The aim of the paper was to examine and experimentally implement a multi-camera person tracking (MCPT) system based on the integration of modern re-identification (ReID) and trajectory association methods. During the research, we were able to gain a comprehensive understanding of the operation and performance of current state-of-the-art single-camera multi-object tracking solutions, with a particular focus on the effects of detector selection, ReID model, and parameter tuning. The proposed system can be divided into two main units: a single-camera and a multi-camera tracking unit. Moreover, this system employs a clustering algorithm to ensure that all individuals are visible at that moment. The implementation of multi-camera experiments, the developed ReID-based trajectory association, and hierarchical clustering made it possible to unify data streams from different viewpoints and consistently track identities. The investigations highlighted challenges in multi-camera environments, such as appearance differences between cameras, partial occlusions, and motion pattern distortions. The successful implementation of multi-camera tracking tasks requires the coordinated operation of multiple complex components, and the developed experimental pipeline was able to demonstrate the advantages and limitations of modern ReID-based methods, as well as point the way towards the development of future person tracking systems.

The study deals with machine learning and computer vision, emphasizing the importance of understanding both low-level and high-level information of classifiers. The paper presents a special multi-output classification, where there are only two independent labels, the color and the type of vehicles in images. For the solution of the multi-output classification task, a new approach was examined, a multi-class classifier with single output. The original multi-output classification is considered as high-level task, while the single output classifier with all combination of color and type classes is a low-level classifier, because its output (a single label) is more detailed. The novelty of the work is the comparison of both approaches, the original high-level classifiers with low-level classifier. The contribution of the paper is the different transformation methods (e.g. stacking-based) from low-level classifier to original high-level classification task. Our results show that low-level classifiers can be a viable alternative, in particular the stacking-based method can enhance the classification accuracy.

We design and analyze primal-dual, feasible interior-point algorithms (IPAs) employing full Newton steps to solve convex optimization problems in standard conic form. Unlike most nonsymmetric cone programming methods, the algorithms presented in this paper require only a logarithmically homogeneous self-concordant barrier (LHSCB) of the primal cone but compute feasible and \varepsilon-optimal solutions to both primal and dual problems in O(p\nulog(1/\varepsilon)) iterations, where \nu is the barrier parameter of the LHSCB; this matches the best currently known theoretical iteration complexity of IPAs for both symmetric and nonsymmetric cone programming. The definition of the neighborhood of the central path and feasible starts ensures that the computed solutions are compatible with the dual certificates framework introduced by Lee, Papp, and Varga [Dual Certificates of Primal Cone Membership, 2025]. Several initialization strategies are discussed, including two-phase methods that can be applied if a strictly feasible primal solution is available and one based on a homogeneous self-dual embedding that allows the rigorous detection of feasible or optimal solutions of large norm. In a detailed study of a classic, notoriously difficult polynomial optimization problem, we demonstrate that the methods are efficient and numerically reliable. Although the standard approach using semidefinite programming fails for this problem with the solvers we tried, the new IPAs compute highly accurate near-optimal solutions that can be certified to be near optimal in exact arithmetic.

Consider a sequence of real-valued functions of a real variable given by a homogeneous linear recursion with differentiable coefficients. We show that if the functions in the sequence are differentiable, then the sequence of derivatives also satisfies a homogeneous linear recursion whose order is at most double the order of original recursion. Similarly to the well-known operations that determine the elementwise sum and product of two linear recursive sequences, the coefficient functions of our recursion for the derivatives are easily computable from the original coefficient functions and their derivatives by direct manipulation of the coefficients of the characteristic polynomial of the recursion, without determining the roots. A simple application, computing linear recursions for derivatives of orthogonal polynomials, is presented.

In Davis and Papp (2022), the authors introduced the concept of dual certificates of (weighted) sum-of-squares polynomials, which are vectors from the dual cone of weighted sums of squares (WSOS) polynomials that can be interpreted as nonnegativity certificates. This initial theoretical work showed that for every polynomial in the interior of a WSOS cone, there exists a rational dual certificate proving that the polynomial is WSOS. In this article, we analyze the complexity of rational dual certificates of WSOS polynomials by bounding the bit sizes of integer dual certificates as a function of parameters such as the degree and the number of variables of the polynomials, or their distance from the boundary of the cone. After providing a general bound, we explore several special cases, such as univariate polynomials nonnegative over the real line or a bounded interval, represented in different commonly used bases. We also provide an algorithm which runs in rational arithmetic and computes a rational certificate with boundable bit size for a WSOS lower bound of the input polynomial.

We prove that every homogeneous convex polyhedron with only one unstable equilibrium (known as a mono-unstable convex polyhedron) has at least 7 vertices. Although it has been long known that no mono-unstable tetrahedra exist, and mono-unstable polyhedra with as few as 18 vertices and faces have been constructed, this is the first nontrivial lower bound on the number of vertices for a mono-unstable polyhedron. There are two main ingredients in the proof. We first establish two types of relationships, both expressible as (non-convex) quadratic inequalities, that the coordinates of the vertices of a mono-unstable convex polyhedron must satisfy, taking into account the combinatorial structure of the polyhedron. Then we use numerical semidefinite optimization algorithms to compute easily and independently verifiable, rigorous certificates that the resulting systems of quadratic inequalities (5943 in total) are indeed inconsistent in each case.

Circuit polynomials are polynomials with properties that make it easy to compute sharp and certifiable global lower bounds for them. Consequently, one may use them to find certifiable lower bounds for any polynomial by writing it as a sum of circuit polynomials with known lower bounds. Recent work has shown that sums of nonnegative circuit polynomials (or SONC polynomials for short) can be used to compute global lower bounds (called SONC bounds) for polynomials in this manner very efficiently both in theory and in practice, if the polynomial is bounded from below and its support satisfies a certain nondegeneracy assumption. The quality of the SONC bound depends on the circuits used in the computation but finding the set of circuits that yield the best attainable SONC bound among the astronomical number of candidate circuits is a non-trivial task that has not been addressed so far. We propose an efficient method to compute the optimal SONC lower bound by iteratively identifying the optimal circuits to use in the SONC bounding process. The method is derived from a new proof of the result that every SONC polynomial decomposes into SONC polynomials on the same support. This proof is based on convex programming duality and motivates a column generation approach that is particularly attractive for sparse polynomials of high degree and with many unknowns. The method is implemented and tested on a large set of sparse polynomial optimization problems with up to 40 unknowns, of degree up to 60, and up to 3000 monomials in the support. The results indicate that the method is efficient in practice and requires only a small number of iterations to identify the optimal circuits.

In the study of monostatic polyhedra, initiated by John H. Conway in 1966, the main question is to construct such an object with the minimal number of faces and vertices. By distinguishing between various material distributions and stability types, this expands into a small family of related questions. While many upper and lower bounds on the necessary numbers of faces and vertices have been established, none of these questions has been so far resolved. Adapting an algorithm presented in Bozóki et al. (2022), here we offer the first complete answer to a question from this family: by using the toolbox of semidefinite optimization to efficiently generate the hundreds of thousands of infeasibility certificates, we provide the first-ever proof for the existence of a monostatic polyhedron with point masses, having minimal number (V=11) of vertices (Theorem 3) and a minimal number (F=8) of faces. We also show that V=11 is the smallest number of vertices that a mono-unstable polyhedron can have in all dimensions greater than 1 (Corollary 6).

BACKGROUND:Stereotactic radiosurgery (SRS) is an established treatment for patients with brain metastases (BMs). However, damage to the healthy brain may limit the tumor dose for patients with multiple lesions.PURPOSE:In this study, we investigate the potential of spatiotemporal fractionation schemes to reduce the biological dose received by the healthy brain in SRS of multiple BMs, and also demonstrate a novel concept of spatiotemporal fractionation for polymetastatic cancer patients that faces less hurdles for clinical implementation.METHODS:Spatiotemporal fractionation (STF) schemes aim at partial hypofractionation in the metastases along with more uniform fractionation in the healthy brain. This is achieved by delivering distinct dose distributions in different fractions, which are designed based on their cumulative biologically effective dose ( BED α / β ${\rm{BED}}_{{{\alpha}}/{{\beta}}}$ ) such that each fraction contributes with high doses to complementary parts of the target volume, while similar dose baths are delivered to the normal tissue. For patients with multiple brain metastases, a novel constrained approach to spatiotemporal fractionation (cSTF) is proposed, which is more robust against setup and biological uncertainties. The approach aims at irradiating entire metastases with possibly different doses, but spatially similar dose distributions in every fraction, where the optimal dose contribution of every fraction to each metastasis is determined using a new planning objective to be added to the BED-based treatment plan optimization problem. The benefits of spatiotemporal fractionation schemes are evaluated for three patients, each with >25 BMs.RESULTS:For the same tumor BED10 and the same brain volume exposed to high doses in all plans, the mean brain BED2 can be reduced compared to uniformly fractionated plans by 9%-12% with the cSTF plans and by 13%-19% with the STF plans. In contrast to the STF plans, the cSTF plans avoid partial irradiation of the individual metastases and are less sensitive to misalignments of the fractional dose distributions when setup errors occur.CONCLUSION:Spatiotemporal fractionation schemes represent an approach to lower the biological dose to the healthy brain in SRS-based treatments of multiple BMs. Although cSTF cannot achieve the full BED reduction of STF, it improves on uniform fractionation and is more robust against both setup errors and biological uncertainties related to partial tumor irradiation.

The fast improvement of deep learning methods resulted in breakthroughs in image classification, object detection, and object tracking. Autonomous driving and traffic monitoring systems, especially the on-premise installed fixed position multi-camera configurations, benefit greatly from recent advances. In this paper, we propose a Multi-Camera Multi-Target (MCMT) vehicle tracking system using a constrained hierarchical clustering solution, which improves trajectory matching, and thus provides a more robust tracking of objects transitioning between cameras. YOLOv5, ByteTrack, and ResNet50-IBN ReID networks are used for vehicle detection and tracking. Static attributes such as vehicle type and vehicle color are determined from ReID features with SVM. The proposed ReID feature-based attribute categorization shows better performance, than its pure CNN counterpart. Single-camera trajectories (SCTs) are combined into multi-camera trajectories (MCTs) using hierarchical agglomerative clustering (HAC) with time and space constraints (our proposed algorithm is denoted by MCT#MAC). Similarities between SCTs are measured by comparing the mean ReID features cumulated on the trajectory. The system was evaluated on more datasets, and our experiments demonstrate that constraining HAC by manipulating the proximity matrix greatly improves the multi-camera IDF1 score.

We present alfonso, an open-source Matlab package for solving conic optimization problems over nonsymmetric convex cones. The implementation is based on the authors’ corrected analysis of a method of Skajaa and Ye. It enables optimization over any convex cone as long as a logarithmically homogeneous self-concordant barrier is available for the cone or its dual. This includes many nonsymmetric cones, for example, hyperbolicity cones and their duals (such as sum-of-squares cones), semidefinite and second-order cone representable cones, power cones, and the exponential cone. Besides enabling the solution of problems that cannot be cast as optimization problems over a symmetric cone, algorithms for nonsymmetric conic optimization also offer performance advantages for problems whose symmetric cone programming representation requires a large number of auxiliary variables or has a special structure that can be exploited in the barrier computation. The worst-case iteration complexity of alfonso is the best known for nonsymmetric cone optimization: [Formula: see text] iterations to reach an ε-optimal solution, where ν is the barrier parameter of the barrier function used in the optimization. Alfonso can be interfaced with a Matlab function (supplied by the user) that computes the Hessian of a barrier function for the cone. A simplified interface is also available to optimize over the direct product of cones for which a barrier function has already been built into the software. This interface can be easily extended to include new cones. Both interfaces are illustrated by solving linear programs. The oracle interface and the efficiency of alfonso are also demonstrated using an optimal design of experiments problem in which the tailored barrier computation greatly decreases the solution time compared with using state-of-the-art, off-the-shelf conic optimization software. Summary of Contribution: The paper describes an open-source Matlab package for optimization over nonsymmetric cones. A particularly important feature of this software is that, unlike other conic optimization software, it enables optimization over any convex cone as long as a suitable barrier function is available for the cone or its dual, not limiting the user to a small number of specific cones. Nonsymmetric cones for which such barriers are already known include, for example, hyperbolicity cones and their duals (such as sum-of-squares cones), semidefinite and second-order cone representable cones, power cones, and the exponential cone. Thus, the scope of this software is far larger than most current conic optimization software. This does not come at the price of efficiency, as the worst-case iteration complexity of our algorithm matches the iteration complexity of the most successful interior-point methods for symmetric cones. Besides enabling the solution of problems that cannot be cast as optimization problems over a symmetric cone, our software can also offer performance advantages for problems whose symmetric cone programming representation requires a large number of auxiliary variables or has a special structure that can be exploited in the barrier computation. This is also demonstrated in this paper via an example in which our code significantly outperforms Mosek 9 and SCS 2.

Objective. Combined proton–photon treatments, where most fractions are delivered with photons and only a few are delivered with protons, may represent a practical approach to optimally use limited proton resources. It has been shown that, when organs at risk (OARs) are located within or near the tumor, the optimal multi-modality treatment uses protons to hypofractionate parts of the target volume and photons to achieve near-uniform fractionation in dose-limiting healthy tissues, thus exploiting the fractionation effect. These plans may be sensitive to range and setup errors, especially misalignments between proton and photon doses. Thus, we developed a novel stochastic optimization method to directly incorporate these uncertainties into the biologically effective dose (BED)-based simultaneous optimization of proton and photon plans. Approach. The method considers the expected value E b and standard deviation σ b of the cumulative BED b in every voxel of a structure. For the target, a piecewise quadratic penalty function of the form b min − E b − 2 σ b + 2 is minimized, aiming for plans in which the expected BED minus two times the standard deviation exceeds the prescribed BED b min . Analogously, E b + 2 σ b − b max + 2 is considered for OARs. Main results. Using a spinal metastasis case and a liver cancer patient, it is demonstrated that the novel stochastic optimization method yields robust combined treatment plans. Tumor coverage and a good sparing of the main OARs are maintained despite range and setup errors, and especially misalignments between proton and photon doses. This is achieved without explicitly considering all combinations of proton and photon error scenarios. Significance. Concerns about range and setup errors for safe clinical implementation of optimized proton–photon radiotherapy can be addressed through an appropriate stochastic planning method.

We study the problem of computing weighted sum-of-squares (WSOS) certificates for positive polynomials over a compact semialgebraic set. Building on the theory of interior-point methods for convex optimization, we introduce the concept of dual cone certificates, which allows us to interpret vectors from the dual of the sum-of-squares cone as rigorous nonnegativity certificates of a WSOS polynomial. Whereas conventional WSOS certificates are alternative representations of the polynomials they certify, dual certificates are distinct from the certified polynomials; moreover, each dual certificate certifies a full-dimensional convex cone of WSOS polynomials. As a result, rational WSOS certificates can be constructed from numerically computed dual certificates at little additional cost, without any rounding or projection steps applied to the numerical certificates. As an additional algorithmic application, we present an almost entirely numerical hybrid algorithm for computing the optimal WSOS lower bound of a given polynomial along with a rational dual certificate, with a polynomial-time computational cost per iteration and linear rate of convergence.

Purpose We consider the following scenario: A radiotherapy clinic has a limited number of proton therapy slots available each day to treat cancer patients of a given tumor site. The clinic's goal is to minimize the expected number of complications in the cohort of all patients of that tumor site treated at the clinic, and thereby maximize the benefit of its limited proton resources. Methods To address this problem, we extend the normal tissue complication probability (NTCP) model-based approach to proton therapy patient selection to the situation of limited resources at a given institution. We assume that, on each day, a newly diagnosed patient is scheduled for treatment at the clinic with some probability and with some benefit Delta NTCP$\Delta NTCP$ from protons over photons, which is drawn from a probability distribution. When a new patient is scheduled for treatment, a decision for protons or photons must be made, and a patient may wait only for a limited amount of time for a proton slot becoming available. The goal is to determine the Delta NTCP$\Delta NTCP$ thresholds for selecting a patient for proton therapy, which optimally balance the competing goals of making use of all available slots while not blocking slots with patients with low benefit. This problem can be formulated as a Markov decision process (MDP) and the optimal thresholds can be determined via a value-policy iteration method. Results The optimal Delta NTCP$\Delta NTCP$ thresholds depend on the number of available proton slots, the average number of patients under treatment, and the distribution of Delta NTCP$\Delta NTCP$ values. In addition, the optimal thresholds depend on the current utilization of the facility. For example, if one proton slot is available and a second frees up shortly, the optimal Delta NTCP$\Delta NTCP$ threshold is lower compared to a situation where all but one slot remain blocked for longer. Conclusions MDP methodology can be used to augment current NTCP model-based patient selection methods to the situation that, on any given day, the number of proton slots is limited. The optimal Delta NTCP$\Delta NTCP$ threshold then depends on the current utilization of the proton facility. Although, the optimal policy yields only a small nominal benefit over a constant threshold, it is more robust against variations in patient load.

The research topic presented in this paper belongs to computer vision problems in the transport application area, where the statistical data of the results give the input for the transport analysis. Although object tracking in a controlled environment could be performed with good results in general, accurate and detailed annotation of vehicles is a common problem in traffic analysis. Such annotation includes static and dynamic attributes of numerous vehicles. Most recent object trackers employ CNNs to compute the so-called re-identification features of the bounding boxes. In this paper we introduce hybrid re-identification features, which combine latent, static, and dynamic attributes to improve tracking. Furthermore, we propose a lightweight solution that could be integgrated in a real-time multi-camera tracking system.

PURPOSE:Proton therapy is a limited resource that is not available to all patients who may benefit from it. We investigated combined proton-photon treatments, in which some fractions are delivered with protons and the remaining fractions with photons, as an approach to maximize the benefit of limited proton therapy resources at a population level.METHODS AND MATERIALS:To quantify differences in normal-tissue complication probability (NTCP) between protons and photons, we considered a cohort of 45 patients with head and neck cancer for whom intensity modulated radiation therapy and intensity modulated proton therapy plans were previously created, in combination with NTCP models for xerostomia and dysphagia considered in the Netherlands for proton patient selection. Assuming limited availability of proton slots, we developed methods to optimally assign proton fractions in combined proton-photon treatments to minimize the average NTCP on a population level. The combined treatments were compared with patient selection strategies in which patients are assigned to single-modality proton or photon treatments.RESULTS:There is a benefit of combined proton-photon treatments compared with patient selection, owing to the nonlinearity of NTCP functions; that is, the initial proton fractions are the most beneficial, whereas additional proton fractions have a decreasing benefit when a flatter part of the NTCP curve is reached. This effect was small for the patient cohort and NTCP models considered, but it may be larger if dose-response relationships are better known. In addition, when proton slots are limited, patient selection methods face a trade-off between leaving slots unused and blocking slots for future patients who may have a larger benefit. Combined proton-photon treatments with flexible proton slot assignment provide a method to make optimal use of all available resources.CONCLUSIONS:Combined proton-photon treatments allow for better use of limited proton therapy resources. The benefit over patient selection schemes depends on the NTCP models and the dose differences between protons and photons.

Photo-based automatic snake species identification could assist in clinical management of snakebites. LifeCLEF announced the SnakeCLEF 2021 challenge, which aimed attention on this task and provided location metadata for most snake images. This paper describes the participation of the BME-TMIT team in this challenge. In order to reduce clutter and drop the unnecessary background, we employed the state-of-the-art EfficientDet object detector, which was fine-tuned on manually annotated images. Detected snakes were then classified by EfficientNet weighted with the likelihood of location information. Based on the official evaluation of SnakeCLEF 2021, our solution achieved an F1 country score of 0.903, which placed our team at rank 1 position in the challenge.

Supervised machine learning tasks often require a large number of labeled training data to set up a model, and then prediction - for example the classification - is carried out based on this model. Nowadays tremendous amount of data is available on the web or in data warehouses, although only a portion of those data is annotated and the labeling process can be tedious, expensive and time consuming. Active learning tries to overcome this problem by reducing the labeling cost through allowing the learning system to iteratively select the data from which it learns. In special case of active learning, the process starts from zero initialized scenario, where the labeled training dataset is empty, and therefore only unsupervised methods can be performed. In this paper a novel query strategy framework is presented for this problem, called Clustering Based Balanced Sampling Framework (CBBSF), which is not only select the initial labeled training dataset, but uniformly selects the items among the categories to get a balanced labeled training dataset. The framework includes an assignment technique to implicitly determine the class membership probabilities. Assignment solution is updated during CBBSF iterations, hence it simulates supervised machine learning more accurately as the process progresses. The proposed Spectral Clustering Based Sampling (SCBS) query startegy realizes the CBBSF framework, and therefore it is applicable in the special zero initialized situation. This selection approach uses ClusterGAN (Clustering using Generative Adversarial Networks) integrated in the spectral clustering algorithm and then it selects an unlabeled instance depending on the class membership probabilities. Global and local versions of SCBS were developed, furthermore, most confident and minimal entropy measures were calculated, thus four different SCBS variants were examined in total. Experimental evaluation was conducted on the MNIST dataset, and the results showed that SCBS outperforms the state-of-the-art zero initialized active learning query strategies.

Given the challenge of gathering labelled training data for machine learning tasks, active learning has become popular. This paper focuses on the beginning of unsupervised active learning, where there are no labelled data at all. The aim of this zero initialised unsupervised active learning is to select the most informative examples - even from an imbalanced dataset - to be labelled manually. Our solution with proposed selection strategy, called Optimally Balanced Entropy-Based Sampling (OBEBS) reaches a balanced training set at each step to avoid imbalanced problems. Two theorems of the optimal solution for selection strategy are also presented and proved in the paper. At the beginning of the active learning, there is not enough information for supervised machine learning method, thus our selection strategy is based on unsupervised learning (clustering). The cluster membership likelihoods of the items are essential for the algorithm to connect the clusters and the classes, i.e., to find assignment between them. For the best assignment, the Hungarian algorithm is used, and single, multi, and adaptive assignment variants of OBEBS method are developed. Based on generated and real images datasets of handwritten digits, the experimental results show that our method surpasses the state-of-the-art methods.