Computing a Compact Spline Representation of the Medial Axis Transform of a 2D Shape

We present a full pipeline for computing the medial axis transform of an arbitrary 2D shape. The instability of the medial axis transform is overcome by a pruning algorithm guided by a user-defined Hausdorff distance threshold. The stable medial axis transform is then approximated by spline curves in 3D to produce a smooth and compact representation. These spline curves are computed by minimizing the approximation error between the input shape and the shape represented by the medial axis transform. Our results on various 2D shapes suggest that our method is practical and effective, and yields faithful and compact representations of medial axis transforms of 2D shapes.Comment: GMP14 (Geometric Modeling and Processing

Distributive and trimedial quasigroups of order 243

We enumerate three classes of non-medial quasigroups of order $243=3^5$ up to isomorphism. There are $17004$ non-medial trimedial quasigroups of order $243$ (extending the work of Kepka, B\'en\'eteau and Lacaze), $92$ non-medial distributive quasigroups of order $243$ (extending the work of Kepka and N\v{e}mec), and $6$ non-medial distributive Mendelsohn quasigroups of order $243$ (extending the work of Donovan, Griggs, McCourt, Opr\v{s}al and Stanovsk\'y). The enumeration technique is based on affine representations over commutative Moufang loops, on properties of automorphism groups of commutative Moufang loops, and on computer calculations with the \texttt{LOOPS} package in \texttt{GAP}

3. The Reformed Formulation

The Protestant movement on the Continent may be divided into three parts: a conservative expression in Lutheranism, a diverse radical expression typified by Anabaptism, and a medial expression in the Reformed churches. The latter arose from two separate representations of the Protestant spirit, both in Switzerland: the Zwinlian in Zurich and, later, the Calvinist in Geneva. [excerpt

Acoustic Correlates to Ambisyllabic Representations in American English

The syllabic affiliation of ambisyllabic consonants (e.g. the /m/ in limit) is unclear. Standard analyses argue for their simultaneous linkage to the preceding and following syllables (Kahn, 1976; Kenstowicz, 1994). However, others have argued that a reformulation of the crucial phonological processes in terms of foot-structure eliminates the need for syllabic representations all together (Jensen, 2000; Kiparsky, 1979). There is even a lack of consensus in the literature about the onsets and codas. It has been argued that there is little to no perceptual evidence through priming experiments for syllable structure (Schiller, Costa, & Colome 2002; Schiller, Meyer, & Levelt 1997). On the contrary, through a syllable tracking task, Nesbitt & Durvasula (2015) argue that listeners do perceive a difference between word-medial onset and codas. Furthermore, they argued that listeners treated words containing ambisyllabic consonants similar to those containing word-medial coda consonants. With so many conflicting findings, the question remains: Are syllabic representations available to speaker/listeners of American English? If so, what acoustic cues are utilized to indicate such representations for ambisyllabic consonants? For this paper, recorded speech was extracted from the Buckeye Corpus (Pitt et al 2007), and analyzed to determine the acoustic effects of word-medial consonants. We compared duration and pitch measurements of vowels preceding ambisyllabic consonants to those preceding word-medial coda and word-medial onset consonants in American English. We conclude that American English speakers have a coda representation for ambisyllabic consonants. They produce vowels preceding these consonants and word-medial coda consonants with a shorter duration and lower pitch than they do vowels preceding word-medial onset consonants

Population-based fitting of medial shape models with correspondence optimization

pre-printA crucial problem in statistical shape analysis is establishing the correspondence of shape features across a population. While many solutions are easy to express using boundary representations, this has been a considerable challenge for medial representations. This paper uses a new 3-D medial model that allows continuous interpolation of the medial manifold and provides a map back and forth between it and the boundary. A measure defined on the medial surface then allows one to write integrals over the boundary and the object interior in medial coordinates, enabling the expression of important object properties in an object-relative coordinate system.We use these integrals to optimize correspondence during model construction, reducing variability due to the model parameterization that could potentially mask true shape change effects. Discrimination and hypothesis testing of populations of shapes are expected to benefit, potentially resulting in improved significance of shape differences between populations even with a smaller sample size

Geometry of isophote curves

In this paper, we consider the intensity surface of a 2D image, we study the evolution of the symmetry sets (and medial axes) of 1-parameter families of iso-intensity curves. This extends the investigation done on 1-parameter families of smooth plane curves (Bruce and Giblin, Giblin and Kimia, etc.) to the general case when the family of curves includes a singular member, as will happen if the curves are obtained by taking plane sections of a smooth surface, at the moment when the plane becomes tangent to the surface. Looking at those surface sections as isophote curves, of the pixel values of an image embedded in the real plane, this allows us to propose to combine object representation using a skeleton or symmetry set representation and the appearance modelling by representing image information as a collection of medial representations for the level-sets of an image.Comment: 15 pages, 7 figure

Specialization of the rostral prefrontal cortex for distinct analogy processes

Analogical reasoning is central to learning and abstract thinking. It involves using a more familiar situation (source) to make inferences about a less familiar situation (target). According to the predominant cognitive models, analogical reasoning includes 1) generation of structured mental representations and 2) mapping based on structural similarities between them. This study used functional magnetic resonance imaging to specify the role of rostral prefrontal cortex (PFC) in these distinct processes. An experimental paradigm was designed that enabled differentiation between these processes, by temporal separation of the presentation of the source and the target. Within rostral PFC, a lateral subregion was activated by analogy task both during study of the source (before the source could be compared with a target) and when the target appeared. This may suggest that this subregion supports fundamental analogy processes such as generating structured representations of stimuli but is not specific to one particular processing stage. By contrast, a dorsomedial subregion of rostral PFC showed an interaction between task (analogy vs. control) and period (more activated when the target appeared). We propose that this region is involved in comparison or mapping processes. These results add to the growing evidence for functional differentiation between rostral PFC subregions

Prosodic constituents in the representation of consonantal sequences in Polish

The aim of this paper is to show what role prosodic constituents, especially the foot and the prosodic word play in Polish phonology. The focus is placed on their function in the representation of extrasyllabic consonants in word-initial, word-medial, and word-final positions. The paper is organized as follows. In the first section, I show that the foot and the prosodic word are well-motivated prosodic constituents in Polish prosody. In the second part, I discuss consonant clusters in Polish focussing on segments that are not parsed into a syllable due to violations of the Sonority Sequencing Generalisation, i.e. extrasyllabic segments. Finally, I analyze possible representations of the extrasyllabic consonants and conclude that both the foot and the prosodic word play a crucial role in terms of licensing. My proposal differs from the ones by Rubach and Booij (1990b) and Rubach (1997) in that I argue that the word-initial sonorants traditionally called extrasyllabic are licenced by the foot and not by the prosodic word (cf. Rubach and Booij (1990b)) or the syllable (cf. Rubach (1997)). For my analysis I adopt the framework of Optimality Theory, cf. McCarthy and Prince (1993), Prince and Smolensky (1993), in which derivational levels are abandoned and only surface representations are evaluated by means of universal constraints

Hippocampal Global Remapping Can Occur without Input from the Medial Entorhinal Cortex.

The high storage capacity of the episodic memory system relies on distinct representations for events that are separated in time and space. The spatial component of these computations includes the formation of independent maps by hippocampal place cells across environments, referred to as global remapping. Such remapping is thought to emerge by the switching of input patterns from specialized spatially selective cells in medial entorhinal cortex (mEC), such as grid and border cells. Although it has been shown that acute manipulations of mEC firing patterns are sufficient for inducing hippocampal remapping, it remains unknown whether specialized spatial mEC inputs are necessary for the reorganization of hippocampal spatial representations. Here, we examined remapping in rats without mEC input to the hippocampus and found that highly distinct spatial maps emerged rapidly in every individual rat. Our data suggest that hippocampal spatial computations do not depend on inputs from specialized cell types in mEC