37 research outputs found
Identifying manifolds underlying group motion in Vicsek agents
Collective motion of animal groups often undergoes changes due to
perturbations. In a topological sense, we describe these changes as switching
between low-dimensional embedding manifolds underlying a group of evolving
agents. To characterize such manifolds, first we introduce a simple mapping of
agents between time-steps. Then, we construct a novel metric which is
susceptible to variations in the collective motion, thus revealing distinct
underlying manifolds. The method is validated through three sample scenarios
simulated using a Vicsek model, namely switching of speed, coordination, and
structure of a group. Combined with a dimensionality reduction technique that
is used to infer the dimensionality of the embedding manifold, this approach
provides an effective model-free framework for the analysis of collective
behavior across animal species.Comment: 12 pages, 6 figures, journal articl
The Recursive Form of Error Bounds for RFS State and Observation with Pd<1
In the target tracking and its engineering applications, recursive state
estimation of the target is of fundamental importance. This paper presents a
recursive performance bound for dynamic estimation and filtering problem, in
the framework of the finite set statistics for the first time. The number of
tracking algorithms with set-valued observations and state of targets is
increased sharply recently. Nevertheless, the bound for these algorithms has
not been fully discussed. Treating the measurement as set, this bound can be
applied when the probability of detection is less than unity. Moreover, the
state is treated as set, which is singleton or empty with certain probability
and accounts for the appearance and the disappearance of the targets. When the
existence of the target state is certain, our bound is as same as the most
accurate results of the bound with probability of detection is less than unity
in the framework of random vector statistics. When the uncertainty is taken
into account, both linear and non-linear applications are presented to confirm
the theory and reveal this bound is more general than previous bounds in the
framework of random vector statistics.In fact, the collection of such
measurements could be treated as a random finite set (RFS)
Localization Recall Precision (LRP): A New Performance Metric for Object Detection
Average precision (AP), the area under the recall-precision (RP) curve, is
the standard performance measure for object detection. Despite its wide
acceptance, it has a number of shortcomings, the most important of which are
(i) the inability to distinguish very different RP curves, and (ii) the lack of
directly measuring bounding box localization accuracy. In this paper, we
propose 'Localization Recall Precision (LRP) Error', a new metric which we
specifically designed for object detection. LRP Error is composed of three
components related to localization, false negative (FN) rate and false positive
(FP) rate. Based on LRP, we introduce the 'Optimal LRP', the minimum achievable
LRP error representing the best achievable configuration of the detector in
terms of recall-precision and the tightness of the boxes. In contrast to AP,
which considers precisions over the entire recall domain, Optimal LRP
determines the 'best' confidence score threshold for a class, which balances
the trade-off between localization and recall-precision. In our experiments, we
show that, for state-of-the-art object (SOTA) detectors, Optimal LRP provides
richer and more discriminative information than AP. We also demonstrate that
the best confidence score thresholds vary significantly among classes and
detectors. Moreover, we present LRP results of a simple online video object
detector which uses a SOTA still image object detector and show that the
class-specific optimized thresholds increase the accuracy against the common
approach of using a general threshold for all classes. At
https://github.com/cancam/LRP we provide the source code that can compute LRP
for the PASCAL VOC and MSCOCO datasets. Our source code can easily be adapted
to other datasets as well.Comment: to appear in ECCV 201