Metrics on the space of sets of trajectories are important for scientists in the field of computer vision, machine learning, robotics, and general artificial intelligence. However, existing notions of closeness between sets of trajectories are either mathematically inconsistent or of limited practical use. In this paper, we outline the limitations in the current mathematically-consistent metrics, which are based on OSPA ( 2008); and the inconsistencies in the heuristic notions of closeness used in practice, whose main ideas are common to the CLEAR MOT measures (Keni and Rainer 2008) widely used in computer vision. In two steps, we then propose a new intuitive metric between sets of trajectories and address these limitations. First, we explain a solution that leads to a metric that is hard to compute. Then we modify this formulation to obtain a metric that is easy to compute while keeping the useful properties of the previous metric. Our notion of closeness is the first demonstrating the following three features: the metric 1) can be quickly computed, 2) incorporates confusion of trajectories' identity in an optimal way, and 3) is a metric in the mathematical sense.
One of the reasons why the CLEAR MOT metrics are widely used is because they create a simple association between @math and @math , i.e., the association between @math and @math does not change often in time. It appears that @cite_44 is one of the first works that describes how to control the number of association changes when computing a similarity measure. The authors do not associate @math and @math independently every time instant but rather use a sequential matching procedure that tries to keep the association from the previous time instant if possible. This is similar to the procedure used in the much more recent CLEAR MOT measures that we discuss in the Introduction.
@cite_44
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We present a multi-cue metric learning framework to tackle the popular yet unsolved Multi-Object Tracking (MOT) problem. One of the key challenges of tracking methods is to effectively compute a similarity score that models multiple cues from the past such as object appearance, motion, or even interactions. This is particularly challenging when objects get occluded or share similar appearance properties with surrounding objects. To address this challenge, we cast the problem as a metric learning task that jointly reasons on multiple cues across time. Our framework learns to encode long-term temporal dependencies across multiple cues with a hierarchical Recurrent Neural Network. We demonstrate the strength of our approach by tracking multiple objects using their appearance, motion, and interactions. Our method outperforms previous works by a large margin on multiple publicly available datasets including the challenging MOT benchmark. Many techniques for association rule mining and feature selection require a suitable metric to capture the dependencies among variables in a data set. For example, metrics such as support, confidence, lift, correlation, and collective strength are often used to determine the interestingness of association patterns. However, many such measures provide conflicting information about the interestingness of a pattern, and the best metric to use for a given application domain is rarely known. In this paper, we present an overview of various measures proposed in the statistics, machine learning and data mining literature. We describe several key properties one should examine in order to select the right measure for a given application domain. A comparative study of these properties is made using twenty one of the existing measures. We show that each measure has different properties which make them useful for some application domains, but not for others. We also present two scenarios in which most of the existing measures agree with each other, namely, support-based pruning and table standardization. Finally, we present an algorithm to select a small set of tables such that an expert can select a desirable measure by looking at just this small set of tables. In this paper, we propose a CNN-based framework for online MOT. This framework utilizes the merits of single object trackers in adapting appearance models and searching for target in the next frame. Simply applying single object tracker for MOT will encounter the problem in computational efficiency and drifted results caused by occlusion. Our framework achieves computational efficiency by sharing features and using ROI-Pooling to obtain individual features for each target. Some online learned target-specific CNN layers are used for adapting the appearance model for each target. In the framework, we introduce spatial-temporal attention mechanism (STAM) to handle the drift caused by occlusion and interaction among targets. The visibility map of the target is learned and used for inferring the spatial attention map. The spatial attention map is then applied to weight the features. Besides, the occlusion status can be estimated from the visibility map, which controls the online updating process via weighted loss on training samples with different occlusion statuses in different frames. It can be considered as temporal attention mechanism. The proposed algorithm achieves 34.3 and 46.0 in MOTA on challenging MOT15 and MOT16 benchmark dataset respectively. Given a metric space @math , @math , @math , and @math , a distribution over mappings @math is called a @math -sensitive hash family if any two points in @math at distance at most @math are mapped by @math to the same value with probability at least @math , and any two points at distance greater than @math are mapped by @math to the same value with probability at most @math . This notion was introduced by Indyk and Motwani in 1998 as the basis for an efficient approximate nearest neighbor search algorithm and has since been used extensively for this purpose. The performance of these algorithms is governed by the parameter @math , and constructing hash families with small @math automatically yields improved nearest neighbor algorithms. Here we show that for @math it is impossible to achieve @math . This almost matches the construction of Indyk and Motwani which achieves @math .