Related papers: Changing Views on Curves and Surfaces
Neural representations of 3D data have been widely adopted across various applications, particularly in recent work leveraging coordinate-based networks to model scalar or vector fields. However, these approaches face inherent challenges,…
Reconstructing 3D geometry and appearance from a sparse set of fixed cameras is a foundational task with broad applications, yet it remains fundamentally constrained by the limited viewpoints. We show that this bound can be broken by…
Visual Place Recognition (VPR) is the process of recognising a previously visited place using visual information, often under varying appearance conditions and viewpoint changes and with computational constraints. VPR is related to the…
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,…
Polytopes are the basic finite data structures for convex sets: they appear as feasible regions in linear optimization, as geometric summaries in algorithms, and as random objects in stochastic geometry. A natural geometric question is…
A very general surface of degree at least four in projective space of dimension three contains no curves other than intersections with surfaces. We find a formula for the degree of the locus of surfaces of degree at least five which contain…
In this paper we first recall the definition of geometical model of the visual cortex, focusing in particular on the geometrical properties of horizontal cortical connectivity. Then we recognize that histograms of edges - co-occurrences are…
The ruled surfaces, i.e., surfaces generated by one parametric set of lines, are widely used in the~field of applied geometry. An~isophote on a surface is a curve consisting of surface points whose normals form a constant angle with some…
This paper gives an overview of a theory for modelling the interaction between geometric image transformations and receptive field responses for a visual observer that views objects and spatio-temporal events in the environment. This…
We present a method that learns a spatiotemporal neural irradiance field for dynamic scenes from a single video. Our learned representation enables free-viewpoint rendering of the input video. Our method builds upon recent advances in…
Vanishing points and vanishing lines are classical geometrical concepts in perspective cameras that have a lineage dating back to 3 centuries. A vanishing point is a point on the image plane where parallel lines in 3D space appear to…
Towards intelligent image editing, object removal should eliminate both the target object and its causal visual artifacts, such as shadows and reflections. However, existing image appearance-based methods either follow strictly mask-aligned…
Cross-view video understanding is an important yet under-explored area in computer vision. In this paper, we introduce a joint parsing framework that integrates view-centric proposals into scene-centric parse graphs that represent a…
AR/VR applications and robots need to know when the scene has changed. An example is when objects are moved, added, or removed from the scene. We propose a 3D object discovery method that is based only on scene changes. Our method does not…
We estimate from below the number of lines meeting each of given 4 disjoint smooth closed curves in a given cyclic order in the real projective 3-space and in a given linear order in the Euclidean 3-space. Similarly, we estimate the number…
We find new examples of complex surfaces with countably many non-isomorphic algebraic structures. Here is one such example: take an elliptic curve $E$ in $\mathbb P^2$ and blow up nine general points on $E$. Then the complement $M$ of the…
Perception research provides strong evidence in favor of part based representation of shapes in human visual system. Despite considerable differences among different theories in terms of how part boundaries are found, there is substantial…
We consider ruled surfaces with finite multiplicity. We study behaviors of the striction curves and the singularities of the ruled surfaces. We also give geometric meanings of invariants related to the ruled surfaces.
Several classes of *-algebras associated to the action of an affine transformation are considered, and an investigation of the interplay between the different classes of algebras is initiated. Connections are established that relate…
Surfaces and curves play an important role in geometric design. In recent years, problem of finding a surface passing through a given curve have attracted much interest. In the present paper, we propose a new method to construct a surface…