Related papers: Edge detection with polynomial frames on the spher…
We propose a method for tracing implicit real algebraic curves defined by polynomials with rank-deficient Jacobians. For a given curve $f^{-1}(0)$, it first utilizes a regularization technique to compute at least one witness point per…
In this paper we introduce a polynomial frame on the unit sphere $\sph$ of $\mathbb{R}^d$, for which every distribution has a wavelet-type decomposition. More importantly, we prove that many function spaces on the sphere $\sph$, such as…
Used in the paper is an overcomplete piecewise-polynomial image model incorporating sparsity. The paper shows that using such a model, the edges in the image can be resolved robustly with respect to noise. Two variants of the proposed…
This paper presents an edge-based defocus blur estimation method from a single defocused image. We first distinguish edges that lie at depth discontinuities (called depth edges, for which the blur estimate is ambiguous) from edges that lie…
In this article, we construct discrete tight frames for $L^2(\mathbb{S}^{d-1})$, $d\geq3$, which consist of localized polynomial wavelets with adjustable degrees of directionality. In contrast to the well studied isotropic case, these…
The purpose of this paper is to present simple and fast methods for computing control points for polynomial curves and polynomial surfaces given explicitly in terms of polynomials (written as sums of monomials). We give recurrence formulae…
Estimating the number of vertices of a two dimensional projection, called a shadow, of a polytope is a fundamental tool for understanding the performance of the shadow simplex method for linear programming among other applications. We prove…
This paper presents a new approach to the detection of discontinuities in the n-th derivative of observational data. This is achieved by performing two polynomial approximations at each interstitial point. The polynomials are coupled by…
A sphere is a fundamental geometric object widely used in (computer aided) geometric design. It possesses rational parameterizations but no parametric polynomial parameterization exists. The present study provides an approach to the optimal…
Edge detection is a critical component of many vision systems, including object detectors and image segmentation algorithms. Patches of edges exhibit well-known forms of local structure, such as straight lines or T-junctions. In this paper…
The estimation of probabilities of network edges from the observed adjacency matrix has important applications to predicting missing links and network denoising. It has usually been addressed by estimating the graphon, a function that…
This paper presents a state-of-the-art approach in object detection for being applied in future SLAM problems. Although, many SLAM methods are proposed to create suitable autonomy for mobile robots namely ground vehicles, they still face…
This paper presents a reliable method to verify the existence of loops along the uncertain trajectory of a robot, based on proprioceptive measurements only, within a bounded-error context. The loop closure detection is one of the key points…
We prove the first polynomial bound on the number of monotonic homotopy moves required to tighten a collection of closed curves on any compact orientable surface, where the number of crossings in the curve is not allowed to increase at any…
Existing semantic segmentation approaches either aim to improve the object's inner consistency by modeling the global context, or refine objects detail along their boundaries by multi-scale feature fusion. In this paper, a new paradigm for…
Modeling deformations of a real object is an important task in computer vision, biomedical engineering and biomechanics. In this paper, we focus on a situation where a three-dimensional object is rotationally deformed about a fixed axis,…
This paper proposes a novel feature called spectrum congruency for describing edges in images. The spectrum congruency is a generalization of the phase congruency, which depicts how much each Fourier components of the image are congruent in…
Detecting edges is a fundamental problem in computer vision with many applications, some involving very noisy images. While most edge detection methods are fast, they perform well only on relatively clean images. Indeed, edges in such…
Edge detection is widely and fundamental feature used in various algorithms in computer vision to determine the edges in an image. The edge detection algorithm is used to determine the edges in an image which are further used by various…
Polynomial ensembles are determinantal point processes associated with (non necessarily orthogonal) projections onto polynomial subspaces. The aim of this survey article is to put forward the use of recurrence coefficients to obtain the…