Statistical analysis of measures of non-convexity

Several measures of non-convexity (departures from convexity) have been introduced in the literature, both for sets and functions. Some of them are of geometric nature, while others are more of topological nature. We address the statistical analysis of some of these measures of non-convexity of a set $S$, by dealing with their estimation based on a sample of points in $S$. We introduce also a new measure of non-convexity. We discuss briefly about these different notions of non-convexity, prove consistency and find the asymptotic distribution for the proposed estimators. We also consider the practical implementation of these estimators and illustrate their applicability to a real data example

Performance evaluation of feature sets for carried object detection in still images

2014 Summer.Includes bibliographical references.Human activity recognition has gathered a lot of interest. The ability to accurately detect carried objects on human beings will directly help activity recognition. This thesis performs evaluation of four different features for carried object detection. To detect carried objects, image chips in a video are extracted by tracking moving objects using an off the shelf tracker. Pixels with similar colors are grouped together by using a superpixel segmentation algorithm. Features are calculated with respect to every superpixel, encoding information regarding their location in the track chip, shape of the superpixel, pose of the person in the track chip, and appearance of the superpixel. ROC curves are used for analyzing the detection of a superpixel as a carried object using these features individually or in a combination. These ROC curves show that the detection using Shape features as they are calculated have very less information. The location features, though simple to calculate, have a significant usable information. Detection using pose of a person in the track chip and appearance of the superpixel depend largely on the data used for their calculation. Pose detections are more likely to be correct if there are no occlusions, while appearance work better if we have high resolution of input images

Influence of nuclei segmentation on breast cancer malignancy classification

Breast Cancer is one of the most deadly cancers affecting middle–aged women. Accurate diagnosis and prognosis are crucial to reduce the high death rate. Nowadays there are numerous diagnostic tools for breast cancer diagnosis. In this paper we discuss a role of nuclear segmentation from fine needle aspiration biopsy (FNA) slides and its influence on malignancy classification. Classification of malignancy plays a very important role during the diagnosis process of breast cancer. Out of all cancer diagnostic tools, FNA slides provide the most valuable information about the cancer malignancy grade which helps to choose an appropriate treatment. This process involves assessing numerous nuclear features and therefore precise segmentation of nuclei is very important. In this work we compare three powerful segmentation approaches and test their impact on the classification of breast cancer malignancy. The studied approaches involve level set segmentation, fuzzy c–means segmentation and textural segmentation based on co–occurrence matrix. Segmented nuclei were used to extract nuclear features for malignancy classification. For classification purposes four different classifiers were trained and tested with previously extracted features. The compared classifiers are Multilayer Perceptron (MLP), Self–Organizing Maps (SOM), Principal Component–based Neural Network (PCA) and Support Vector Machines (SVM). The presented results show that level set segmentation yields the best results over the three compared approaches and leads to a good feature extraction with a lowest average error rate of 6.51% over four different classifiers. The best performance was recorded for multilayer perceptron with an error rate of 3.07% using fuzzy c–means segmentation

Carried object detection and tracking using geometric shape models and spatio-temporal consistency

This paper proposes a novel approach that detects and tracks carried objects by modelling the person-carried object relationship that is characteristic of the carry event. In order to detect a generic class of carried objects, we propose the use of geometric shape models, instead of using pre-trained object class models or solely relying on protrusions. In order to track the carried objects, we propose a novel optimization procedure that combines spatio-temporal consistency characteristic of the carry event, with conventional properties such as appearance and motion smoothness respectively. The proposed approach substantially outperforms a state-of-the-art approach on two challenging datasets PETS2006 and MINDSEYE2012

MapSets: Visualizing embedded and clustered graphs

In addition to objects and relationships between them, groups or clusters of objects are an essential part of many real-world datasets: party affiliation in political networks, types of living organisms in the tree of life, movie genres in the internet movie database. In recent visualization methods, such group information is conveyed by explicit regions that enclose related elements. However, when in addition to fixed cluster membership, the input elements also have fixed positions in space (e.g., geo-referenced data), it becomes difficult to produce readable visualizations. In such fixed-clustering and fixed-embedding settings, some methods produce fragmented regions, while other produce contiguous (connected) regions that may contain overlaps even if the input clusters are disjoint. Both fragmented regions and unnecessary overlaps have a detrimental effect on the interpretation of the drawing. With this in mind, we propose MapSets: a visualization technique that combines the advantages of both methods, producing maps with non-fragmented and non-overlapping regions. The proposed method relies on a theoretically sound geometric algorithm which guarantees contiguity and disjointness of the regions, and also optimizes the convexity of the regions. A fully functional implementation is available in an online system and is used in a comparison with related earlier methods. © 2015, Brown University. All right reserved.National Science Foundation, NSF: 111597

MapSets: Visualizing embedded and clustered graphs

We describe MapSets, a method for visualizing embedded and clustered graphs. The proposed method relies on a theoretically sound geometric algorithm, which guarantees the contiguity and disjointness of the regions representing the clusters, and also optimizes the convexity of the regions. A fully functional implementation is available online and is used in a comparison with related earlier methods. © Springer-Verlag Berlin Heidelberg 2014

Mesures de regularitat per a polígons convexos

Al llarg d'aquesta memòria, hem plantejat possibles mesures de regularitat, totes elles justificades, per a un n-gon convex qualsevol que han donat lloc a problemes de geometria discreta i computacional. A més, hem estat capaços d'oferir algorismes per al seu càlcul de complexitat baixa (i, en alguns casos, òptima) i, per tant, realitzables. Els mètodes proposats són, en algunes ocasions, l'aplicació de resultats més generals, en d'altres, algorismes ad hoc, i, en d'altres, un estudi acurat permet transformar el problema que s'ha de resoldre en un altre problema d'optimització geomètrica que té una solució eficient coneguda

Mesures de regularitat per a polígons convexos

Al llarg d'aquesta memòria, hem plantejat possibles mesures de regularitat, totes elles justificades, per a un n-gon convex qualsevol que han donat lloc a problemes de geometria discreta i computacional. A més, hem estat capaços d'oferir algorismes per al seu càlcul de complexitat baixa (i, en alguns casos, òptima) i, per tant, realitzables. Els mètodes proposats són, en algunes ocasions, l'aplicació de resultats més generals, en d'altres, algorismes ad hoc, i, en d'altres, un estudi acurat permet transformar el problema que s'ha de resoldre en un altre problema d'optimització geomètrica que té una solució eficient coneguda

Morphometrics of Southern Ocean diatoms using high throughput imaging and semi-automated image analysis

Since the ADIAC project, which ended more than 15 years ago, not much progress in automating morphometric analysis of diatoms from slide-mounted material has been published, and no ready-to-use system has become available. This thesis work is the first to implement such a system completely, covering all aspects of the underlying imaging and image processing pipeline, by combining a commercially available slide scanning microscope with my diatom morphometry software SHERPA. I was able to show the applicability as well as the potential of this approach by executing a series of smaller and two large-scale morphometry projects. The extensive sampling sizes, which were made possible only by the new workflow, enabled the first observations of life cycle related size distribution changes of Fragilariopsis kerguelensis in its natural habitat, leading to hypotheses on influences of reproduction, grazing and environmental changes in one of the most important diatom species of the Southern Ocean. In a second large-scale investigation, SHERPA's precise morphometric measurements revealed a second F. kerguelensis morphotype, which has not been recognized before, even though the species, as well as the very material I analyzed, have been investigated intensely before by experienced diatomists; a result not disqualifying their work, but rather underlining that explicit and precise quantification of morphological information has a strong potential to generate novel scientific insights. This new morphotype has implications on the utilization of paleo-proxies which are based on geometrical valve features of F. kerguelensis. Differentiating both morphotypes might improve established methods and possibly provides a new proxy for summer sea surface temperature