System and a method for learning features on geometric domains
First Claim
1. A computer-system-implemented method for extracting hierarchical features from data defined on a geometric domain, comprising applying on said data at least an intrinsic convolution layer, the data being stored on a memory of a computer system, the method including the steps of:
- applying, by a processor of the computer system, a patch operator to extract a local representation of the input data around a point on the geometric domain and outputting a correlation of said local representation resulting from the extraction with a plurality of templates;
defining, by the processor, a local system of multi-dimensional pseudo-coordinates around a point on the geometric domain;
computing, by the processor, a plurality of weighting functions acting on said pseudo coordinates;
storing said weighting functions on the memory of the computer system; and
applying, by the processor, said weighting functions to define said patch operator, thereby improving the ability of the computer system to apply a deep learning method to said data.
5 Assignments
0 Petitions
Accused Products
Abstract
A method for extracting hierarchical features from data defined on a geometric domain is provided. The method includes applying on said data at least an intrinsic convolution layer, including the steps of applying a patch operator to extract a local representation of the input data around a point on the geometric domain and outputting the correlation of a patch resulting from the extraction with a plurality of templates. A system to implement the method is also described.
30 Citations
81 Claims
-
1. A computer-system-implemented method for extracting hierarchical features from data defined on a geometric domain, comprising applying on said data at least an intrinsic convolution layer, the data being stored on a memory of a computer system, the method including the steps of:
-
applying, by a processor of the computer system, a patch operator to extract a local representation of the input data around a point on the geometric domain and outputting a correlation of said local representation resulting from the extraction with a plurality of templates; defining, by the processor, a local system of multi-dimensional pseudo-coordinates around a point on the geometric domain; computing, by the processor, a plurality of weighting functions acting on said pseudo coordinates; storing said weighting functions on the memory of the computer system; and applying, by the processor, said weighting functions to define said patch operator, thereby improving the ability of the computer system to apply a deep learning method to said data. - View Dependent Claims (2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17)
-
-
18. A computer-system-implemented method for extracting hierarchical features from data defined on a geometric domain, comprising applying on said data at least an intrinsic convolution layer, the data being stored on a memory of a computer system, the method including the steps of:
-
applying, by a processor of the computer system, a patch operator to extract a local representation of the input data around a point on the geometric domain and outputting a correlation of said local representation resulting from the extraction with a plurality of templates; and further applying at least one of the following layers; a linear layer, including outputting a weighted linear combination of input data; a non-linear layer, including applying a non-linear function to input data; a spatial pooling layer, including; determining a subset of points on the geometric domain; for each point of said subset, determining the neighbours on the geometric domain; and computing an aggregation operation on input data over the neighbours for all the points of said subset; a covariance layer, including computing a covariance matrix of input data over all the points of the geometric; a fully connected layer, including outputting a weighted linear combination of input data at all the points of the geometric domain, wherein each layer has input data and output data stored on the memory of the computer system, and output data of one layer are given as input data to another layer, thereby improving the ability of the computer system to apply a deep learning method to said data. - View Dependent Claims (19, 20, 21, 22, 23, 24, 25)
-
-
26. A computer-system-implemented. method for extracting hierarchical features from data defined on a geometric domain, comprising applying on said data at least an intrinsic convolution layer, the data being stored on a memory of a computer system, the method including the steps of:
-
applying, by a processor of the computer system, a patch operator to extract a local representation of the input data around a point on the geometric domain and outputting a correlation of said local representation resulting from the extraction with a plurality of templates; wherein the patch operator inputs data on geometric domain and said point on said domain, and outputs the local representation of said data around said point, thereby improving the ability of the computer system to apply a deep learning method to said data, wherein the local representation is one or more of the following; data represented in a local intrinsic polar system of coordinates; data transformed by a windowed Fourier transform; data weighted by anisotropic diffusion kernels. - View Dependent Claims (27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38)
-
-
39. A computer-system-implemented method for extracting hierarchical features from data defined on a geometric domain. comprising applying on said data at least an intrinsic convolution layer, the data being stored on a memory of a computer system, the method including the steps of:
-
applying, by a processor of the computer system, a patch operator to extract a local representation of the input data around a point on the geometric domain and outputting a correlation of said local representation resulting from the extraction with a plurality of templates; including extracting hierarchical features from data defined on another geometric domain, applying on data defined on said another geometric domain at least the intrinsic convolution layer, including the steps of; applying a patch operator to extract a local representation of further input data around a point on the another geometric domain and outputting the correlation of a patch resulting from the extraction of the local representation of the further input data with said plurality of templates, thereby improving the ability of the computer system to apply a deep learning method to said data, wherein data defined on the geometric domain are associated to a first geometric object and said data are defined on the additional geometric domain are associated to a second geometric object, and wherein a similarity of the first object to the second object is measured based on the hierarchical features extracted from data defined on the geometric object and the hierarchical features extracted from data defined on said another geometric object. - View Dependent Claims (40, 41)
-
-
42. A computer-system-implemented method for extracting hierarchical features from data defined on a geometric domain comprising applying on said data at least an intrinsic convolution layer, the data being stored on a memory of a computer system, the method including the steps of:
-
applying, by a processor of the computer system, a patch operator to extract a local representation of the input data around a point on the geometric domain and outputting a correlation of said local representation resulting from the extraction with a plurality of templates, thereby improving the ability of the computer system to apply a deep learning method to said data; wherein said extracted hierarchical features are used for determining correspondences between objects from a class of geometric objects, provided as a plurality of data defined on a corresponding plurality of geometric domains, and an first object associated to said data defined on the geometric domain. - View Dependent Claims (43, 44)
-
-
45. A computer system for extracting hierarchical features from data defined on a geometric domain, comprising a memory and a processor for applying on said data at least an intrinsic convolution layer, where said computer system is configured to:
-
apply, by the processor, a patch operator for extracting a local representation of the input data around a point on the geometric domain and to return as output a correlation of said local representation resulting from the extraction with a plurality of templates; define, by the processor, a local system of multi-dimensional pseudo-coordinates around a point on the geometric domain; compute, by the processor, a plurality of weighting functions acting on said pseudo -coordinates; store said weighting functions on the memory; and apply, by the processor, said weighting functions to define the patch operator, thereby improving the ability of the computer system to apply a deep learning method to said data. - View Dependent Claims (46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60)
-
-
61. A computer system for extracting hierarchical features from data defined on a geometric domain, comprising a memory and a processor for applying on said data at least an intrinsic convolution layer, where said computer system is configured to:
-
apply, by the processor, a patch operator for extracting a local representation of the input data around a point on the geometric domain and to return as output a correlation of said local representation resulting from the extraction with a plurality or templates; apply at least another layer among the following layers; a linear layer, including outputting a weighted linear combination of input data; a non-linear layer, including applying a non-linear function to input data; a spatial pooling layer, wherein; a subset of points on the geometric domain are determined; for each point of said subset, the neighbours on the geometric domain are determined; and an aggregation operation on input data over the neighbours for all the points of said subset is computed; a covariance layer, wherein a covariance matrix of input data over all the points of the geometric domain is computed; a fully connected layer, having as output a weighted linear combination of input data at all the points of the geometric domain, wherein each layer has input data and output data stored on the memory of the computer system, and said system comprehends means that are configured to provide as input data to a layer the output data of another layer, thereby improving the ability of the computer system to apply a deep learning method to said data. - View Dependent Claims (62, 63, 64, 65, 66, 67, 68)
-
-
69. A computer system for extracting hierarchical features from data defined on a geometric domain, comprising a memory and a processor for applying on said data at least an intrinsic convolution layer, said data being stored on the memory of the computer system, where said computer system is configured to:
-
apply, by the processor, a patch operator for extracting a local representation of the input data around a point on the geometric domain and to return as output a correlation of said local representation resulting from the extraction with a plurality of templates; wherein the patch operator is configured to input data on geometric domain and said point on said domain, and to output the local representation of said data around said point, thereby improving the ability of the computer system to apply a deep learning method to said data, wherein the local representation is one or more of the following; data represented in a local intrinsic polar system of coordinates; data transformed by a windowed Fourier transform; data weighted by anisotropic diffusion kernels. - View Dependent Claims (70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81)
-
Specification