Curved Geometric Networks for Visual Anomaly Recognition
- URL: http://arxiv.org/abs/2208.01188v1
- Date: Tue, 2 Aug 2022 01:15:39 GMT
- Title: Curved Geometric Networks for Visual Anomaly Recognition
- Authors: Jie Hong, Pengfei Fang, Weihao Li, Junlin Han, Lars Petersson and
Mehrtash Harandi
- Abstract summary: Learning a latent embedding to understand the underlying nature of data distribution is often formulated in Euclidean spaces with zero curvature.
In this work, we investigate benefits of the curved space for analyzing anomalies or out-of-distribution objects in data.
- Score: 39.91252195360767
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: Learning a latent embedding to understand the underlying nature of data
distribution is often formulated in Euclidean spaces with zero curvature.
However, the success of the geometry constraints, posed in the embedding space,
indicates that curved spaces might encode more structural information, leading
to better discriminative power and hence richer representations. In this work,
we investigate benefits of the curved space for analyzing anomalies or
out-of-distribution objects in data. This is achieved by considering embeddings
via three geometry constraints, namely, spherical geometry (with positive
curvature), hyperbolic geometry (with negative curvature) or mixed geometry
(with both positive and negative curvatures). Three geometric constraints can
be chosen interchangeably in a unified design given the task at hand. Tailored
for the embeddings in the curved space, we also formulate functions to compute
the anomaly score. Two types of geometric modules (i.e., Geometric-in-One and
Geometric-in-Two models) are proposed to plug in the original Euclidean
classifier, and anomaly scores are computed from the curved embeddings. We
evaluate the resulting designs under a diverse set of visual recognition
scenarios, including image detection (multi-class OOD detection and one-class
anomaly detection) and segmentation (multi-class anomaly segmentation and
one-class anomaly segmentation). The empirical results show the effectiveness
of our proposal through the consistent improvement over various scenarios.
Related papers
- Geometry Distributions [51.4061133324376]
We propose a novel geometric data representation that models geometry as distributions.
Our approach uses diffusion models with a novel network architecture to learn surface point distributions.
We evaluate our representation qualitatively and quantitatively across various object types, demonstrating its effectiveness in achieving high geometric fidelity.
arXiv Detail & Related papers (2024-11-25T04:06:48Z) - Adaptive Surface Normal Constraint for Geometric Estimation from Monocular Images [56.86175251327466]
We introduce a novel approach to learn geometries such as depth and surface normal from images while incorporating geometric context.
Our approach extracts geometric context that encodes the geometric variations present in the input image and correlates depth estimation with geometric constraints.
Our method unifies depth and surface normal estimations within a cohesive framework, which enables the generation of high-quality 3D geometry from images.
arXiv Detail & Related papers (2024-02-08T17:57:59Z) - Exploring Data Geometry for Continual Learning [64.4358878435983]
We study continual learning from a novel perspective by exploring data geometry for the non-stationary stream of data.
Our method dynamically expands the geometry of the underlying space to match growing geometric structures induced by new data.
Experiments show that our method achieves better performance than baseline methods designed in Euclidean space.
arXiv Detail & Related papers (2023-04-08T06:35:25Z) - Differential Geometry in Neural Implicits [0.6198237241838558]
We introduce a neural implicit framework that bridges discrete differential geometry of triangle meshes and continuous differential geometry of neural implicit surfaces.
It exploits the differentiable properties of neural networks and the discrete geometry of triangle meshes to approximate them as the zero-level sets of neural implicit functions.
arXiv Detail & Related papers (2022-01-23T13:40:45Z) - Theoretical bounds on data requirements for the ray-based classification [0.0]
A new classification framework has been proposed in which the intersections of a set of one-dimensional representations, called rays, with the boundaries of the shape are used to identify the specific geometry.
Here, we establish a bound on the number of rays necessary for shape classification, defined by key angular metrics, for arbitrary convex shapes.
This result enables a different approach for estimating high-dimensional shapes using substantially fewer data elements than volumetric or surface-based approaches.
arXiv Detail & Related papers (2021-03-17T11:38:45Z) - Self-supervised Geometric Perception [96.89966337518854]
Self-supervised geometric perception is a framework to learn a feature descriptor for correspondence matching without any ground-truth geometric model labels.
We show that SGP achieves state-of-the-art performance that is on-par or superior to the supervised oracles trained using ground-truth labels.
arXiv Detail & Related papers (2021-03-04T15:34:43Z) - Identifying the latent space geometry of network models through analysis
of curvature [7.644165047073435]
We present a method to consistently estimate the manifold type, dimension, and curvature from an empirically relevant class of latent spaces.
Our core insight comes by representing the graph as a noisy distance matrix based on the ties between cliques.
arXiv Detail & Related papers (2020-12-19T00:35:29Z) - Primal-Dual Mesh Convolutional Neural Networks [62.165239866312334]
We propose a primal-dual framework drawn from the graph-neural-network literature to triangle meshes.
Our method takes features for both edges and faces of a 3D mesh as input and dynamically aggregates them.
We provide theoretical insights of our approach using tools from the mesh-simplification literature.
arXiv Detail & Related papers (2020-10-23T14:49:02Z) - Geometric Attention for Prediction of Differential Properties in 3D
Point Clouds [32.68259334785767]
In this study, we present a geometric attention mechanism that can provide such properties in a learnable fashion.
We establish the usefulness of the proposed technique with several experiments on the prediction of normal vectors and the extraction of feature lines.
arXiv Detail & Related papers (2020-07-06T07:40:26Z)
This list is automatically generated from the titles and abstracts of the papers in this site.
This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.