Autonomous path planning for radar and sonar sensing faces significant challenges arising from dynamic targets, obstacle occlusions, and low signal-to-noise (SNR) conditions. We propose a hierarchical sensor scheduling framework that combines a long-horizon strategic planner, based on the Rapidly-exploring Random Tree star (RRT*) algorithm, with a fast-adapting tactical planner. Efficient coordination of the two planners is achieved via a novel message passing mechanism, enabling guidance of the sensor out of complex environments while maintaining effective target tracking. Additionally, we introduce an RRT* rerooting strategy that significantly reduces computation time and so expedites the update of the strategic plan. Extensive simulation results demonstrate that our proposed fusion approach outperforms conventional stand-alone short-term and long-term planners in challenging scenarios and low-SNR regimes,

We present a sensor scheduling algorithm to plan the motion of multiple autonomous platforms for cooperative tracking of targets within a region that contains obstacles and occlusions. The platforms have kinematic constraints and their sensors have restricted field of view and range. The proposed algorithm is a variant of the Rapidly exploring Random Tree star algorithm (RRT*) that has been adapted to the problem of determining paths for multiple independent kinematically constrained platforms to optimise their tracking performance. To guide the scheduling algorithm, we define a tracking cost based on the Posterior Cramér Rao Bound (PCRB) derived from the predicted positions of the platforms and targets. Through simulations of generated paths, we show that the algorithm generates rational plans for tracking targets and that the tracking cost accurately predicts the realised performance of the platforms.

This paper presents an algorithm of improving the range resolution of passive synthetic aperture radar (SAR) images by combining multiple terrestrial digital video broadcasting (DVB-T) channels while also suppressing artefacts arising from the direct transmit-receive signal. The proposed algorithm has two parts: spectral estimation techniques for combining DVB-T channels and direct signal suppression (DSS) techniques based on modified CLEAN and sub-aperture imagery-based minimum pixel selection (SA-MIPS). Those capabilities can be achieved with a single-channel, wideband receiver and at shorter ranges and are thus consistent with drone-based operation. The performance of the techniques is demonstrated through both simulation and real-world experiments with a drone-based demonstrator.

This paper deals with the exploitation of shadow regions in high-resolution drone-borne synthetic aperture radar (SAR) images and utilizing them for accurate target height and shape estimation. While prior research has shown the potential of SAR shadows for height estimation, these efforts have primarily focused on airborne and spaceborne platforms and lack a theoretical analysis for assessing achievable performance. In contrast, this work introduces a processing chain for target height and shape extraction and proposes a theoretical framework to evaluate system performance. The study demonstrates that the geometric flexibility and maneuverability of drones offer significant advantages in height estimation accuracy compared to conventional SAR platforms. The proposed method is validated using experimental data from a 24 GHz INRAS radar-equipped drone-borne SAR system, showing strong alignment between the extracted 2D shapes and height estimates and the theoretical predictions. Additionally, the study highlights how multi-perspective drone imagery enables the reconstruction of three-dimensional structures, further extending the potential of drone-borne SAR systems.

The focus of this letter is the estimation of a delay between two signals. Such a problem is common in signal processing and particularly challenging when the delay is non-stationary in nature. Our proposed solution is based on an all-pass filter framework comprising of two elements: a time delay is equivalent to all-pass filtering and an all-pass filter can be represented in terms of a ratio of a finite impulse response (FIR) filter and its time reversal. Using these elements, we propose an adaptive filtering algorithm with an LMS style update that estimates the FIR filter coefficients and the time delay. Specifically, at each time step, the algorithm updates the filter coefficients based on a gradient descent update and then extracts an estimate of the time delay from the filter. We validate our algorithm on synthetic data demonstrating that it is both accurate and capable of tracking time-varying delays.

Physiological motion, such as cardiac and respiratory motion, during Magnetic Resonance (MR) image acquisition can cause image artifacts. Motion correction techniques have been proposed to compensate for these types of motion during thoracic scans, relying on accurate motion estimation from undersampled motion-resolved reconstruction. A particular interest and challenge lie in the derivation of reliable non-rigid motion fields from the undersampled motion-resolved data. Motion estimation is usually formulated in image space via diffusion, parametric-spline, or optical flow methods. However, image-based registration can be impaired by remaining aliasing artifacts due to the undersampled motion-resolved reconstruction. In this work, we describe a formalism to perform non-rigid registration directly in the sampled Fourier space, i.e. k-space. We propose a deep-learning based approach to perform fast and accurate non-rigid registration from the undersampled k-space data. The basic working principle originates from the Local All-Pass (LAP) technique, a recently introduced optical flow-based registration. The proposed LAPNet is compared against traditional and deep learning image-based registrations and tested on fully-sampled and highly-accelerated (with two undersampling strategies) 3D respiratory motion-resolved MR images in a cohort of 40 patients with suspected liver or lung metastases and 25 healthy subjects. The proposed LAPNet provided consistent and superior performance to image-based approaches throughout different sampling trajectories and acceleration factors.

Image registration is a required step in many practical applications that involve the acquisition of multiple related images. In this paper, we propose a methodology to deal with both the geometric and intensity transformations in the image registration problem. The main idea is to modify an accurate and fast elastic registration algorithm (Local All-Pass-LAP) so that it returns a parametric displacement field, and to estimate the intensity changes by fitting another parametric expression. Although we demonstrate the methodology using a low-order parametric model, our approach is highly flexible and easily allows substantially richer parametrisations, while requiring only limited extra computation cost. In addition, we propose two novel quantitative criteria to evaluate the accuracy of the alignment of two images ("salience correlation") and the number of degrees of freedom ("parsimony") of a displacement field, respectively. Experimental results on both synthetic and real images demonstrate the high accuracy and computational efficiency of our methodology. Furthermore, we demonstrate that the resulting displacement fields are more parsimonious than the ones obtained in other state-of-the-art image registration approaches.

High-quality video frame interpolation often necessitates accurate motion estimation, which can be obtained using modern optical flow methods. In this paper, we use the recently proposed Local All-Pass (LAP) algorithm to compute the optical flow between two consecutive frames. The resulting flow field is used to perform interpolation using cubic splines. We compare the interpolation results against a well-known optical flow estimation algorithm as well as against a recent con-volutional neural network scheme for video frame interpolation. Qualitative and quantitative results show that the LAP algorithm performs fast, high-quality video frame interpolation, and perceptually outperforms the neural network and the Lucas-Kanade method on a variety of test sequences.

Image registration is a significant step in a wide range of practical applications and it is a fundamental problem in various computer vision tasks. In this paper, we propose a highly accurate and fast parametric registration method for mobile phone photos. The proposed algorithm is based on a fast and accurate elastic registration algorithm, the Local All-Pass (LAP) algorithm, which performs in a coarse-to-fine manner. At each iteration, the LAP displacement field is fitted by a parametric model. Thus the image registration problem is equivalent to finding a few parameters to describe the displacement field. The fitting step can be performed very efficiently by solving a linear system of equations. In terms of the fitting model, it is easy to change the type of models to do the parametric fitting for specific applications. Experimental results on both synthetic and real images demonstrate the high accuracy and computational efficiency of the proposed algorithm.

Realistic reasoning applications typically involve many interrelated variables and require the interpretation of data that is both heterogeneous in nature and affected by various types of uncertainty. Accordingly, in this paper we investigate the performance of valuation based algebra networks for reasoning in uncertain multivariate systems. Specifically, we consider networks built from two different approaches to modelling uncertainty: possibility theory and Dempster-Shafer evidence theory. To compare these differing networks, we propose a new possibilistic counterpart to the uncertain implication rule that exists in evidential networks. Using the Captain's decision problem, we analyse the performance of these networks when estimating the number of days a ship will be delayed based on a mixture of uncertain knowledge. We demonstrate that the evidential network is more cautious to changes in uncertainty whereas the possibilistic network is more sensitive. This characteristic could allow the possibilistic network to be used to perform sensitivity analysis on a system.

Sonobuoy fields, comprising a network of sonar transmitters and receivers, are used to find and track underwater targets. For a given environment and sonobuoy field layout, the performance of such a field depends on the scheduling, that is, deciding which source should transmit, and which waveform should be transmitted at any given time. In this paper, we explore the choice of cost function used in myopic scheduling and its effect on tracking performance. Specifically, we consider 5 different cost functions derived from the predicted error covariance matrix of the track. Importantly, our cost functions combine both positional and velocity covariance information to allow the scheduler to choose the optimum source-waveform action. Using realistic multistatic sonobuoy simulations, we demonstrate that each cost function results in a different choice of source-waveform actions, which in turn affects the performance of the scheduler. In particular, we show there is a trade-off between position and velocity error performance such that no one cost function is superior in both.

Estimation of conduction velocity (CV) is an important task in the analysis of surface electromyography (sEMG). The problem can be framed as estimation of a time-varying delay (TVD) between electrode recordings. In this paper we present an algorithm which incorporates information from multiple electrodes into a single TVD estimation. The algorithm uses a common all-pass filter to relate two groups of signals at a local level. We also address a current limitation of CV estimators by providing an automated way of identifying the innervation zone from a set of electrode recordings, thus allowing incorporation of the entire array into the estimation. We validate the algorithm on both synthetic and real sEMG data with results showing the proposed algorithm is both robust and accurate.

Sonobuoy fields, comprising a network of transmitters and receivers, are commonly deployed to find and track underwater targets. For a given environment and sonobuoy field layout, the performance of such a field depends on the scheduling, that is, deciding which source should transmit, and which from a library of available waveforms should be transmitted at any given time. In this paper, we propose a novel scheduling framework based on multi-objective optimization. Specifically, we pose the two tasks of the sonobuoy field-tracking and searching-as separate, competing, objective functions. Using this framework, we propose a characterization of scheduling based on Pareto optimality. This characterization describes the trade-off between the search-track objectives and is demonstrated on realistic multistatic sonobuoy simulations.

This paper deals with the estimation of a deformation that describes the geometric transformation between two images. To solve this problem, we propose a novel framework that relies upon the brightness consistency hypothesis-a pixel's intensity is maintained throughout the transformation. Instead of assuming small distortion and linearizing the problem (e.g. via Taylor Series expansion), we propose to interpret the brightness hypothesis as an all-pass filtering relation between the two images. The key advantages of this new interpretation are that no restrictions are placed on the amplitude of the deformation or on the spatial variations of the images. Moreover, by converting the all-pass filtering to a linear forward-backward filtering relation, our solution to the estimation problem equates to solving a linear system of equations, which leads to a highly efficient implementation. Using this framework, we develop a fast algorithm that relates one image to another, on a local level, using an all-pass filter and then extracts the deformation from the filter-hence the name "Local All-Pass" (LAP) algorithm. The effectiveness of this algorithm is demonstrated on a variety of synthetic and real deformations that are found in applications, such as image registration and motion estimation. In particular, when compared with a selection of image registration algorithms, the LAP obtains very accurate results for significantly reduced computation time and is very robust to noise corruption.

We propose an efficient method for image registration based on iteratively fitting a parametric model to the output of an elastic registration. It combines the flexibility of elastic registration — able to estimate complex deformations — with the robustness of parametric registration — able to estimate very large displacement. Our approach is made feasible by using the recent Local All-Pass (LAP) algorithm; a fast and accurate filter-based method for estimating the local deformation between two images. Moreover, at each iteration we fit a linear parametric model to the local deformation which is equivalent to solving a linear system of equations (very fast and efficient). We use a quadratic polynomial model however the framework can easily be extended to more complicated models. The significant advantage of the proposed method is its robustness to model mis-match (e.g. noise and blurring). Experimental results on synthetic images and real images demonstrate that the proposed algorithm is highly accurate and outperforms a selection of image registration approaches.

Video phylogeny research about joint analysis of correlated video sequences has shown the possibility of developing interesting forensic applications. As an example, it is possible to study the provenance of near-duplicate (ND) video sequences, i.e., videos generated from the same original one through content preserving transformations. To perform this kind of analysis, accurate detection of ND videos is paramount. In this paper, we propose an algorithm for ND video detection and clustering in a challenging setup. Specifically, we analyze a scenario in which many videos, depicting the same event, are recorded by different users. This situation is critical as non-ND videos acquired from very close viewpoints run the risk of being incorrectly detected as ND. The proposed approach leverages on robust hashing properties and the concept of sensor noise traces.

Recently, sampling theory has been broadened to include a class of non-bandlimited signals that possess finite rate of innovation (FRI). In this paper, we consider the problem of determining the minimum rate of innovation (RI) in a noisy setting. First, we adapt a recent model-fitting algorithm for FRI recovery and demonstrate that it achieves the Cramer-Rao bounds. Using this algorithm, we then present a framework to estimate the minimum RI based on fitting the sparsest model to the noisy samples whilst satisfying a mean squared error (MSE) criterion - a signal is recovered if the output MSE is less than the input MSE. Specifically, given a RI, we use the MSE criterion to judge whether our model-fitting has been a success or a failure. Using this output, we present a Dichotomic algorithm that performs a binary search for the minimum RI and demonstrate that it obtains a sparser RI estimate than an existing information criterion approach.

The optical flow is a velocity field that describes the motion of pixels within a sequence (or set) of images. Its estimation plays an important role in areas such as motion compensation, object tracking and image registration. In this paper, we present a novel framework to estimate the optical flow using local all-pass filters. Instead of using the optical flow equation, the framework is based on relating one image to another, on a local level, using an all-pass filter and then extracting the optical flow from the filter. Using this framework, we present a fast novel algorithm for estimating a smoothly varying optical flow, which we term the Local All-Pass (LAP) algorithm. We demonstrate that this algorithm is consistent and accurate, and that it outperforms three state-of-the-art algorithms when estimating constant and smoothly varying flows. We also show initial competitive results for real images.

Estimating the displacements between two images is often addressed using a small displacement assumption, which leads to what is known as the optical flow equation. We study the quality of the underlying approximation for the recently developed Local All-Pass (LAP) optical flow algorithm, which is based on another approach - displacements result from filtering. While the simplest version of LAP computes only first-order differences, we show that the order of LAP approximation is quadratic, unlike standard optical flow equation based algorithms for which this approximation is only linear. More generally, the order of approximation of the LAP algorithm is twice larger than the differentiation order involved. The key step in the derivation is the use of Padé approximants.

Accurate and robust spot tracking is a necessary tool for quantitative motion analysis in fluorescence microscopy images. Few trackers however consider the underlying dynamics present in biological systems. For example, the collective motion of cells often exhibits both fast dynamics, i.e. Brownian motion, and slow dynamics, i.e. time-invariant stationary motion. In this paper, we propose a novel, multi-frame, tracker that exploits this stationary motion. More precisely, we first estimate the stationary motion and then use it to guide the spot tracker. We obtain the stationary motion by adapting a recent optical flow algorithm that relates one image to another locally using an all-pass filter. We perform this operation over all the image frames simultaneously and estimate a single, stationary optical flow. We compare the proposed tracker with two existing techniques and show that our approach is more robust to high noise and varying structure. In addition, we also show initial experiments on real microscopy images.

Recently, classical sampling theory has been broadened to include a class of non-bandlimited signals that possess finite rate of innovation (FRI). In this paper we consider the reconstruction of a periodic stream of Diracs from noisy samples. We demonstrate that its noiseless FRI samples can be represented as a ratio of two polynomials. Using this structure as a model, we propose recovering the FRI signal using a model fitting approach rather than an annihilation method. We present an algorithm that fits this model to the noisy samples and demonstrate that it has low computation cost and is more reliable than two state-of-the-art methods.

The plenoptic function is a powerful tool to analyze the properties of multi-view image data sets. In particular, the understanding of the spectral properties of the plenoptic function is essential in many computer vision applications, including image-based rendering. In this paper, we derive for the first time an exact closed-form expression of the plenoptic spectrum of a slanted plane with finite width and use this expression as the elementary building block to derive the plenoptic spectrum of more sophisticated scenes. This is achieved by approximating the geometry of the scene with a set of slanted planes and evaluating the closed-form expression for each plane in the set. We then use this closed-form expression to revisit uniform plenoptic sampling. In this context, we derive a new Nyquist rate for the plenoptic sampling of a slanted plane and a new reconstruction filter. Through numerical simulations, on both real and synthetic scenes, we show that the new filter outperforms alternative existing filters.

Image based rendering is a technique for producing arbitrary viewpoints of a scene using multiple images instead of exact object models. The recent emergence of low-price, fast, and reliable cameras for measuring depth makes possible the augmentation of traditional color images with depth images. This combination promises to improve the rendering quality of an arbitrary viewpoint and thus have a great impact on IBR. A key issue is to understand, for any particular scene of interest, how many depth images and how many color images are necessary in order to obtain good rendering results. In this paper, using a framework akin to the plenoptic function, we perform a spectral analysis of multi-view depth images in order to determine the relationship between the number of depth and color images required. Our analysis is then validated using both synthetic and real images.

The plenoptic function enables Image-based rendering (IBR) to be viewed in terms of sampling and reconstruction. Thus the spatial sampling rate can be determined through spectral analysis of the plenoptic function. In this paper we present a method of non-uniformly sampling a scene, with a smoothly varying surface, given a finite number of samples. This method approximates such a scene with a set of slanted planes subject to the constraint of finite number of samples. We use the recent spectral analysis of a single slanted plane to determine a piecewise constant spatial sampling rate for the scene. Finally, we show that this sampling rate results in a non-uniform sampling scheme that reconstructs the plenoptic function beyond that of uniform sampling.

The plenoptic function enables Image-based rendering (IBR) to be viewed in terms of sampling and reconstruction. Thus the spatial sampling rate can be determined through spectral analysis of the plenoptic function. In this paper we examine the bandwidth of the plenoptic function when both the field of view and the scene width are finite. This analysis is carried out on two planar Lambertian scenes, a fronto-parallel plane and a slanted plane, and in both cases the texture is bandlimited. We derive an exact closed-form expression for the plenoptic spectrum of a slanted plane with sinusoidal texture. We show that in both cases the finite constraints lead to band-unlimited spectra. By determining the essential bandwidth, we derive a sampling curve that gives an adequate camera spacing for a given distance between the scene and the camera line.