ANSIG – An Analytic Signature for Permutation-Invariant Two Dimensional Shape Representation

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ANSIG – An Analytic Signature for Permutation-Invariant Two Dimensional Shape Representation José J. Rodrigues, Pedro M. Q. Aguiar, João M. F. Xavier quotient space Goal: an unique representation for each shape Problem: shape representation (arbitrary sets of 2D points) Approach: permutation invariant representation Geometric transformations Translation and scale: Rotation: SHAPE TO CLASSIFY M Á X SHAPE 1 Similarit y SHAPE 3 Similarit y SHAPE 2 Similarit y S H A P E 2 Shape-based classification Ilustrations Sampling density: Point permutation is a quagmire: ANSIG: same signature same shape Storage, alignment, and comparison of ANSIGs: (equivariant) (invariant) ( inva riant) Experiments

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ANSIG – An Analytic Signature for Permutation-Invariant Two Dimensional Shape Representation José J. Rodrigues, Pedro M. Q. Aguiar, João M. F. Xavier. Problem: shape representation (arbitrary sets of 2D points). Geometric transformations. Ilustrations. Experiments. quotient space. - PowerPoint PPT Presentation

Transcript of ANSIG – An Analytic Signature for Permutation-Invariant Two Dimensional Shape Representation

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ANSIG – An Analytic Signature for Permutation-InvariantTwo Dimensional Shape Representation

José J. Rodrigues, Pedro M. Q. Aguiar, João M. F. Xavier

quotient space

Goal: an unique representation for each shape

Problem: shape representation(arbitrary sets of 2D points)

Approach: permutation invariant representation

Geometric transformations

Translation and scale:

Rotation:

SHAPE TO CLASSIFY

MÁX

SHAPE 1

Similarity

SHAPE 3

Similarity

SHAPE 2

Similarity

SHAPE

2

Shape-based classification

Ilustrations

Sampling density:

Point permutation is a quagmire:

ANSIG:

same signature same shape

Storage, alignment, and comparison of ANSIGs:

(equivariant)

(invariant)

( invariant)

Experiments

Circular permutation

Circular permutation

Symmetry and molecules · Symmetry and molecules: Symmetry operations (e.g., permutation-inversion operations) for a molecule leave the molecular Hamiltonian invariant. They can be

Symmetry and molecules · Symmetry and molecules: Symmetry operations (e.g., permutation-inversion operations) for a molecule leave the molecular Hamiltonian invariant. They can be

Few-shot Action Recognition with Permutation-invariant Attention · 2020. 7. 18. · Few-shot Action Recognition with Permutation-invariant Attention HongguangZhang 1;23 5,LiZhang

Few-shot Action Recognition with Permutation-invariant Attention · 2020. 7. 18. · Few-shot Action Recognition with Permutation-invariant Attention HongguangZhang 1;23 5,LiZhang

Sparse permutation invariant covariance estimationbickel/Rothman et al 2008.pdfa permutation-invariant estimator. The method is compared to other es-timators on simulated data and

Sparse permutation invariant covariance estimationbickel/Rothman et al 2008.pdfa permutation-invariant estimator. The method is compared to other es-timators on simulated data and

Permutation Invariant Representations and Graph Deep …rvbalan/PRESENTATIONS/MITTalk2019.pdfGCN (Kipf and Welling (’16)) choses A˜ = I + A; GNN (Scarselli et.al. (’08), Bronstein

Permutation Invariant Representations and Graph Deep …rvbalan/PRESENTATIONS/MITTalk2019.pdfGCN (Kipf and Welling (’16)) choses A˜ = I + A; GNN (Scarselli et.al. (’08), Bronstein

Finiteness theorems and algorithms for permutation invariant chains of Laurent lattice ideals

Finiteness theorems and algorithms for permutation invariant chains of Laurent lattice ideals

Permutation graphsandapplications

Permutation graphsandapplications

Permutation Tests Hal Whitehead BIOL4062/5062. Introduction to permutation tests Exact and randomized permutation tests Permutation tests using standard.

Permutation Tests Hal Whitehead BIOL4062/5062. Introduction to permutation tests Exact and randomized permutation tests Permutation tests using standard.

Single Channel Speech Separation with Constrained ...Single Channel Speech Separation with Constrained Utterance Level Permutation Invariant Training Using Grid LSTM Chenglin Xu1,2,

Single Channel Speech Separation with Constrained ...Single Channel Speech Separation with Constrained Utterance Level Permutation Invariant Training Using Grid LSTM Chenglin Xu1,2,

Burst Image Deblurring Using Permutation Invariant Convolutional …openaccess.thecvf.com/content_ECCV_2018/papers/Miika... · 2018-08-28 · Burst Image Deblurring Using Permutation

Burst Image Deblurring Using Permutation Invariant Convolutional …openaccess.thecvf.com/content_ECCV_2018/papers/Miika... · 2018-08-28 · Burst Image Deblurring Using Permutation

Permutation Groups:

Permutation Groups:

Mapping Images to Scene Graphs with Permutation …...Mapping Images to Scene Graphs with Permutation-Invariant Structured Prediction Roei Herzig Tel Aviv University roeiherzig@mail.tau.ac.il

Mapping Images to Scene Graphs with Permutation …...Mapping Images to Scene Graphs with Permutation-Invariant Structured Prediction Roei Herzig Tel Aviv University [email protected]

ORTHOGONAL INVARIANCE AND IDENTIFIABILITY · where f is a permutation-invariant function on Rn and λ is the mapping assigning to each matrix X ∈S the vector of its eigenvalues

ORTHOGONAL INVARIANCE AND IDENTIFIABILITY · where f is a permutation-invariant function on Rn and λ is the mapping assigning to each matrix X ∈S the vector of its eigenvalues

Permutation and Combination - careercouncillor.comcareercouncillor.com/pdf/Permutation_and_Combination.po.pdf · Permutation and Combination Permutation implies arrangement where

Permutation and Combination - careercouncillor.comcareercouncillor.com/pdf/Permutation_and_Combination.po.pdf · Permutation and Combination Permutation implies arrangement where

On two ways to use determinantal point processes …...DPP( ;K N) defines a probability measure over sets since (3) is invariant by permutation, the orthonormality of the ˚ ks yields

On two ways to use determinantal point processes …...DPP( ;K N) defines a probability measure over sets since (3) is invariant by permutation, the orthonormality of the ˚ ks yields

Permutation invariance and unitarily invariant measureswatrous/TQI/TQI.7.pdf392 Permutation invariance and unitarily invariant measures One may observe that W W = W and W 1 = W = W

Permutation invariance and unitarily invariant measureswatrous/TQI/TQI.7.pdf392 Permutation invariance and unitarily invariant measures One may observe that W W = W and W 1 = W = W

On the Design of Bit Permutation Based Ciphers · Substitution-bit Permutation network (SbPN) is a subclassi - cation of Substitution-Permutation network, where the permutation layer

On the Design of Bit Permutation Based Ciphers · Substitution-bit Permutation network (SbPN) is a subclassi - cation of Substitution-Permutation network, where the permutation layer

Algebra - permutation

Algebra - permutation

Permutation & COmbination

Permutation & COmbination

Set Transformer: A Framework for Attention-based Permutation … · 2019-05-28 · Set Transformer: A Framework for Attention-based Permutation-Invariant Neural Networks Juho Lee

Set Transformer: A Framework for Attention-based Permutation … · 2019-05-28 · Set Transformer: A Framework for Attention-based Permutation-Invariant Neural Networks Juho Lee