Mach edges: local features predicted by 3rd derivative spatial filtering

Edges are key points of information in visual scenes. One important class of models supposes that edges correspond to the steepest parts of the luminance profile, implying that they can be found as peaks and troughs in the response of a gradient (1st derivative) filter, or as zero-crossings in the 2nd derivative (ZCs). We tested those ideas using a stimulus that has no local peaks of gradient and no ZCs, at any scale. The stimulus profile is analogous to the Mach ramp, but it is the luminance gradient (not the absolute luminance) that increases as a linear ramp between two plateaux; the luminance profile is a blurred triangle-wave. For all image-blurs tested, observers marked edges at or close to the corner points in the gradient profile, even though these were not gradient maxima. These Mach edges correspond to peaks and troughs in the 3rd derivative. Thus Mach edges are inconsistent with many standard edge-detection schemes, but are nicely predicted by a recent model that finds edge points with a 2-stage sequence of 1st then 2nd derivative operators, each followed by a half-wave rectifier.

Mach edges: a critical test of the nonlinear 3rd derivative model for edge-detection

Feature detection is a crucial stage of visual processing. In previous feature-marking experiments we found that peaks in the 3rd derivative of the luminance profile can signify edges where there are no 1st derivative peaks nor 2nd derivative zero-crossings (Wallis and George 'Mach edges' (the edges of Mach bands) were nicely predicted by a new nonlinear model based on 3rd derivative filtering. As a critical test of the model, we now use a new class of stimuli, formed by adding a linear luminance ramp to the blurred triangle waves used previously. The ramp has no effect on the second or higher derivatives, but the nonlinear model predicts a shift from seeing two edges to seeing only one edge as the added ramp gradient increases. In experiment 1, subjects judged whether one or two edges were visible on each trial. In experiment 2, subjects used a cursor to mark perceived edges and bars. The position and polarity of the marked edges were close to model predictions. Both experiments produced the predicted shift from two to one Mach edge, but the shift was less complete than predicted. We conclude that the model is a useful predictor of edge perception, but needs some modification.

Mach edges: a key role for 3rd derivative filters in spatial vision

Edges are key points of information in visual scenes. One important class of models supposes that edges correspond to the steepest parts of the luminance profile, implying that they can be found as peaks and troughs in the response of a gradient (first-derivative) filter, or as zero-crossings (ZCs) in the second-derivative. A variety of multi-scale models are based on this idea. We tested this approach by devising a stimulus that has no local peaks of gradient and no ZCs, at any scale. Our stimulus profile is analogous to the classic Mach-band stimulus, but it is the local luminance gradient (not the absolute luminance) that increases as a linear ramp between two plateaux. The luminance profile is a smoothed triangle wave and is obtained by integrating the gradient profile. Subjects used a cursor to mark the position and polarity of perceived edges. For all the ramp-widths tested, observers marked edges at or close to the corner points in the gradient profile, even though these were not gradient maxima. These new Mach edges correspond to peaks and troughs in the third-derivative. They are analogous to Mach bands - light and dark bars are seen where there are no luminance peaks but there are peaks in the second derivative. Here, peaks in the third derivative were seen as light-to-dark edges, troughs as dark-to-light edges. Thus Mach edges are inconsistent with many standard edge detectors, but are nicely predicted by a new model that uses a (nonlinear) third-derivative operator to find edge points.

Sustainable supplier management in the automotive industry:leading the 3rd revolution through collaboration

The omnipresent global economic crisis has had a particularly dramatic effect on the global automotive industry. It has increased the need for a 3rd revolution and the move towards mass-collaboration between all industrial players that may ultimately lead to a governance model based on partnership-focused collaborative relationships. The first two revolutions were led by the US and Japan respectively, but we propose that this time, the European automotive industry will lead the way in the 3rd revolution. This new book provides an operations and supply chain management perspective while focusing on the issue of sustainable supplier management. © 2010 by Nova Science Publishers, Inc. All Rights Reserved.

Intellectual property law 3rd edition

The Law Express series is designed to help you revise effectively. This book is your guide to understanding essential concepts, remembering and applying key legislation and making your answers stand out!

Intellectual property law 3rd edition

The Law Express series is designed to help you revise effectively. This book is your guide to understanding essential concepts, remembering and applying key legislation and making your answers stand out!

Social determinants of fruit and vegetable intake and validation of Pro-Children Eating Habits Questionnaire for 3rd and 5th grade children

BACKGROUND: The Pro Children Eating Habits Questionnaire has been evaluated as a valid and reliable tool in Europe to measure determinants of fruit and vegetable intake for children; however, it has not been validation for United States populations. The purpose of this study was to (1) assess the reliability and discrimination validity of fruit and vegetable correlates for the Pro Children Eating Habits Questionnaire; (2) investigate the predictive validity of determinants of fruit and vegetable consumption for multi-ethnic elementary school children; and, (3) to assess the association of social determinants with fruit and vegetable consumption. METHODS: One hundred and thirty elementary school students from the 3rd and 5th grades completed this cross-sectional study. RESULTS: Fruit and vegetable determinants, had satisfactory internal consistencies. No differences were found between the test and the retest for the individual questions with the exception of the question for mean perceived vegetable intake. The discriminatory validity indicated the questionnaire could show differences across grade and gender levels for barriers of fruit and vegetables but not for other factors. Grade together with gender explained barriers to eating fruit and vegetables. Greater availability of fruit in the home and school was associated with higher frequency of consumption. CONCLUSIONS: The results of this study indicate the Pro-Children Eating Habits Questionnaire may be a reliable and valid tool for assessing fruit and vegetable consumption of children in the United States.

Candice Bergen covering Democratic National Convention with Betty Schlein (3rd from left)

General note: Title and date provided by Bettye Lane.

Complete Public Law Text, Cases and Materials, 3rd edition

Complete Public Law: Text, Cases, and Materials combines extracts from key primary and secondary materials with clear explanatory text to provide a complete resource for students of constitutional and administrative law. Clear, concise explanation of key legal principles is combined with a wide range of extracts, from statutes, case law and academic materials to provide a complete resource for students The authors use straightforward and uncomplicated language to ensure legal concepts and the complexities of the British constitution are easily understood Learning features such as thinking points, diagrams, useful notes, summary points and reflective questions provide valuable support for students and encourage them to engage with the subject A helpful 'case study' chapter on human rights, terrorism and the courts illustrates how the Human Rights Act has been used in practice across the legal system, providing extra insight into the importance of both human rights law and the process of judicial review The 'Judicial review: putting it all together in problem answers' chapter pulls together strands from previous chapters to provide a checklist of issues to be considered in order to diagnose a judicial review problem and advise a client

Two years survival rate of Class II ART restorations in primary molars using two ways to avoid saliva contamination

AIM To compare the survival rates of Class II Atraumatic Restorative Treatment (ART) restorations placed in primary molars using cotton rolls or rubber dam as isolation methods. METHODS A total of 232 children, 6-7 years old, both genders, were selected having one primary molar with proximal dentine lesion. The children were randomly assigned into two groups: control group with Class II ART restoration made using cotton rolls and experimental group using rubber dam. The restorations were evaluated by eight calibrated evaluators (Kappa > 0.8) after 6, 12, 18 and 24 months. RESULTS A total of 48 (20.7%) children were considered dropout, after 24 months. The cumulative survival rate after 6, 12, 18 and 24 months was 61.4%, 39.0%, 29.1% and 18.0%, respectively for the control group, and 64.1%, 55.1%, 40.1% and 32.1%, respectively for the rubber dam group. The log rank test for censored data showed no statistical significant difference between the groups (P = 0.07). The univariate Cox Regression showed no statistical significant difference after adjusting for independent variables (P > 0.05). CONCLUSION Both groups had similar survival rates, and after 2 years, the use of rubber dam does not increase the success of Class II ART restorations significantly.

Nspirations And Imports From Bronze Age Pontic Cultures In The Development Of Communities Living Between The Wieprz And Horyn Rivers From The 3rd/2nd To The Middle Of The 2nd Millennium BC

This publication constitutes the fruits of National Science Centre research projects (grant no 2011/01/M/HS3/02142 – 6 articles) and the National Programme for the Development of the Humanities (grant no 0108/NPH3/H12/82/2014 – 3 articles). We would like to acknowledge and at the same time express our sincere gratitude for the generosity shown by the following at the Adam Mickiewicz University in making this publication possible: the Dean of the Department of History, Institute of Pre-history and the Eastern Institute.

Late eneolithic and bronze age prologue pontic societies . Forest-steppe middle dniester and prut drainage basins in the 4th/3rd-2nd millennium bc: a history of investigations

The paper presents a historiographic context helpful in the current investigations of the cultural contacts between the societies of the east and west of Europe in the borderland of Podolia and moldova in the late Eneolithic and the prologue of the Bronze age . The focus is on the state of research (chiefly taxonomic and topogenetic) into the sequence of taxa in the age of early ‘barrow-building’, identified in the funerary rituals of societies settling the forest-steppe of the north- western Black Sea Coast in the 4th/3rd-2nd millennium BC .