Cause I’m a Genial Imprecise Point: Outlier Detection for Uncertain Data

Supervised object detection models are trained to recognize certain objects. These models are classified into two types: single-stage detectors and two-stage detectors. The single-stage detectors just need one pass through the model to anticipate all the bounding boxes, whereas the two-stage detectors require to first estimate the image portions where the object could be located. Due to their speed and simplicity, single-stage anchor-based models are used in many industrial settings. Training such models require bounding boxes that describe the spatial location of an object, which are usually drawn by an expert. However, the question remains, how much area should be considered when drawing the bounding boxes? In this paper, we demonstrate the effects that the size and placement of a rectangular bounding box can have on the performance of the anchor-based models. For this, we first perform experiments on a synthetically generated binary dataset and then on a real-world object detection dataset. Our results show that fixing the size of the bounding boxes can help in improving the performance of the model in the case of single class object detection (approximately 50% improvement in mAP@[.5:.95] for real world dataset). Furthermore, we also demonstrate how freely available tools can be combined for obtaining the best possible semi automated object labeling pipeline.

Imprecise points are regions in which one point should be placed. We study computing the largest and smallest possible values of various basic geometric measures on sets of imprecise points, such as the diameter, width, closest pair, smallest enclosing circle, and smallest enclosing bounding box. We give efficient algorithms for most of these problems, and identify the hardness of others.

This report will cover the testing of the Ballistic Research Laboratory-Computer-Aided Design's (BRL-CAD's) ray-tracer on the primitive Bag of Triangles (BoTs). Two programs were created to accommodate each component of this project. The first program created all possible triangles (BoTs) given a bounding box and step size that is specified by the user. The second program fired multiple rays toward various locations on each triangle in the database. The results of these tests were classified as a success or failure; the percentages of success were graphed against the different tolerance levels to determine the accuracy of the ray-tracer on BoTs. These data could be useful in understanding how BRL-CAD's ray-tracer performs in comparison to the Air Force's ray-tracer, FASTGEN, on BoTs.

R-trees can be used to store and query sets of point data in two or more dimensions. An easy way to construct and maintain R-trees for two-dimensional points, due to Kamel and Faloutsos, is to keep the points in the order in which they appear along the Hilbert curve. The R-tree will then store bounding boxes of points along contiguous sections of the curve, and the efficiency of the R-tree depends on the size of the bounding boxes---smaller is better. Since there are many different ways to generalize the Hilbert curve to higher dimensions, this raises the question which generalization results in the smallest bounding boxes. Familiar methods, such as the one by Butz, can result in curve sections whose bounding boxes are a factor $\Omega(2^{d/2})$ larger than the volume traversed by that section of the curve. Most of the volume bounded by such bounding boxes would not contain any data points. In this paper we present a new way of generalizing Hilbert's curve to higher dimensions, which results in much tighter bounding boxes: they have at most 4 times the volume of the part of the curve covered, independent of the number of dimensions. Moreover, we prove that a factor 4 is asymptotically optimal.

Parkinsonism as an outlier detection problem

This paper mainly studies on the potential safety hazards in the obstacle recognition and processing system (ORPS) of the self-driving cars, which is constructed by deep learning architecture. We perform an attack that embeds a backdoor in the Mask R-CNN in ORPS by poisoning the dataset. Under normal circumstances, the backdoored model can accurately identify obstacles (vehicles). However, under certain circumstances, triggering the backdoor in the backdoored model may lead to change the size (bounding box and mask) and confidence of the detected obstacles, which may cause serious accidents. The experiment result shows that it is possible to embed a backdoor in ORPS. We can see that the backdoored network can obviously change the size of bounding box and corresponding mask of those poisoned instances. But on the other hand, embedding a backdoor in the deep learning based model will only slightly affect the accuracy of detecting objects without backdoor triggers, which is imperceptible for users. Eventually, we hope that our simple work can arouse people’s attention to the self-driving technology and even other deep learning based models. It brings motivation about how to judge or detect the existence of the backdoors in these systems.

Spatial data structures form a core ingredient of many geometric algorithms, both in theory and in practice. Many of these data structures, especially the ones used in practice, are based on partitioning the underlying space (examples are binary space partitions and decompositions of polygons) or partitioning the set of objects (examples are bounding-volume hierarchies). The efficiency of such data structures---and, hence, of the algorithms that use them---depends on certain characteristics of the partitioning. For example the performance of many algorithms that use binary space partitions (BSPs) depends on the size of the BSPs. Similarly, the performance of answering range queries using bounding-volume hierarchies (BVHs) depends on the so-called crossing number that can be associated with the partitioning on which the BVH is based. Much research has been done on the problem of computing partitioning whose characteristics are good in the worst case. In this thesis, we studied the problem from a different point of view, namely instance-optimality. In particular, we considered the following question: given a class of geometric partitioning structures---like BSPs, simplicial partitions, polygon triangulations, …---and a cost function---like size or crossing number---can we design an algorithm that computes a structure whose cost is optimal or close to optimal for any input instance (rather than only worst-case optimal). We studied the problem of finding optimal data structures for some of the most important spatial data structures. As an example having a set of n points and an input parameter r, It has been proved that there are input sets for which any simplicial partitions has crossing number ¿(vr). It has also been shown that for any set of n input points and the parameter r one can make a simplicial partition with stabbing number O(vr). However, there are input point sets for which one can make simplicial partition with lower stabbing number. As an example when the points are on a diagonal, one can always make a simplicial partition with stabbing number 1. We started our research by studying BSPs for line segments in the plane, where the cost function is the size of the BSPs. A popular type of BSPs for line segments are the so-called auto-partitions. We proved that finding an optimal auto-partition is NP-hard. In fact, finding out if a set of input segments admits an auto-partition without any cuts is already NP-hard. We also studied the relation between two other types of BSPs, called free and restricted BSPs, and showed that the number of cuts of an optimal restricted BSP for a set of segments in R2 is at most twice the number of cuts of an optimal free BSP for that set. The details are being represented in Chapter 1 of the thesis. Then we turned our attention to so-called rectilinear r-partitions for planar point sets, with the crossing number as cost function. A rectilinear r-partition of a point set P is a partitioning of P into r subsets, each having roughly |P|/r points. The crossing number of the partition is defined using the bounding boxes of the subsets; in particular, it is the maximum number of bounding boxes that can be intersected by any horizontal or vertical line. We performed some theoretical as well as experimental studies on rectilinear r-partitions. On the theoretical side, we proved that computing a rectilinear r-partition with optimal stabbing number for a given set of points and parameter r is NP-hard. We also proposed an exact algorithm for finding optimal rectilinear r-partitions whose running time is polynomial when r is a constant, and a faster 2-approximation algorithm. Our last theoretical result showed that considering only partitions whose bounding boxes are disjoint is not sufficient for finding optimal rectilinear r-partitions. On the experimental side, we performed a comparison between four different heuristics for constructing rectilinear r-partitions. The so-called windmill KD-tree gave the best results. Chapter 2 of the thesis describes all the details of our research on rectilinear r-partitions. We studied another spatial data structure in Chapter 3 of the thesis. Decomposition of the interior of polygons is one of the fundamental problems in computational geometry. In case of a simple polygon one usually wants to make a Steiner triangulation of it, and when we have a rectilinear polygon at hand, one typically wants to make a rectilinear decomposition for it. Due to this reason there are algorithms which make Steiner triangulations and rectangular decompositions with low stabbing number. These algorithms are worst-case optimal. However, similar to the two previous data structures, there are polygons for which one can make decompositions with lower stabbing numbers. In 3 we proposed a 3-approximation for finding an optimal rectangular decomposition of a rectilinear polygon. We also proposed an O(1)-approximation for finding optimal Steiner triangulation of a simple polygon. Finally, in Chapter 4 of the thesis, we considered another optimization problem, namely how to approximate a piecewise-linear function F: R ¿R with another piecewise-linear function with fewer pieces. Here one can distinguish two versions of the problem. The first one is called the min-k problem; the goal is then to approximate the function within a given error e such that the resulting function has the minimum number of links. The second one is called the min-e problem; here the goal is to find an approximation with at most k links (for a given k) such that the error is minimized. These problems have already been studied before. Our contribution is to consider the problem for so-called uncertain functions, where the value of the input function F at its vertices is given as a discrete set of different values, each with an associated probability. We show how to compute an approximation that minimizes the expected error.

It is sometimes necessary to determine the optimal value for a direction dependent quantity. Using a search technique based on Powell's quadratic convergent method such an optimal direction can be approximated. The necessary geometric transformations in n-dimensional space are introduced. As an example we consider the approximation of the minimum bounding box of a set of three-dimensional points. Minimum bounding boxes can significantly improve accuracy and efficiency of the calculations in modern brachytherapy treatment planning of the volumes of objects or the dose distribution inside an object. A covariance matrix based approximation method for the minimum bounding box is compared with the results of the search method. The benefits of the use of optimal oriented bounding boxes in brachytherapy treatment planning systems are demonstrated and discussed.

The paper presents the problem of outlier detection in the rule knowledge bases. Unusual (rare) rules, regarded here as the deviation, should be the subject of analysis experts and knowledge engineers because they can influence the efficiency of inference in decision support systems. The author presents a different approach in finding outliers in the rules. The experiments with their results are also presented in the paper.

Assume that a set of imprecise points is given, where each point is specified by a region in which the point may lie. We study the problem of computing the smallest and largest possible tours and convex hulls, measured by length, and in the latter case also by area. Generally we assume the imprecision region to be a square, but we discuss the case where it is a segment or circle as well. We give polynomial time algorithms for several variants of this problem, ranging in running time from O(n) to O(n 13), and prove NP-hardness for some geometric problems on imprecise points.KeywordsLine SegmentConvex HullExtreme PointMinimum Span TreeTangent PointThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Restricted default theories: Expressive power and outlier detection tasks

Introduced by Agarwal, Har-Peled, and Varadarajan [J. ACM, 2004], an epsilon-kernel of a point set is a coreset that can be used to approximate the width, minimum enclosing cylinder, minimum bounding box, and solve various related geometric optimization problems. Such coresets form one of the most important tools in the design of linear-time approximation algorithms in computational geometry, as well as efficient insertion-only streaming algorithms and dynamic (non-streaming) data structures. In this paper, we continue the theme and explore dynamic streaming algorithms (in the so-called turnstile model). Andoni and Nguyen [SODA 2012] described a dynamic streaming algorithm for maintaining a (1+epsilon)-approximation of the width using O(polylog U) space and update time for a point set in [U]^d for any constant dimension d and any constant epsilon>0. Their sketch, based on a polynomial method, does not explicitly maintain an epsilon-kernel. We extend their method to maintain an epsilon-kernel, and at the same time reduce some of logarithmic factors. As an application, we obtain the first randomized dynamic streaming algorithm for the width problem (and related geometric optimization problems) that supports k outliers, using poly(k, log U) space and time.

Traditional geometric algorithms are often presented as if input imprecision does not exist, even though it is often unavoidable. We argue that in some cases, it may be desirable for geometric algorithms to treat this imprecision as an explicit component of the input, and to reflect this imprecision in the output. Starting with three problems from computational geometry whose inputs are planar point sets (Voronoi diagrams, convex hulls, and smallest bounding discs), we recast these as problems where each input point’s location is imprecise, but known to lie within a particular region of uncertainty. Where algorithms to solve each of the original problems produce a single geometric object as output, the algorithms that we present typically produce either guaranteed or possible output objects. A guaranteed object represents qualities that can be guaranteed for every point set that is consistent with the uncertain regions, and a possible object represents qualities that exist for at least one such point set. By dealing with input imprecision explicitly, these guaranteed and possible objects can represent a more accurate view of what can be reliably inferred from the input data.

High-altitude work poses significant safety risks, and wearing safety belts is crucial to prevent falls and ensure worker safety. However, manual monitoring of safety belt usage is time consuming and prone to errors. In this paper, we propose an improved high-altitude safety belt detection algorithm based on the YOLOv8 model to address these challenges. Our paper introduces several improvements to enhance its performance in detecting safety belts. First, to enhance the feature extraction capability, we introduce a BiFormer attention mechanism. Moreover, we used a lightweight upsampling operator instead of the original upsampling layer to better preserve and recover detailed information without adding an excessive computational burden. Meanwhile, Slim-neck was introduced into the neck layer. Additionally, extra auxiliary training heads were incorporated into the head layer to enhance the detection capability. Lastly, to optimize the prediction of bounding box position and size, we replaced the original loss function with MPDIOU. We evaluated our algorithm using a dataset collected from high-altitude work scenarios and demonstrated its effectiveness in detecting safety belts with high accuracy. Compared to the original YOLOv8 model, the improved model achieves P (precision), R (recall), and mAP (mean average precision) values of 98%, 91.4%, and 97.3%, respectively. These values represent an improvement of 5.1%, 0.5%, and 1.2%, respectively, compared to the original model. The proposed algorithm has the potential to improve workplace safety and reduce the risk of accidents in high-altitude work environments.

Bone age assessment based on X-ray Images can accurately determine the actual bone age of adolescents. Accurate extraction of the key regions of interest (ROIs) in X-ray images is required to accurately assess bone age. However, existing ROI extraction methods can only extract a few targets and have poor extraction accuracy. Thus, the strict demands for imaging in the medical field via these methods are difficult. In this article, we propose a multitarget interested region extraction method for wrist X-ray images based on optimized AlexNet and two-class combined model, named OATC, which can simultaneously extract multiple ROIs with high accuracy. Specifically, the square-wave scanning algorithm was implemented to obtain the bounding box size of each bone ROI according to the shape information of the wrist. Then, the optimized AlexNet was used to obtain the key point coordinates of each bone ROI. Bone ROIs could be extracted by combining key point coordinates with the bone bounding box size. Finally, the two-classification model was combined to improve the accuracy of ROI extraction. Experiments conducted on our wrist X-ray image dataset showed that OTAC has a fast convergence speed and small deviation. The average accuracy of extracting 14 ROIs reached 95.57%, which are 7.76% and 4.68% higher than that of VGG16 and AlexNet, respectively.