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Lezoray_Slides_EI2023.pdf

 Lezoray_Slides_EI2023.pdf

Olivier Lézoray

January 18, 2023
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  1. 3D MESH SALIENCY FROM LOCAL SPIRAL HOP DESCRIPTORS IS&T Electronic

    Imaging 2023 Olivier L ´ EZORAY1, Anass NOURI2 1Normandie Univ, UNICAEN, ENSICAEN, CNRS, GREYC, Caen, FRANCE 2Laboratoire des Syst` emes ´ Electroniques, Traitement de l’Information, M´ ecanique et ´ Energ´ etique, Ibn Tofail University, Kenitra, MOROCCO [email protected] https://lezoray.users.greyc.fr
  2. Outline 1. Introduction 2. Local spiral hop descriptors 3. Roughness,

    geometric and spectral saliencies 4. Results 5. Conclusion O. L´ ezoray & A. Nouri 3D Mesh Saliency from local spiral hop descriptors 2 / 28
  3. Outline 1. Introduction 2. Local spiral hop descriptors 3. Roughness,

    geometric and spectral saliencies 4. Results 5. Conclusion O. L´ ezoray & A. Nouri 3D Mesh Saliency from local spiral hop descriptors 3 / 28
  4. Introduction Recent technological advances have led to the generation of

    huge amounts of 3D data Even with cheap hardware and software, one can easily generate 3D data: 3D data acquisition with common smartphone (e.g., Photogrammetry) O. L´ ezoray & A. Nouri 3D Mesh Saliency from local spiral hop descriptors 4 / 28
  5. New applications Fields With this proliferation of such 3D Data,

    new application fields have appeared Digital Forensics, Cultural Heritage, Body Scanning One often needs to know which regions from a 3D mesh are important: adaptive simplification or decimation, viewpoint selection O. L´ ezoray & A. Nouri 3D Mesh Saliency from local spiral hop descriptors 5 / 28
  6. 3D Data Saliency Saliency for images ? Salient regions of

    an image are visually more noticeable by their contrast with respect to surrounding regions Saliency for 3D meshes ? If a point from the 3D data stands out strongly from its surrounding, then, it could be considered as a salient 3D point. Our approach We locally study the geometry of the mesh vertices’ normals A local normal-based descriptor is built for each vertex according to a spiral path within a k-hop neighborhood. Geometric and spectral saliencies are defined from this descriptor and combined with a roughness measure O. L´ ezoray & A. Nouri 3D Mesh Saliency from local spiral hop descriptors 6 / 28
  7. Outline 1. Introduction 2. Local spiral hop descriptors 3. Roughness,

    geometric and spectral saliencies 4. Results 5. Conclusion O. L´ ezoray & A. Nouri 3D Mesh Saliency from local spiral hop descriptors 7 / 28
  8. Outline 1. Introduction 2. Local spiral hop descriptors 3. Roughness,

    geometric and spectral saliencies 4. Results 5. Conclusion O. L´ ezoray & A. Nouri 3D Mesh Saliency from local spiral hop descriptors 8 / 28
  9. Local spiral hop descriptors Notations A mesh M is represented

    by a graph G = (V,E) with V = {v1,...,vm} and E ⊂ V×V vi ∼ vj is used to denote two adjacent vertices N (vi) = {vj,vj ∼ vi} gives the set of all the adjacent vertices to vi within a 1-hop (vertices that can be reached in one walk). Lim et al. have proposed local spiral hop descriptors: the surrounding vertices of one vertex can be enumerated by following a spiral O. L´ ezoray & A. Nouri 3D Mesh Saliency from local spiral hop descriptors 9 / 28
  10. Local spiral hop descriptors Definitions Rk(vi) = k-ring(vi) is an

    ordered set of vertices whose shortest path to vi is exactly k-hops long vi R1 7 R1 1 R1 2 R1 3 R1 4 R1 5 R1 6 R2 1 R2 2 R2 3 R2 4 R2 5 R2 6 R2 7 R2 8 R2 9 R2 10 R2 11 R2 12 R2 13 O. L´ ezoray & A. Nouri 3D Mesh Saliency from local spiral hop descriptors 10 / 28
  11. Local spiral hop descriptors Definitions Rk(vi) = k-ring(vi) is an

    ordered set of vertices whose shortest path to vi is exactly k-hops long ⇒ R0(vi) = {vi} vi R1 7 R1 1 R1 2 R1 3 R1 4 R1 5 R1 6 R2 1 R2 2 R2 3 R2 4 R2 5 R2 6 R2 7 R2 8 R2 9 R2 10 R2 11 R2 12 R2 13 0-ring(vi) O. L´ ezoray & A. Nouri 3D Mesh Saliency from local spiral hop descriptors 10 / 28
  12. Local spiral hop descriptors Definitions Rk(vi) = k-ring(vi) is an

    ordered set of vertices whose shortest path to vi is exactly k-hops long ⇒ R0(vi) = {vi} and R1(vi) = N (vi) vi R1 7 R1 1 R1 2 R1 3 R1 4 R1 5 R1 6 R2 1 R2 2 R2 3 R2 4 R2 5 R2 6 R2 7 R2 8 R2 9 R2 10 R2 11 R2 12 R2 13 1-ring(vi) O. L´ ezoray & A. Nouri 3D Mesh Saliency from local spiral hop descriptors 10 / 28
  13. Local spiral hop descriptors Definitions Rk(vi) = k-ring(vi) is an

    ordered set of vertices whose shortest path to vi is exactly k-hops long ⇒ R0(vi) = {vi} and R1(vi) = N (vi) k-disk(vi) = l=0,...,k Rl(vi) is the set of vertices that can be reached from vi in 0 to k walks. vi R1 7 R1 1 R1 2 R1 3 R1 4 R1 5 R1 6 R2 1 R2 2 R2 3 R2 4 R2 5 R2 6 R2 7 R2 8 R2 9 R2 10 R2 11 R2 12 R2 13 1-disk(vi) O. L´ ezoray & A. Nouri 3D Mesh Saliency from local spiral hop descriptors 10 / 28
  14. Local spiral hop descriptors Definitions Rk(vi) = k-ring(vi) is an

    ordered set of vertices whose shortest path to vi is exactly k-hops long ⇒ R0(vi) = {vi} and R1(vi) = N (vi) k-disk(vi) = l=0,...,k Rl(vi) is the set of vertices that can be reached from vi in 0 to k walks. R(k+1)(vi) = N (R(k)(vi))\k-disk(vi) is the set of vertices that can be reached in 1 walk from Rk(vi) without going through its k-disk (that contains vertices that can be reached from vi in 0 to k walks) vi R1 7 R1 1 R1 2 R1 3 R1 4 R1 5 R1 6 R2 1 R2 2 R2 3 R2 4 R2 5 R2 6 R2 7 R2 8 R2 9 R2 10 R2 11 R2 12 R2 13 2-ring(vi) O. L´ ezoray & A. Nouri 3D Mesh Saliency from local spiral hop descriptors 10 / 28
  15. Local spiral hop descriptors Definitions The local spiral hop operator

    Sp(vi,k) is an ordered sequence from the concatenation of the ordered rings Sp(vi,k) = (vi,1-ring(vi),...,k-ring(vi)) = R0 1 (vi),R1 1 (vi),R1 2 (vi),...,Rk |Rk| (vi) It has 2 degrees of freedom: the direction (clockwise or counterclockwise) of the rings and the first chosen vertex R1 1 (vi) We fix : the orientation clockwise the initial vertex R1 1 (vi) is the one in the direction of the shortest geodesic path to vi: R1 1 (vi) = arg min vj∈N (vi) dG(vi,vj) O. L´ ezoray & A. Nouri 3D Mesh Saliency from local spiral hop descriptors 11 / 28
  16. Local spiral hop descriptors Comparison The size of the operator

    Sp(vi,k) varies for the vertices Lim et al. either truncate or zero-pad each spiral depending on its size to compare two local spiral hop descriptors We propose a more accurate hierarchical comparison d(Sp(vi,k),Sp(vj,k)) = k ∑ l=0 d(Rl(vi),Rl(vj)) Two k-rings are compared by mapping the vertices of the largest ring to the smallest one: d(Rl(vi),Rl(vj)) = |Rl (vi)| ∑ n=0 d(Rl n (vi),Rl n (vj)) with n = n·|Rl (vj)| |Rl (vi)| and |Rl(vi)| > |Rl(vj)| First vertex descriptor Second vertex descriptor 0-hop 1-hop 2-hop The distance between two vertices is then the distance between their graph signal vectors: d(Rl n (vi),Rl m (vj)) = F(Rl n (vi))−F(Rl m (vj)) 2 that are vertex normal vectors: F(vi) = n(vi) O. L´ ezoray & A. Nouri 3D Mesh Saliency from local spiral hop descriptors 12 / 28
  17. Local spiral hop descriptors Comparison The size of the operator

    Sp(vi,k) varies for the vertices Lim et al. either truncate or zero-pad each spiral depending on its size to compare two local spiral hop descriptors We propose a more accurate hierarchical comparison d(Sp(vi,k),Sp(vj,k)) = k ∑ l=0 d(Rl(vi),Rl(vj)) Two k-rings are compared by mapping the vertices of the largest ring to the smallest one: d(Rl(vi),Rl(vj)) = |Rl (vi)| ∑ n=0 d(Rl n (vi),Rl n (vj)) with n = n·|Rl (vj)| |Rl (vi)| and |Rl(vi)| > |Rl(vj)| First vertex descriptor Second vertex descriptor 0-hop 1-hop 2-hop The distance between two vertices is then the distance between their graph signal vectors: d(Rl n (vi),Rl m (vj)) = F(Rl n (vi))−F(Rl m (vj)) 2 that are vertex normal vectors: F(vi) = n(vi) O. L´ ezoray & A. Nouri 3D Mesh Saliency from local spiral hop descriptors 12 / 28
  18. Local spiral hop descriptors Comparison The size of the operator

    Sp(vi,k) varies for the vertices Lim et al. either truncate or zero-pad each spiral depending on its size to compare two local spiral hop descriptors We propose a more accurate hierarchical comparison d(Sp(vi,k),Sp(vj,k)) = k ∑ l=0 d(Rl(vi),Rl(vj)) Two k-rings are compared by mapping the vertices of the largest ring to the smallest one: d(Rl(vi),Rl(vj)) = |Rl (vi)| ∑ n=0 d(Rl n (vi),Rl n (vj)) with n = n·|Rl (vj)| |Rl (vi)| and |Rl(vi)| > |Rl(vj)| First vertex descriptor Second vertex descriptor 0-hop 1-hop 2-hop The distance between two vertices is then the distance between their graph signal vectors: d(Rl n (vi),Rl m (vj)) = F(Rl n (vi))−F(Rl m (vj)) 2 that are vertex normal vectors: F(vi) = n(vi) O. L´ ezoray & A. Nouri 3D Mesh Saliency from local spiral hop descriptors 12 / 28
  19. Local spiral hop descriptors Comparison The size of the operator

    Sp(vi,k) varies for the vertices Lim et al. either truncate or zero-pad each spiral depending on its size to compare two local spiral hop descriptors We propose a more accurate hierarchical comparison d(Sp(vi,k),Sp(vj,k)) = k ∑ l=0 d(Rl(vi),Rl(vj)) Two k-rings are compared by mapping the vertices of the largest ring to the smallest one: d(Rl(vi),Rl(vj)) = |Rl (vi)| ∑ n=0 d(Rl n (vi),Rl n (vj)) with n = n·|Rl (vj)| |Rl (vi)| and |Rl(vi)| > |Rl(vj)| First vertex descriptor Second vertex descriptor 0-hop 1-hop 2-hop The distance between two vertices is then the distance between their graph signal vectors: d(Rl n (vi),Rl m (vj)) = F(Rl n (vi))−F(Rl m (vj)) 2 that are vertex normal vectors: F(vi) = n(vi) O. L´ ezoray & A. Nouri 3D Mesh Saliency from local spiral hop descriptors 12 / 28
  20. Local spiral hop descriptors Comparison The size of the operator

    Sp(vi,k) varies for the vertices Lim et al. either truncate or zero-pad each spiral depending on its size to compare two local spiral hop descriptors We propose a more accurate hierarchical comparison d(Sp(vi,k),Sp(vj,k)) = k ∑ l=0 d(Rl(vi),Rl(vj)) Two k-rings are compared by mapping the vertices of the largest ring to the smallest one: d(Rl(vi),Rl(vj)) = |Rl (vi)| ∑ n=0 d(Rl n (vi),Rl n (vj)) with n = n·|Rl (vj)| |Rl (vi)| and |Rl(vi)| > |Rl(vj)| First vertex descriptor Second vertex descriptor 0-hop 1-hop 2-hop The distance between two vertices is then the distance between their graph signal vectors: d(Rl n (vi),Rl m (vj)) = F(Rl n (vi))−F(Rl m (vj)) 2 that are vertex normal vectors: F(vi) = n(vi) O. L´ ezoray & A. Nouri 3D Mesh Saliency from local spiral hop descriptors 12 / 28
  21. Local spiral hop descriptors Comparison The size of the operator

    Sp(vi,k) varies for the vertices Lim et al. either truncate or zero-pad each spiral depending on its size to compare two local spiral hop descriptors We propose a more accurate hierarchical comparison d(Sp(vi,k),Sp(vj,k)) = k ∑ l=0 d(Rl(vi),Rl(vj)) Two k-rings are compared by mapping the vertices of the largest ring to the smallest one: d(Rl(vi),Rl(vj)) = |Rl (vi)| ∑ n=0 d(Rl n (vi),Rl n (vj)) with n = n·|Rl (vj)| |Rl (vi)| and |Rl(vi)| > |Rl(vj)| First vertex descriptor Second vertex descriptor 0-hop 1-hop 2-hop The distance between two vertices is then the distance between their graph signal vectors: d(Rl n (vi),Rl m (vj)) = F(Rl n (vi))−F(Rl m (vj)) 2 that are vertex normal vectors: F(vi) = n(vi) O. L´ ezoray & A. Nouri 3D Mesh Saliency from local spiral hop descriptors 12 / 28
  22. Local spiral hop descriptors Comparison The size of the operator

    Sp(vi,k) varies for the vertices Lim et al. either truncate or zero-pad each spiral depending on its size to compare two local spiral hop descriptors We propose a more accurate hierarchical comparison d(Sp(vi,k),Sp(vj,k)) = k ∑ l=0 d(Rl(vi),Rl(vj)) Two k-rings are compared by mapping the vertices of the largest ring to the smallest one: d(Rl(vi),Rl(vj)) = |Rl (vi)| ∑ n=0 d(Rl n (vi),Rl n (vj)) with n = n·|Rl (vj)| |Rl (vi)| and |Rl(vi)| > |Rl(vj)| First vertex descriptor Second vertex descriptor 0-hop 1-hop 2-hop The distance between two vertices is then the distance between their graph signal vectors: d(Rl n (vi),Rl m (vj)) = F(Rl n (vi))−F(Rl m (vj)) 2 that are vertex normal vectors: F(vi) = n(vi) O. L´ ezoray & A. Nouri 3D Mesh Saliency from local spiral hop descriptors 12 / 28
  23. Local spiral hop descriptors Comparison The size of the operator

    Sp(vi,k) varies for the vertices Lim et al. either truncate or zero-pad each spiral depending on its size to compare two local spiral hop descriptors We propose a more accurate hierarchical comparison d(Sp(vi,k),Sp(vj,k)) = k ∑ l=0 d(Rl(vi),Rl(vj)) Two k-rings are compared by mapping the vertices of the largest ring to the smallest one: d(Rl(vi),Rl(vj)) = |Rl (vi)| ∑ n=0 d(Rl n (vi),Rl n (vj)) with n = n·|Rl (vj)| |Rl (vi)| and |Rl(vi)| > |Rl(vj)| First vertex descriptor Second vertex descriptor 0-hop 1-hop 2-hop The distance between two vertices is then the distance between their graph signal vectors: d(Rl n (vi),Rl m (vj)) = F(Rl n (vi))−F(Rl m (vj)) 2 that are vertex normal vectors: F(vi) = n(vi) O. L´ ezoray & A. Nouri 3D Mesh Saliency from local spiral hop descriptors 12 / 28
  24. Local spiral hop descriptors Comparison The size of the operator

    Sp(vi,k) varies for the vertices Lim et al. either truncate or zero-pad each spiral depending on its size to compare two local spiral hop descriptors We propose a more accurate hierarchical comparison d(Sp(vi,k),Sp(vj,k)) = k ∑ l=0 d(Rl(vi),Rl(vj)) Two k-rings are compared by mapping the vertices of the largest ring to the smallest one: d(Rl(vi),Rl(vj)) = |Rl (vi)| ∑ n=0 d(Rl n (vi),Rl n (vj)) with n = n·|Rl (vj)| |Rl (vi)| and |Rl(vi)| > |Rl(vj)| First vertex descriptor Second vertex descriptor 0-hop 1-hop 2-hop The distance between two vertices is then the distance between their graph signal vectors: d(Rl n (vi),Rl m (vj)) = F(Rl n (vi))−F(Rl m (vj)) 2 that are vertex normal vectors: F(vi) = n(vi) O. L´ ezoray & A. Nouri 3D Mesh Saliency from local spiral hop descriptors 12 / 28
  25. Local spiral hop descriptors Comparison The size of the operator

    Sp(vi,k) varies for the vertices Lim et al. either truncate or zero-pad each spiral depending on its size to compare two local spiral hop descriptors We propose a more accurate hierarchical comparison d(Sp(vi,k),Sp(vj,k)) = k ∑ l=0 d(Rl(vi),Rl(vj)) Two k-rings are compared by mapping the vertices of the largest ring to the smallest one: d(Rl(vi),Rl(vj)) = |Rl (vi)| ∑ n=0 d(Rl n (vi),Rl n (vj)) with n = n·|Rl (vj)| |Rl (vi)| and |Rl(vi)| > |Rl(vj)| First vertex descriptor Second vertex descriptor 0-hop 1-hop 2-hop The distance between two vertices is then the distance between their graph signal vectors: d(Rl n (vi),Rl m (vj)) = F(Rl n (vi))−F(Rl m (vj)) 2 that are vertex normal vectors: F(vi) = n(vi) O. L´ ezoray & A. Nouri 3D Mesh Saliency from local spiral hop descriptors 12 / 28
  26. Local spiral hop descriptors Comparison The size of the operator

    Sp(vi,k) varies for the vertices Lim et al. either truncate or zero-pad each spiral depending on its size to compare two local spiral hop descriptors We propose a more accurate hierarchical comparison d(Sp(vi,k),Sp(vj,k)) = k ∑ l=0 d(Rl(vi),Rl(vj)) Two k-rings are compared by mapping the vertices of the largest ring to the smallest one: d(Rl(vi),Rl(vj)) = |Rl (vi)| ∑ n=0 d(Rl n (vi),Rl n (vj)) with n = n·|Rl (vj)| |Rl (vi)| and |Rl(vi)| > |Rl(vj)| First vertex descriptor Second vertex descriptor 0-hop 1-hop 2-hop The distance between two vertices is then the distance between their graph signal vectors: d(Rl n (vi),Rl m (vj)) = F(Rl n (vi))−F(Rl m (vj)) 2 that are vertex normal vectors: F(vi) = n(vi) O. L´ ezoray & A. Nouri 3D Mesh Saliency from local spiral hop descriptors 12 / 28
  27. Local spiral hop descriptors Comparison The size of the operator

    Sp(vi,k) varies for the vertices Lim et al. either truncate or zero-pad each spiral depending on its size to compare two local spiral hop descriptors We propose a more accurate hierarchical comparison d(Sp(vi,k),Sp(vj,k)) = k ∑ l=0 d(Rl(vi),Rl(vj)) Two k-rings are compared by mapping the vertices of the largest ring to the smallest one: d(Rl(vi),Rl(vj)) = |Rl (vi)| ∑ n=0 d(Rl n (vi),Rl n (vj)) with n = n·|Rl (vj)| |Rl (vi)| and |Rl(vi)| > |Rl(vj)| First vertex descriptor Second vertex descriptor 0-hop 1-hop 2-hop The distance between two vertices is then the distance between their graph signal vectors: d(Rl n (vi),Rl m (vj)) = F(Rl n (vi))−F(Rl m (vj)) 2 that are vertex normal vectors: F(vi) = n(vi) O. L´ ezoray & A. Nouri 3D Mesh Saliency from local spiral hop descriptors 12 / 28
  28. Local spiral hop descriptors Comparison The size of the operator

    Sp(vi,k) varies for the vertices Lim et al. either truncate or zero-pad each spiral depending on its size to compare two local spiral hop descriptors We propose a more accurate hierarchical comparison d(Sp(vi,k),Sp(vj,k)) = k ∑ l=0 d(Rl(vi),Rl(vj)) Two k-rings are compared by mapping the vertices of the largest ring to the smallest one: d(Rl(vi),Rl(vj)) = |Rl (vi)| ∑ n=0 d(Rl n (vi),Rl n (vj)) with n = n·|Rl (vj)| |Rl (vi)| and |Rl(vi)| > |Rl(vj)| First vertex descriptor Second vertex descriptor 0-hop 1-hop 2-hop The distance between two vertices is then the distance between their graph signal vectors: d(Rl n (vi),Rl m (vj)) = F(Rl n (vi))−F(Rl m (vj)) 2 that are vertex normal vectors: F(vi) = n(vi) O. L´ ezoray & A. Nouri 3D Mesh Saliency from local spiral hop descriptors 12 / 28
  29. Local spiral hop descriptors Comparison The size of the operator

    Sp(vi,k) varies for the vertices Lim et al. either truncate or zero-pad each spiral depending on its size to compare two local spiral hop descriptors We propose a more accurate hierarchical comparison d(Sp(vi,k),Sp(vj,k)) = k ∑ l=0 d(Rl(vi),Rl(vj)) Two k-rings are compared by mapping the vertices of the largest ring to the smallest one: d(Rl(vi),Rl(vj)) = |Rl (vi)| ∑ n=0 d(Rl n (vi),Rl n (vj)) with n = n·|Rl (vj)| |Rl (vi)| and |Rl(vi)| > |Rl(vj)| First vertex descriptor Second vertex descriptor 0-hop 1-hop 2-hop The distance between two vertices is then the distance between their graph signal vectors: d(Rl n (vi),Rl m (vj)) = F(Rl n (vi))−F(Rl m (vj)) 2 that are vertex normal vectors: F(vi) = n(vi) O. L´ ezoray & A. Nouri 3D Mesh Saliency from local spiral hop descriptors 12 / 28
  30. Outline 1. Introduction 2. Local spiral hop descriptors 3. Roughness,

    geometric and spectral saliencies 4. Results 5. Conclusion O. L´ ezoray & A. Nouri 3D Mesh Saliency from local spiral hop descriptors 13 / 28
  31. Outline 1. Introduction 2. Local spiral hop descriptors 3. Roughness,

    geometric and spectral saliencies 4. Results 5. Conclusion O. L´ ezoray & A. Nouri 3D Mesh Saliency from local spiral hop descriptors 14 / 28
  32. Roughness Chen et al. have shown that curvature plays an

    important role for saliency detection Lee et al. have proposed the first mesh saliency detection based on differences between Gaussian-weighted mean curvatures We consider the more robust notion of roughness (from Wang et al.) that we extend to large neighborhoods (by taking γ powers of the Laplacian) R(vi) = κ(vi)− ∑ vj∈γ-rings(vi) Lγ i j ·κ(vj) ∑ vj∈γ-rings(vi) Lγ i j with γ-rings(vi) = γ-disk(vi)\{vi} and κ(vi) the mean curvature. O. L´ ezoray & A. Nouri 3D Mesh Saliency from local spiral hop descriptors 15 / 28
  33. Geometric and spectral saliencies Definitions Gradient operator We define the

    gradient at a vertex vi as the nonlocal vector of all the distances between the spiral descriptors of vi and its neighbors within its γ-rings(vi): ∇f(vi) = [d(Sp(vi,k),Sp(vj,k)),vj ∈ γ-rings(vi)]T with γ-rings(vi) = γ-disk(vi)\{vi}. One needs to have γ > k: the support of the gradient is larger than the spiral descriptor support. O. L´ ezoray & A. Nouri 3D Mesh Saliency from local spiral hop descriptors 16 / 28
  34. Geometric and spectral saliencies Definitions Geometric saliency The geometric saliency

    is the normalized L1 norm of the gradient: GS(vi) = 1 |γ-rings(vi)| ∇f(vi) 1 = 1 |γ-rings(vi)| ∑ vj∈γ-rings(vi) d(Sp(vi,k),Sp(vj,k)) O. L´ ezoray & A. Nouri 3D Mesh Saliency from local spiral hop descriptors 17 / 28
  35. Geometric and spectral saliencies Definitions Spectral saliency The structure tensor

    J is the outer product of the gradient: J(vi) = ∇T f(vi)·∇f(vi). Its eigenvalues provide a discriminative description of the local geometry by summarizing the distribution of the gradients The spectral saliency is defined as the Structure Tensor Total Variation (STTV): SS(vi) = |γ-rings(vi)| ∑ j=1 λ2 j with λj the eigenvalues of J(vi). O. L´ ezoray & A. Nouri 3D Mesh Saliency from local spiral hop descriptors 18 / 28
  36. Roughness, Geometric and spectral saliencies O. L´ ezoray & A.

    Nouri 3D Mesh Saliency from local spiral hop descriptors 19 / 28
  37. Geometric and spectral saliencies Definitions Saliency We have three different

    measures: Roughness : based on based on differences of curvatures, it tends to be very sensitive to small changes. Geometric saliency: smooth and robust to small changes. Spectral saliency: very localized and robust to small changes. To merge these informations altogether into a single saliency measure, we weight the roughness by the sum of the normalized geometric and spectral saliencies: S(vi) = Kσ R(vi)· GS(vi)+SS(vi) with Kσ a Gaussian smoothing. O. L´ ezoray & A. Nouri 3D Mesh Saliency from local spiral hop descriptors 20 / 28
  38. Outline 1. Introduction 2. Local spiral hop descriptors 3. Roughness,

    geometric and spectral saliencies 4. Results 5. Conclusion O. L´ ezoray & A. Nouri 3D Mesh Saliency from local spiral hop descriptors 21 / 28
  39. Outline 1. Introduction 2. Local spiral hop descriptors 3. Roughness,

    geometric and spectral saliencies 4. Results 5. Conclusion O. L´ ezoray & A. Nouri 3D Mesh Saliency from local spiral hop descriptors 22 / 28
  40. Results R(vi) GS(vi) SS(vi) S(vi) Roughness Geometric Spectral Final Figure:

    Saliency computation on 3-rings with 2-hop spiral descriptors Sp(vi,2). Warm colors mean high values of saliency. O. L´ ezoray & A. Nouri 3D Mesh Saliency from local spiral hop descriptors 23 / 28
  41. Results R(vi) GS(vi) SS(vi) S(vi) Roughness Geometric Spectral Final Figure:

    Saliency computation on 3-rings with 2-hop spiral descriptors Sp(vi,2). Warm colors mean high values of saliency. O. L´ ezoray & A. Nouri 3D Mesh Saliency from local spiral hop descriptors 23 / 28
  42. Results R(vi) GS(vi) SS(vi) S(vi) Roughness Geometric Spectral Final Figure:

    Saliency computation on 3-rings with 2-hop spiral descriptors Sp(vi,2). Warm colors mean high values of saliency. O. L´ ezoray & A. Nouri 3D Mesh Saliency from local spiral hop descriptors 23 / 28
  43. Results R(vi) GS(vi) SS(vi) S(vi) Roughness Geometric Spectral Final Figure:

    Saliency computation on 3-rings with 2-hop spiral descriptors Sp(vi,2). Warm colors mean high values of saliency. O. L´ ezoray & A. Nouri 3D Mesh Saliency from local spiral hop descriptors 23 / 28
  44. Results Figure: From left to right : Ground truth of

    Chen et al., saliency detection methods of Sun et al., Song et al., Song et al., Ours (first scale), Ours (second scale), Ours (third scale), Ours (fusion of the scales by max) O. L´ ezoray & A. Nouri 3D Mesh Saliency from local spiral hop descriptors 24 / 28
  45. Results Figure: From left to right : Ground truth of

    Chen et al., saliency detection methods of Sun et al., Song et al., Song et al., Ours (first scale), Ours (second scale), Ours (third scale), Ours (fusion of O. L´ ezoray & A. Nouri 3D Mesh Saliency from local spiral hop descriptors 24 / 28
  46. Outline 1. Introduction 2. Local spiral hop descriptors 3. Roughness,

    geometric and spectral saliencies 4. Results 5. Conclusion O. L´ ezoray & A. Nouri 3D Mesh Saliency from local spiral hop descriptors 25 / 28
  47. Outline 1. Introduction 2. Local spiral hop descriptors 3. Roughness,

    geometric and spectral saliencies 4. Results 5. Conclusion O. L´ ezoray & A. Nouri 3D Mesh Saliency from local spiral hop descriptors 26 / 28
  48. Conclusion Our contribution We have proposed a local normal-based descriptor

    built for each vertex according to a spiral path within a k-hop neighborhood. a hierarchical comparison between two local spiral hop descriptors a nonlocal gradient for each vertex as the vector of the descriptors’ comparison geometric and spectral saliencies from the norm of the gradient and the structure tensor total variation a saliency measure combining both saliencies weighted by a roughness measure O. L´ ezoray & A. Nouri 3D Mesh Saliency from local spiral hop descriptors 27 / 28
  49. The End Publications available at : https://lezoray.users.greyc.fr O. L´ ezoray

    & A. Nouri 3D Mesh Saliency from local spiral hop descriptors 28 / 28