2,724 research outputs found
Learning SO(3) Equivariant Representations with Spherical CNNs
We address the problem of 3D rotation equivariance in convolutional neural
networks. 3D rotations have been a challenging nuisance in 3D classification
tasks requiring higher capacity and extended data augmentation in order to
tackle it. We model 3D data with multi-valued spherical functions and we
propose a novel spherical convolutional network that implements exact
convolutions on the sphere by realizing them in the spherical harmonic domain.
Resulting filters have local symmetry and are localized by enforcing smooth
spectra. We apply a novel pooling on the spectral domain and our operations are
independent of the underlying spherical resolution throughout the network. We
show that networks with much lower capacity and without requiring data
augmentation can exhibit performance comparable to the state of the art in
standard retrieval and classification benchmarks.Comment: Camera-ready. Accepted to ECCV'18 as oral presentatio
Spherical harmonics descriptor for 2D-image retrieval
In this paper, spherical harmonics are proposed as shape descriptors for 2D images. We introduce the concept of connectivity; 2D images are decomposed using connectivity, which is followed by 3D model construction. Spherical harmonics are obtained for 3D models and used as descriptors for the underlying 2D shapes. Difference between two images is computed as the Euclidean distance between their spherical harmonics descriptors. Experiments are performed to test the effectiveness of spherical harmonics for retrieval of 2D images. Item S8 within the MPEG-7 still images content set is used for performing experiments; this dataset consists of 3621 still images. Experimental results show that the proposed descriptors for 2D images are effective<br /
Spherical harmonics coeffcients for ligand-based virtual screening of cyclooxygenase inhibitors
Background: Molecular descriptors are essential for many applications in computational chemistry, such as ligand-based similarity searching. Spherical harmonics have previously been suggested as comprehensive descriptors of molecular structure and properties. We investigate a spherical harmonics descriptor for shape-based virtual screening. Methodology/Principal Findings: We introduce and validate a partially rotation-invariant three-dimensional molecular shape descriptor based on the norm of spherical harmonics expansion coefficients. Using this molecular representation, we parameterize molecular surfaces, i.e., isosurfaces of spatial molecular property distributions. We validate the shape descriptor in a comprehensive retrospective virtual screening experiment. In a prospective study, we virtually screen a large compound library for cyclooxygenase inhibitors, using a self-organizing map as a pre-filter and the shape descriptor for candidate prioritization. Conclusions/Significance: 12 compounds were tested in vitro for direct enzyme inhibition and in a whole blood assay. Active compounds containing a triazole scaffold were identified as direct cyclooxygenase-1 inhibitors. This outcome corroborates the usefulness of spherical harmonics for representation of molecular shape in virtual screening of large compound collections. The combination of pharmacophore and shape-based filtering of screening candidates proved to be a straightforward approach to finding novel bioactive chemotypes with minimal experimental effort
View subspaces for indexing and retrieval of 3D models
View-based indexing schemes for 3D object retrieval are gaining popularity
since they provide good retrieval results. These schemes are coherent with the
theory that humans recognize objects based on their 2D appearances. The
viewbased techniques also allow users to search with various queries such as
binary images, range images and even 2D sketches. The previous view-based
techniques use classical 2D shape descriptors such as Fourier invariants,
Zernike moments, Scale Invariant Feature Transform-based local features and 2D
Digital Fourier Transform coefficients. These methods describe each object
independent of others. In this work, we explore data driven subspace models,
such as Principal Component Analysis, Independent Component Analysis and
Nonnegative Matrix Factorization to describe the shape information of the
views. We treat the depth images obtained from various points of the view
sphere as 2D intensity images and train a subspace to extract the inherent
structure of the views within a database. We also show the benefit of
categorizing shapes according to their eigenvalue spread. Both the shape
categorization and data-driven feature set conjectures are tested on the PSB
database and compared with the competitor view-based 3D shape retrieval
algorithmsComment: Three-Dimensional Image Processing (3DIP) and Applications
(Proceedings Volume) Proceedings of SPIE Volume: 7526 Editor(s): Atilla M.
Baskurt ISBN: 9780819479198 Date: 2 February 201
From 3D Point Clouds to Pose-Normalised Depth Maps
We consider the problem of generating either pairwise-aligned or pose-normalised depth maps from noisy 3D point clouds in a relatively unrestricted poses. Our system is deployed in a 3D face alignment application and consists of the following four stages: (i) data filtering, (ii) nose tip identification and sub-vertex localisation, (iii) computation of the (relative) face orientation, (iv) generation of either a pose aligned or a pose normalised depth map. We generate an implicit radial basis function (RBF) model of the facial surface and this is employed within all four stages of the process. For example, in stage (ii), construction of novel invariant features is based on sampling this RBF over a set of concentric spheres to give a spherically-sampled RBF (SSR) shape histogram. In stage (iii), a second novel descriptor, called an isoradius contour curvature signal, is defined, which allows rotational alignment to be determined using a simple process of 1D correlation. We test our system on both the University of York (UoY) 3D face dataset and the Face Recognition Grand Challenge (FRGC) 3D data. For the more challenging UoY data, our SSR descriptors significantly outperform three variants of spin images, successfully identifying nose vertices at a rate of 99.6%. Nose localisation performance on the higher quality FRGC data, which has only small pose variations, is 99.9%. Our best system successfully normalises the pose of 3D faces at rates of 99.1% (UoY data) and 99.6% (FRGC data)
Corners-based composite descriptor for shapes
In this paper, a composite descriptor for shape retrieval is proposed. The composite descriptor is obtained based upon corner-points and shape region. In an earlier paper, we proposed a composite descriptor based on shape region and shape contour, however, the descriptor was not effective for all perspective and geometric transformations. Hence, we modify the composite descriptor by replacing contour features with corner-points features. The proposed descriptor is obtained from Generic FourierDescriptors (GFD) of the shape region and the GFD ofthe corner-points. We study the performance of the proposed composite descriptor. The proposed method is evaluated using Item S8 within the MPEG-7 Still Images Content Set. Experimental results show that the proposed descriptor is effective.<br /
Learning Equivariant Representations
State-of-the-art deep learning systems often require large amounts of data
and computation. For this reason, leveraging known or unknown structure of the
data is paramount. Convolutional neural networks (CNNs) are successful examples
of this principle, their defining characteristic being the shift-equivariance.
By sliding a filter over the input, when the input shifts, the response shifts
by the same amount, exploiting the structure of natural images where semantic
content is independent of absolute pixel positions. This property is essential
to the success of CNNs in audio, image and video recognition tasks. In this
thesis, we extend equivariance to other kinds of transformations, such as
rotation and scaling. We propose equivariant models for different
transformations defined by groups of symmetries. The main contributions are (i)
polar transformer networks, achieving equivariance to the group of similarities
on the plane, (ii) equivariant multi-view networks, achieving equivariance to
the group of symmetries of the icosahedron, (iii) spherical CNNs, achieving
equivariance to the continuous 3D rotation group, (iv) cross-domain image
embeddings, achieving equivariance to 3D rotations for 2D inputs, and (v)
spin-weighted spherical CNNs, generalizing the spherical CNNs and achieving
equivariance to 3D rotations for spherical vector fields. Applications include
image classification, 3D shape classification and retrieval, panoramic image
classification and segmentation, shape alignment and pose estimation. What
these models have in common is that they leverage symmetries in the data to
reduce sample and model complexity and improve generalization performance. The
advantages are more significant on (but not limited to) challenging tasks where
data is limited or input perturbations such as arbitrary rotations are present
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