Invariant Detector Research Articles

Interpretable conservation laws as sparse invariants.

Discovering conservation laws for a given dynamical system is important but challenging. In a theorist setup (differential equationsand basis functions are both known), we propose the sparse invariant detector (SID), an algorithm that autodiscovers conservation laws from differential equations. Its algorithmic simplicity allows robustness and interpretability of the discovered conserved quantities. We show that SID is able to rediscover known and even discover new conservation laws in a variety of systems. For two examples in fluid mechanics and atmospheric chemistry, SID discovers 14 and 3 conserved quantities, respectively, where only 12 and 2 were previously known to domain experts.

A path integral formulation for particle detectors: the Unruh-DeWitt model as a line defect

Particle detectors are an ubiquitous tool for probing quantum fields in the context of relativistic quantum information (RQI). We formulate the Unruh-DeWitt (UDW) particle detector model in terms of the path integral formalism. The formulation is able to recover the results of the model in general globally hyperbolic spacetimes and for arbitrary detector trajectories. Integrating out the detector’s degrees of freedom yields a line defect that allows one to express the transition probability in terms of Feynman diagrams. Inspired by the light-matter interaction, we propose a gauge invariant detector model whose associated line defect is related to the derivative of a Wilson line. This is another instance where nonlocal operators in gauge theories can be interpreted as physical probes for quantum fields.

Optimal Reordering Trace Files for Improving Software Testing Suitcase

An invariant can be described as an essential relationship between program variables. The invariants are very useful in software checking and verification. The tools that are used to detect invariants are invariant detectors. There are two types of invariant detectors: dynamic invariant detectors and static invariant detectors. Daikon software is an available computer program that implements a special case of a dynamic invariant detection algorithm. Daikon proposes a dynamic invariant detection algorithm based on several runs of the tested program; then, it gathers the values of its variables, and finally, it detects relationships between the variables based on a simple statistical analysis. This method has some drawbacks. One of its biggest drawbacks is its overwhelming time order. It is observed that the runtime for the Daikon invariant detection tool is dependent on the ordering of traces in the trace file. A mechanism is proposed in order to reduce differences in adjacent trace files. It is done by applying some special techniques of mutation/crossover in genetic algorithm (GA). An experiment is run to assess the benefits of this approach. Experimental findings reveal that the runtime of the proposed dynamic invariant detection algorithm is superior to the main approach with respect to these improvements.

Adaptive Radar Detection in Low-Rank Heterogeneous Clutter via Invariance Theory

This paper addresses adaptive detection of a range distributed target in the presence of dominant heterogeneous clutter, which is (possibly) low-rank and lies in a known subspace, plus Gaussian thermal noise. First, this problem is transformed into an equivalent binary hypothesis test with observations having block-diagonal covariance matrices. Then an invariance analysis is conducted on the resulting hypothesis test. Data and unknown parameters are compressed into a maximal invariant and an induced maximal invariant, respectively, w.r.t. a suitable transformation group. This suggests to focus attention on invariant detectors and to establish the relationship between invariance and constant false alarm rate (CFAR) property. According to this guideline, two tunable invariant detectors exploiting the aforementioned covariance structure are devised, and they are shown to ensure bounded CFAR and standard CFAR properties, respectively. Finally, the CFAR behavior of the proposed detectors as well as their detection performance is assessed via numerical simulations.

Invariance Theory for Adaptive Detection in Non-Gaussian Clutter

This paper studies the problem of detecting range-spread targets in (possibly non-Gaussian) clutter whose joint distribution belongs to a very general family of complex matrix-variate elliptically contoured distributions. Within the family, we explore invariance with respect to both the distributional type and relevant parameters. Several groups are used to describe these invariance mechanisms, and a relationship is revealed between the group invariance and the constant false alarm rate (CFAR) properties in terms of model parameters, the generator function, or both. We then build a maximal invariant framework for the detection problem. This involves deriving the corresponding maximal invariants as well as their statistical characterizations. Using these results, we put forward several maximal invariant detectors, all of which are fully CFAR in that their false alarm rates are completely independent of the underlying clutter distribution. Numerical results show that all the proposed fully CFAR detectors are effective, and for the considered simulation setup, one of them outperforms the others and several existing ones.

Adaptive Radar Detection in Gaussian Disturbance With Structured Covariance Matrix via Invariance Theory

This paper deals with adaptive radar detection of targets in the presence of Gaussian disturbance sharing a block-diagonal covariance structure. The problem is formulated according to a very general signal model, which contains the point-like, range-spread, and subspace target (or targets) as special instances. Hence, a unified study on the resulting adaptive detection problem is handled with the use of the invariance theory. The obtained results, including an appropriate transformation group, a maximal invariant and an induced maximal invariant, are proven consistent with those existing in the literature for some simple scenarios. Meanwhile, since the widely-used generalized likelihood ratio detector does not admit a closed form expression, new invariant detectors and their CFAR versions are proposed in this general scenario. Finally, their detection performance is assessed and validated via numerical examples.

Testing Equality of Multiple Power Spectral Density Matrices

This paper studies the existence of optimal invariant detectors for determining whether $P$ multivariate processes have the same power spectral density. This problem finds application in multiple fields, including physical layer security and cognitive radio. For Gaussian observations, we prove that the optimal invariant detector, i.e., the uniformly most powerful invariant test, does not exist. Additionally, we consider the challenging case of close hypotheses, where we study the existence of the locally most powerful invariant test (LMPIT). The LMPIT is obtained in the closed form only for univariate signals. In the multivariate case, it is shown that the LMPIT does not exist. However, the corresponding proof naturally suggests an LMPIT-inspired detector that outperforms previously proposed detectors.

Invariant Adaptive Detection of Range-Spread Targets Under Structured Noise Covariance

The invariance principle is adopted to develop an exhaustive study for adaptive detection of range-spread targets in Gaussian noise sharing a block-diagonal covariance structure. For this problem, the usual generalized likelihood ratio principle is intractable. In this paper, we first determine the largest group of affine transformations that does not alter the decision problem. Then, a maximal invariant identified by this group is derived, which can characterize the totality of the invariant detectors and extends the existing results for the point-target case. A theoretical performance analysis of the maximal invariant is also given. Finally, we propose two classes of invariant detectors, which are distinguished by whether a constant false alarm rate (CFAR) is maintained. Numerical experiments are provided for a comparison of the proposed detectors, where a tradeoff between the CFARness and the improved performance has been observed and studied.

Integration gain limitations in passive coherent location radars for manoeuvring target detection

The lack of transmission antenna gain in passive coherent location (PCL) systems can be circumvented somewhat by the fact that most broadcast waveforms are continuous waveforms and that the lengthening of the integration time can help to increase signal energy. However, with the increase of integration time, a PCL system encounters some limitations in detecting manoeuvring targets. To investigate this, the uniformly most powerful invariant (UMPI) detector presented by Zaimbashi et al. is considered. The detection performance of the UMPI detector in a closed-form expression for a manoeuvring target is obtained. The theoretical findings accompanied by simulation results demonstrate that a manoeuvring target can seriously degrade the detection performance of the UMPI detector when using long integration times.

Multiband FM‐based PBR system in presence of model mismatch

The effect of the complex amplitude mismatch (CAM) on the performance of multiband uniformly most powerful invariant (M-UMPI) detector is studied. This optimum invariant detector assumed a fully correlated amplitude over different frequency channels (DFCs) to improve target range resolution (TRR). In this case, we obtain a closed-form expression for the detection probability of the M-UMPI under the CAM. Some simulation results are provided to evaluate the detection performance loss as well as degradation in TRR of the M-UMPI detector when there are different types of CAM over DFCs.

Invariant subspace detector in distributed multiple‐input multiple output radar: geometry gain helps improving moving target detection

To detect moving targets in a distributed multiple-input multiple output (MIMO) radars, it is preferable to null the clutter rather than whiten the clutter. This is mainly because clutter nulling approaches do not require range training data to form a sample covariance estimate of clutter in each transmit-receive pair, especially in the distributed MIMO radars with non-homogeneous clutter. Moreover, geometry diversity of the distributed MIMO helps improve moving target detection since for a given target velocity, different transmit-receive pairs produce different Doppler frequencies that are less likely to be all small and reside in the clutter nulling region. Based on these facts, the authors consider a subspace model for clutter and derive a uniformly most powerful invariant (UMPI) detector as an optimum invariant test. In this case, analytical expressions for calculating the false alarm and detection probabilities for Swerling 0 and Swerling 1 target models are derived in the closed-forms. Moreover, theoretical and numerical analyses of the proposed UMPI test are represented for several scenarios. More importantly, the simulation results show that the proposed subspace-based UMPI detector can attain the predetermined false alarm probability and superior detection performance in the presence of correlated clutter. Finally, authors consider a situation in which perfect waveform separations at the local receivers are no longer valid, and see the detection performance degradation of the proposed optimal detector designed for ideal waveform separations.

Coincidence of Maximal Invariants for Two Adaptive Radar Detection Problems

This letter deals with adaptive radar detection of targets embedded in Gaussian clutter plus range-distributed subspace-structured jamming by exploiting the invariance theory. The class of invariant detectors which ensure the constant false alarm rate property has been characterized by designing the maximal invariant statistic for the studied detection problem. The achievement of this letter is the coincidence of the obtained maximal invariant with that derived assuming range-concentrated jamming.

Exploiting affine invariant regions and leaf edge shapes for weed detection

In this article, local features extracted from field images are evaluated for weed detection. Several scale and affine invariant detectors from computer vision literature along with high performance descriptors were applied. Field dataset contained a total of 474 plant images of sugar beet and creeping thistle, divided into six groups based on illumination, age, and camera to plant distance. To establish a performance baseline, leaf image retrieval potential of the selected features was first assessed on a publicly available leaf database containing flatbed scanned images of 15 tree species. Then a comparison with the field data retrieval highlighted the trade-off due to the field challenges. Adopting a comprehensive approach, edge shape detectors and homogeneous surface detecting affine invariant regions were fused. In order to integrate vegetation indices as local features, a new local vegetation color descriptor was introduced which used various combinations of color indices and offered a very high precision. Retrieval in the field data was evaluated group-wise. Although, the impact of the sunlight was found to be very low on shape features, but relatively higher precisions were obtained for younger plants under a shade (overall more than 80%). The weed detection accuracy was assessed using the Bag-of-Visual-Word scheme with KNN and SVM classifiers. The assessment showed that with an SVM classifier, a fusion of surface color and edge shapes boosted the overall classification accuracy to as high as 99.07% with a very low false negative rate (2%).

Adaptive Radar Detection of a Subspace Signal Embedded in Subspace Structured Plus Gaussian Interference Via Invariance

This paper deals with adaptive radar detection of a subspace signal competing with two sources of interference. The former is Gaussian with unknown covariance matrix and accounts for the joint presence of clutter plus thermal noise. The latter is structured as a subspace signal and models coherent pulsed jammers impinging on the radar antenna. The problem is solved via the Principle of Invariance which is based on the identification of a suitable group of transformations leaving the considered hypothesis testing problem invariant. A maximal invariant statistic, which completely characterizes the class of invariant decision rules and significantly compresses the original data domain, as well as its statistical characterization are determined. Thus, the existence of the optimum invariant detector is addressed together with the design of practically implementable invariant decision rules. At the analysis stage, the performance of some receivers belonging to the new invariant class is established through the use of analytic expressions.

Invariant Rules for Multipolarization SAR Change Detection

This paper deals with coherent (in the sense that both amplitudes and relative phases of the polarimetric returns are used to construct the decision statistic) multipolarization synthetic aperture radar (SAR) change detection assuming the availability of reference and test images collected from $N$ multiple polarimetric channels. At the design stage, the change detection problem is formulated as a binary hypothesis testing problem, and the principle of invariance is used to come up with decision rules sharing the constant false alarm rate property. The maximal invariant statistic and the maximal invariant in the parameter space are obtained. Hence, the optimum invariant test is devised proving that a uniformly most powerful invariant detector does not exist. Based on this, the class of suboptimum invariant receivers, which also includes the generalized likelihood ratio test, is considered. At the analysis stage, the performance of some tests, belonging to the aforementioned class, is assessed and compared with the optimum clairvoyant invariant detector. Finally, detection maps on real high-resolution SAR data are computed showing the effectiveness of the considered invariant decision structures.

Rotation angle recovery for rotation invariant detector in lying pose human body detection

A method for rotation-invariant lying-pose human body detection in overlooking images is proposed. The rotation-invariant histogram of oriented gradient using Fourier analysis in polar coordinate is exploited as descriptor for lying-pose human body. And then the authors used the exhaustive sliding window search strategy with multiple scale scan to localise human body. Finally, principal component analysis (PCA) is used to determine the rotation angle of the exhaustive sliding window based on the classifier output scores. Experiments on their built XiaMen University Lying-Pose Dataset (XMULP) show the effectiveness of their proposed method.

Static analysis based invariant detection for commodity operating systems

Recent interest in runtime attestation requires modeling of a program's runtime behavior to formulate its integrity properties. In this paper, we study the possibility of employing static source code analysis to derive integrity models of a commodity operating systems kernel. We develop a precise and static analysis-based data invariant detection tool that overcomes several technical challenges: field-sensitivity, array-sensitivity, and pointer analysis. We apply our tool to Linux kernel 2.4.32 and Windows Research Kernel (WRK). For Linux kernel 2.4.32, our tool identifies 284,471 data invariants that are critical to its runtime integrity, e.g., we use them to detect ten real-world Linux rootkits. Furthermore, comparison with the result of a dynamic invariant detector reveals 17,182 variables that can cause false alarms for the dynamic detector in the constant invariants category. Our tool also works successfully for WRK and reports 202,992 invariants, which we use to detect nine real-world Windows malware and one synthetic Windows malware. When compared with a dynamic invariant detector, we see similar results in terms of false alarms. Our experience suggests that static analysis is a viable option for automated integrity property derivation, and it can have very low false positive rate and very low false negative rate (e.g., for the constant invariants of WRK, the false positive rate is one out of 100,822 and the false negative rate is 0.007% or seven out of 100,822).

Robot mapping using local invariant feature detectors

Purpose – To build a persistent map with visual landmarks is one of the most important steps for implementing the visual simultaneous localization and mapping (SLAM). The corner detector is a common method utilized to detect visual landmarks for constructing a map of the environment. However, due to the scale-variant characteristic of corner detection, extensive computational cost is needed to recover the scale and orientation of corner features in SLAM tasks. The purpose of this paper is to build the map using a local invariant feature detector, namely speeded-up robust features (SURF), to detect scale- and orientation-invariant features as well as provide a robust representation of visual landmarks for SLAM. Design/methodology/approach – SURF are scale- and orientation-invariant features which have higher repeatability than that obtained by other detection methods. Furthermore, SURF algorithms have better processing speed than other scale-invariant detection method. The procedures of detection, description and matching of regular SURF algorithms are modified in this paper in order to provide a robust representation of visual landmarks in SLAM. The sparse representation is also used to describe the environmental map and to reduce the computational complexity in state estimation using extended Kalman filter (EKF). Furthermore, the effective procedures of data association and map management for SURF features in SLAM are also designed to improve the accuracy of robot state estimation. Findings – Experimental works were carried out on an actual system with binocular vision sensors to prove the feasibility and effectiveness of the proposed algorithms. EKF SLAM with the modified SURF algorithms was applied in the experiments including the evaluation of accurate state estimation as well as the implementation of large-area SLAM. The performance of the modified SURF algorithms was compared with those obtained by regular SURF algorithms. The results show that the SURF with less-dimensional descriptors is the most suitable representation of visual landmarks. Meanwhile, the integrated system is successfully validated to fulfill the capabilities of visual SLAM system. Originality/value – The contribution of this paper is the novel approach to overcome the problem of recovering the scale and orientation of visual landmarks in SLAM tasks. This research also extends the usability of local invariant feature detectors in SLAM tasks by utilizing its robust representation of visual landmarks. Furthermore, data association and map management designed for SURF-based mapping in this paper also give another perspective for improving the robustness of SLAM systems.

Invariant Target Detection in Multiband FM-Based Passive Bistatic Radar

FM-based passive bistatic radars (PBRs) exploiting a single broadcasted channel suffer from time-varying detection performance due to the time-varying program content of the transmitted signal as well as the propagation condition of that channel. To circumvent this matter, it is a viable idea to exploit multiple broadcasted channels from a single transmitter for detection. In this case, we formulate the problem of detecting a target in the presence of interference signals such as receiver noise, direct signal, multipath/clutter echoes and interfering targets as a composite hypothesis test. To address this, we derive a multiband uniformly most powerful invariant (UMPI) test as an optimal invariant detector. Closed-form expressions for calculating false alarm probability and detection probability for the target models of Swerling 0 and Swerling 1 are derived. A thorough performance assessment is also given, and the results show the robustness of the proposed multiband detector against the time-varying program content of FM radio channels. In addition to the reliable detection performance, a multiband PBR system offers advantages in terms of combined diversity gain and frequency diversity gain as compared with a single band PBR system. The former happens due to the joint exploitation of multiple broadcasted channels for detection, while the latter occurs when independent returns are received from one target over different frequency channels.

Remote Sensing Image Matching using Sift And Affine Transformation

paper presents remote sensing image matching using sift algorithm and affine transformation. The novelty in our approach is to find the features in the reference image and then match the input image with that of reference image using Affine Transformation. Both synthetic and real data have been considered in this work for the evaluation of the proposed methodology. After registering the image, the outliers are removed. A speeded up affine invariant detector is proposed in this paper for local feature extraction. The experimental results show that the proposed algorithm decreases the redundancy of key points and speeds up the implementation. It is able to account for differences in spectral content, rotation, scale, translation, different viewpoint, and change in illumination. The proposed technique improves the computational efficiency and decrease the storage requirement.