The Parameterized Complexity of Guarding Almost Convex Polygons

The Art Gallery problem is a fundamental visibility problem in Computational Geometry. The input consists of a simple polygon P, (possibly infinite) sets G and C of points within P, and an integer k; the task is to decide if at most k guards can be placed on points in G so that every point in C is visible to at least one guard. In the classic formulation of Art Gallery, G and C consist of all the points within P. Other well-known variants restrict G and C to consist either of all the points on the boundary of P or of all the vertices of P. Recently, three new important discoveries were made: the above mentioned variants of Art Gallery are all W[1]-hard with respect to k [Bonnet and Miltzow, ESA'16], the classic variant has an O(log k)-approximation algorithm [Bonnet and Miltzow, SoCG'17], and it may require irrational guards [Abrahamsen et al., SoCG'17]. Building upon the third result, the classic variant and the case where G consists only of all the points on the boundary of P were both shown to be ∃ℝ-complete [Abrahamsen et al., STOC'18]. Even when both G and C consist only of all the points on the boundary of P, the problem is not known to be in NP. Given the first discovery, the following question was posed by Giannopoulos [Lorentz Center Workshop, 2016]: Is Art Gallery FPT with respect to r, the number of reflex vertices? In light of the developments above, we focus on the variant where G and C consist of all the vertices of P, called Vertex-Vertex Art Gallery. Apart from being a variant of Art Gallery, this case can also be viewed as the classic Dominating Set problem in the visibility graph of a polygon. In this article, we show that the answer to the question by Giannopoulos is positive: Vertex-Vertex Art Gallery is solvable in time r^O(r²)n^O(1). Furthermore, our approach extends to assert that Vertex-Boundary Art Gallery and Boundary-Vertex Art Gallery are both FPT as well. To this end, we utilize structural properties of "almost convex polygons" to present a two-stage reduction from Vertex-Vertex Art Gallery to a new constraint satisfaction problem (whose solution is also provided in this paper) where constraints have arity 2 and involve monotone functions.publishedVersio

Proceedings of the 2015 Berry Summer Thesis Institute

Thanks to a gift from the Berry Family Foundation and the Berry family, the University Honors Program launched the Berry Summer Thesis Institute in 2012. The institute introduces students in the University Honors Program to intensive research, scholarship opportunities and professional development. Each student pursues a 12-week summer thesis research project under the guidance of a UD faculty mentor. This contains the product of the students\u27 research

Consciousness, time and science epistemology: an existentialist approach

In this work, the author presents an updated state-of-the-art study about the fundamental concept of time, integrating approaches coming from all branches of human cognitive disciplines. The author points out that there is a rational relation for the nature of time (arché) coming from human disciplines and scientific ones, thus proposing an overall vision of it for the first time. Implications of this proposal are shown providing an existentialist approach to the meaning of “time” concept

Analysis of visitors’ mobility patterns through random walk in the Louvre Museum

This paper proposes a random walk model to analyze visitors' mobility patterns in a large museum. Visitors' available time makes their visiting styles different, resulting in dissimilarity in the order and number of visited places and in path sequence length. We analyze all this by comparing a simulation model and observed data, which provide us the strength of the visitors' mobility patterns. The obtained results indicate that shorter stay-type visitors exhibit stronger patterns than those with the longer stay-type, confirming that the former are more selective than the latter in terms of their visitation type.Comment: 16 pages, 5 figures, 4 table

Person Re-identification with Deep Learning

In this work, we survey the state of the art of person re-identification and introduce the basics of the deep learning method for implementing this task. Moreover, we propose a new structure for this task. The core content of our work is to optimize the model that is composed of a pre-trained network to distinguish images from different people with representative features. The experiment is implemented on three public person datasets and evaluated with evaluation metrics that are mean Average Precision (mAP) and Cumulative Matching Characteristic (CMC). We take the BNNeck structure proposed by Luo et al. [25] as the baseline model. It adopts several tricks for the training, such as the mini-batch strategy of loading images, data augmentation for improving the model’s robustness, dynamic learning rate, label-smoothing regularization, and the L2 regularization to reach a remarkable performance. Inspired from that, we propose a novel structure named SplitReID that trains the model in separated feature embedding spaces with multiple losses, which outperforms the BNNeck structure and achieves competitive performance on three datasets. Additionally, the SplitReID structure holds the property of lightweight computation complexity that it requires fewer parameters for the training and inference compared to the BNNeck structure. Person re-identification can be deployed without high-resolution images and fixed angle of pedestrians with the deep learning method to achieve outstanding performance. Therefore, it holds an immeasurable prospect in practical applications, especially for the security fields, even though there are still some challenges like occlusions to be overcome

Wearable device-based gait recognition using angle embedded gait dynamic images and a convolutional neural network

The widespread installation of inertial sensors in smartphones and other wearable devices provides a valuable opportunity to identify people by analyzing their gait patterns, for either cooperative or non-cooperative circumstances. However, it is still a challenging task to reliably extract discriminative features for gait recognition with noisy and complex data sequences collected from casually worn wearable devices like smartphones. To cope with this problem, we propose a novel image-based gait recognition approach using the Convolutional Neural Network (CNN) without the need to manually extract discriminative features. The CNN’s input image, which is encoded straightforwardly from the inertial sensor data sequences, is called Angle Embedded Gait Dynamic Image (AE-GDI). AE-GDI is a new two-dimensional representation of gait dynamics, which is invariant to rotation and translation. The performance of the proposed approach in gait authentication and gait labeling is evaluated using two datasets: (1) the McGill University dataset, which is collected under realistic conditions; and (2) the Osaka University dataset with the largest number of subjects. Experimental results show that the proposed approach achieves competitive recognition accuracy over existing approaches and provides an effective parametric solution for identification among a large number of subjects by gait patterns

Gait recognition and understanding based on hierarchical temporal memory using 3D gait semantic folding

Gait recognition and understanding systems have shown a wide-ranging application prospect. However, their use of unstructured data from image and video has affected their performance, e.g., they are easily influenced by multi-views, occlusion, clothes, and object carrying conditions. This paper addresses these problems using a realistic 3-dimensional (3D) human structural data and sequential pattern learning framework with top-down attention modulating mechanism based on Hierarchical Temporal Memory (HTM). First, an accurate 2-dimensional (2D) to 3D human body pose and shape semantic parameters estimation method is proposed, which exploits the advantages of an instance-level body parsing model and a virtual dressing method. Second, by using gait semantic folding, the estimated body parameters are encoded using a sparse 2D matrix to construct the structural gait semantic image. In order to achieve time-based gait recognition, an HTM Network is constructed to obtain the sequence-level gait sparse distribution representations (SL-GSDRs). A top-down attention mechanism is introduced to deal with various conditions including multi-views by refining the SL-GSDRs, according to prior knowledge. The proposed gait learning model not only aids gait recognition tasks to overcome the difficulties in real application scenarios but also provides the structured gait semantic images for visual cognition. Experimental analyses on CMU MoBo, CASIA B, TUM-IITKGP, and KY4D datasets show a significant performance gain in terms of accuracy and robustness

Nearest solution to references method for multicriteria decision-making problems

In MCDM problems, the decision maker is often ready to adopt the closest solution to the reference values in a choice or ranking problem. The reference values represent the desired results as established subjectively by the decision maker or determined through various scientific tools. In a criterion, the reference value could be the maximum value, the minimum value, or a specific value or range. Also, the acceptances degrees of ranges outside the reference may differ from each other in a criterion. Furthermore, measurements in a criterion may have been obtained with any of the nominal, ordinal, interval, and ratio scales. For the decision problems, including qualitative criteria, the solution cannot be achieved without scaling of criteria with the existing MCDM methods. The purpose of this study is to propose the Nearest Solution to References (REF) Method, a novel reference-based MCDM method, for the solution of decision problems having mixed data structure where references can be determined for criteria

Enabling Open-Set Person Re-Identification for Real-World Scenarios

Person re-identification (re-ID) is a significant problem of computer vision with increasing scientific attention. To date, numerous studies have been conducted to improve the accuracy and robustness of person re-ID to meet the practical demands. However, most of the previous efforts concentrated on solving the closed-set variant of the problem, where a query is assumed to always have a correct match within the set of known people (the gallery set). However, this assumption is usually not valid for the industrial re-ID use cases. In this study, we focus on the open-set person re-ID problem, where, in addition to the similarity ranking, the solution is expected to detect the presence or absence of a given query identity within the gallery set. To determine good practices and to assess the practicality of the person re-ID in industrial applications, first, we convert popular closed-set person re-ID datasets into the open-set scenario. Second, we compare performance of eight state-of-the-art closed-set person re-ID methods under the open-set conditions. Third, we experimentally determine the efficiency of using different loss function combinations for the open-set problem. Finally, we investigate the impact of a statistics-driven gallery refinement approach on the open-set person re-ID performance in the low false-acceptance rate (FAR) region, while simultaneously reducing the computational demands of retrieval. Results show an average detection and identification rate increase of 8.38% and 3.39% on the DukeMTMC-reID and Market1501 datasets, respectively, for a FAR of 1%