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Region extraction is a very common task in both Computer Science and Engineering with several applications in object recognition and motion analysis, among others. Most of the literature focuses on regions delimited by straight lines, often in the special case of intersection detection among two unstructured meshes. While classical region extraction algorithms for line drawings and mesh intersection algorithms have proved to be able to deal with many applications, the advances in Isogeometric Analysis require a generalization of such problem to the case in which the regions to be extracted are bounded by an arbitrary number of curved segments. In this work we present a novel region extraction algorithm that allows a precise numerical integration of functions defined in different spline spaces. The presented algorithm has several interesting applications in contact problems, mortar methods, and quasi-interpolation problems.

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Existing works on motion deblurring either ignore the effects of depth-dependent blur or work with the assumption of a multi-layered scene wherein each layer is modeled in the form of fronto-parallel plane. In this work, we consider the case of 3D scenes with piecewise planar structure i.e., a scene that can be modeled as a combination of multiple planes with arbitrary orientations. We first propose an approach for estimation of normal of a planar scene from a single motion blurred observation. We then develop an algorithm for automatic recovery of number of planes, the parameters corresponding to each plane, and camera motion from a single motion blurred image of a multiplanar 3D scene. Finally, we propose a first-of-its-kind approach to recover the planar geometry and latent image of the scene by adopting an alternating minimization framework built on our findings. Experiments on synthetic and real data reveal that our proposed method achieves state-of-the-art results.

Functional quantile regression (FQR) is a useful alternative to mean regression for functional data as it provides a comprehensive understanding of how scalar predictors influence the conditional distribution of functional responses. In this article, we study the FQR model for densely sampled, high-dimensional functional data without relying on parametric error or independent stochastic process assumptions, with the focus being on statistical inference under this challenging regime along with scalable implementation. This is achieved by a simple but powerful distributed strategy, in which we first perform separate quantile regression to compute $M$-estimators at each sampling location, and then carry out estimation and inference for the entire coefficient functions by properly exploiting the uncertainty quantification and dependence structures of $M$-estimators. We derive a uniform Bahadur representation and a strong Gaussian approximation result for the $M$-estimators on the discrete sampling grid, leading to dimension reduction and serving as the basis for inference. An interpolation-based estimator with minimax optimality and a Bayesian alternative to improve upon finite sample performance are discussed. Large sample properties for point and simultaneous interval estimators are established. The obtained minimax optimal rate under the FQR model shows an interesting phase transition phenomenon that has been previously observed in functional mean regression. The proposed methods are illustrated via simulations and an application to a mass spectrometry proteomics dataset.

In selection processes such as hiring, promotion, and college admissions, implicit bias toward socially-salient attributes such as race, gender, or sexual orientation of candidates is known to produce persistent inequality and reduce aggregate utility for the decision maker. Interventions such as the Rooney Rule and its generalizations, which require the decision maker to select at least a specified number of individuals from each affected group, have been proposed to mitigate the adverse effects of implicit bias in selection. Recent works have established that such lower-bound constraints can be very effective in improving aggregate utility in the case when each individual belongs to at most one affected group. However, in several settings, individuals may belong to multiple affected groups and, consequently, face more extreme implicit bias due to this intersectionality. We consider independently drawn utilities and show that, in the intersectional case, the aforementioned non-intersectional constraints can only recover part of the total utility achievable in the absence of implicit bias. On the other hand, we show that if one includes appropriate lower-bound constraints on the intersections, almost all the utility achievable in the absence of implicit bias can be recovered. Thus, intersectional constraints can offer a significant advantage over a reductionist dimension-by-dimension non-intersectional approach to reducing inequality.

We present an implicit-explicit finite volume scheme for isentropic two phase flow in all Mach number regimes. The underlying model belongs to the class of symmetric hyperbolic thermodynamically compatible models. The key element of the scheme consists of a linearisation of pressure and enthalpy terms at a reference state. The resulting stiff linear parts are integrated implicitly, whereas the non-linear higher order and transport terms are treated explicitly. Due to the flux splitting, the scheme is stable under a CFL condition which determined by the resolution of the slow material waves and allows large time steps even in the presence of fast acoustic waves. Further the singular Mach number limits of the model are studied and the asymptotic preserving property of the scheme is proven. In numerical simulations the consistency with single phase flow, accuracy and the approximation of material waves in different Mach number regimes are assessed.

Intersection over Union (IoU) is the most popular evaluation metric used in the object detection benchmarks. However, there is a gap between optimizing the commonly used distance losses for regressing the parameters of a bounding box and maximizing this metric value. The optimal objective for a metric is the metric itself. In the case of axis-aligned 2D bounding boxes, it can be shown that $IoU$ can be directly used as a regression loss. However, $IoU$ has a plateau making it infeasible to optimize in the case of non-overlapping bounding boxes. In this paper, we address the weaknesses of $IoU$ by introducing a generalized version as both a new loss and a new metric. By incorporating this generalized $IoU$ ($GIoU$) as a loss into the state-of-the art object detection frameworks, we show a consistent improvement on their performance using both the standard, $IoU$ based, and new, $GIoU$ based, performance measures on popular object detection benchmarks such as PASCAL VOC and MS COCO.

Machine learning methods are powerful in distinguishing different phases of matter in an automated way and provide a new perspective on the study of physical phenomena. We train a Restricted Boltzmann Machine (RBM) on data constructed with spin configurations sampled from the Ising Hamiltonian at different values of temperature and external magnetic field using Monte Carlo methods. From the trained machine we obtain the flow of iterative reconstruction of spin state configurations to faithfully reproduce the observables of the physical system. We find that the flow of the trained RBM approaches the spin configurations of the maximal possible specific heat which resemble the near criticality region of the Ising model. In the special case of the vanishing magnetic field the trained RBM converges to the critical point of the Renormalization Group (RG) flow of the lattice model. Our results suggest an alternative explanation of how the machine identifies the physical phase transitions, by recognizing certain properties of the configuration like the maximization of the specific heat, instead of associating directly the recognition procedure with the RG flow and its fixed points. Then from the reconstructed data we deduce the critical exponent associated to the magnetization to find satisfactory agreement with the actual physical value. We assume no prior knowledge about the criticality of the system and its Hamiltonian.

This paper addresses the problem of head detection in crowded environments. Our detection is based entirely on the geometric consistency across cameras with overlapping fields of view, and no additional learning process is required. We propose a fully unsupervised method for inferring scene and camera geometry, in contrast to existing algorithms which require specific calibration procedures. Moreover, we avoid relying on the presence of body parts other than heads or on background subtraction, which have limited effectiveness under heavy clutter. We cast the head detection problem as a stereo MRF-based optimization of a dense pedestrian height map, and we introduce a constraint which aligns the height gradient according to the vertical vanishing point direction. We validate the method in an outdoor setting with varying pedestrian density levels. With only three views, our approach is able to detect simultaneously tens of heavily occluded pedestrians across a large, homogeneous area.

Although it is well believed for years that modeling relations between objects would help object recognition, there has not been evidence that the idea is working in the deep learning era. All state-of-the-art object detection systems still rely on recognizing object instances individually, without exploiting their relations during learning. This work proposes an object relation module. It processes a set of objects simultaneously through interaction between their appearance feature and geometry, thus allowing modeling of their relations. It is lightweight and in-place. It does not require additional supervision and is easy to embed in existing networks. It is shown effective on improving object recognition and duplicate removal steps in the modern object detection pipeline. It verifies the efficacy of modeling object relations in CNN based detection. It gives rise to the first fully end-to-end object detector.

While most steps in the modern object detection methods are learnable, the region feature extraction step remains largely hand-crafted, featured by RoI pooling methods. This work proposes a general viewpoint that unifies existing region feature extraction methods and a novel method that is end-to-end learnable. The proposed method removes most heuristic choices and outperforms its RoI pooling counterparts. It moves further towards fully learnable object detection.

This work presents a region-growing image segmentation approach based on superpixel decomposition. From an initial contour-constrained over-segmentation of the input image, the image segmentation is achieved by iteratively merging similar superpixels into regions. This approach raises two key issues: (1) how to compute the similarity between superpixels in order to perform accurate merging and (2) in which order those superpixels must be merged together. In this perspective, we firstly introduce a robust adaptive multi-scale superpixel similarity in which region comparisons are made both at content and common border level. Secondly, we propose a global merging strategy to efficiently guide the region merging process. Such strategy uses an adpative merging criterion to ensure that best region aggregations are given highest priorities. This allows to reach a final segmentation into consistent regions with strong boundary adherence. We perform experiments on the BSDS500 image dataset to highlight to which extent our method compares favorably against other well-known image segmentation algorithms. The obtained results demonstrate the promising potential of the proposed approach.

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