection algorithms and helps to understand why Gaussian models are so effective. To assess the influence of the center bias on salient object detection, we integrate an explicit Gaussian center bias model into two state-of-the-art salient object detection algorithms. This way, first, we quantify the influence of the Gaussian center bias on pixel- and segment-based salient object detection. Second, we improve the performance in terms of F1 score, Fb score, area under the recall-precision curve, area under the receiver operating characteristic curve, and hit-rate on the well-known data set by Achanta and Liu. Third, by debiasing Cheng et al.'s region contrast model, we exemplarily demonstrate that implicit center biases are partially responsible for the outstanding performance of state-of-the-art algorithms. Last but not least, as a result of debiasing Cheng et al.'s algorithm, we introduce a non-biased salient object detection method, which is of interest for applications in which the image data is not likely to have a photographer's center bias (e.g., image data of surveillance cameras or autonomous robots)