heat kernel signature

include/cinolib/HKS.cpp

@@ -0,0 +1,93 @@
+/********************************************************************************
+*  This file is part of CinoLib                                                 *
+*  Copyright(C) 2025: Marco Livesu                                              *
+*                                                                               *
+*  The MIT License                                                              *
+*                                                                               *
+*  Permission is hereby granted, free of charge, to any person obtaining a      *
+*  copy of this software and associated documentation files (the "Software"),   *
+*  to deal in the Software without restriction, including without limitation    *
+*  the rights to use, copy, modify, merge, publish, distribute, sublicense,     *
+*  and/or sell copies of the Software, and to permit persons to whom the        *
+*  Software is furnished to do so, subject to the following conditions:         *
+*                                                                               *
+*  The above copyright notice and this permission notice shall be included in   *
+*  all copies or substantial portions of the Software.                          *
+*                                                                               *
+*  THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR   *
+*  IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,     *
+*  FITNESS FOR A PARTICULAR PURPOSE AND NON INFRINGEMENT. IN NO EVENT SHALL THE *
+*  AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER       *
+*  LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING      *
+*  FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS *
+*  IN THE SOFTWARE.                                                             *
+*                                                                               *
+*  Author(s):                                                                   *
+*                                                                               *
+*     Marco Livesu ([email protected])                                     *
+*     http://pers.ge.imati.cnr.it/livesu/                                       *
+*                                                                               *
+*     Italian National Research Council (CNR)                                   *
+*     Institute for Applied Mathematics and Information Technologies (IMATI)    *
+*     Via de Marini, 6                                                          *
+*     16149 Genoa,                                                              *
+*     Italy                                                                     *
+*********************************************************************************/
+#include <cinolib/HKS.h>
+#include <cinolib/laplacian.h>
+#include <cinolib/linear_solvers.h>
+#include <cinolib/scalar_field.h>
+#include <cinolib/vertex_mass.h>
+#include <cinolib/sampling.h>
+
+namespace cinolib
+{
+
+template<class M, class V, class E, class P>
+CINO_INLINE
+Eigen::MatrixXd HKS(      AbstractMesh<M,V,E,P> & m,
+                    const std::vector<uint>     & landmarks,
+                    const uint                    n_timesteps,
+                    const bool                    normalize_mesh,
+                    const bool                    normalize_columns,
+                    const bool                    verbose)
+{
+    if(normalize_mesh) m.normalize_bbox();
+
+    uint n_rows = m.num_verts();
+    uint n_cols = landmarks.size()*n_timesteps;
+    Eigen::MatrixXd A(n_rows,n_cols);
+
+    Eigen::SparseMatrix<double> L  = laplacian(m, COTANGENT);
+    Eigen::SparseMatrix<double> MM = mass_matrix(m);
+
+    // This is what Dorian Nogneng and Maks Ovsjanikov do in their reference code for the paper:
+    //
+    //      Informative Descriptor Preservation via Commutativity for Shape Matching
+    //      Eurographics 2017
+    //
+    std::vector<double> timesteps = sample_within_interval(log(0.005), log(0.2), n_timesteps);
+    for(uint i=0; i<n_timesteps; ++i) timesteps[i] = exp(timesteps[i]);
+
+    uint col = 0;
+    for(auto t : timesteps)
+    {
+        Eigen::SimplicialLLT<Eigen::SparseMatrix<double>> solver(MM - t*L);
+        assert(solver.info() == Eigen::Success);
+
+        for(auto v : landmarks)
+        {
+            if(verbose) std::cout << "column " << col << ": time step " << t << ", landmark " << v << std::endl;
+
+            Eigen::VectorXd rhs = Eigen::VectorXd::Zero(m.num_verts());
+            rhs[v] = 1.0;
+            ScalarField f = solver.solve(rhs).eval();
+            if(normalize_columns) f.normalize_in_01(); // Useful for visualization but "physically wrong"...
+            for(uint vid=0; vid<m.num_verts(); ++vid) A.coeffRef(vid,col) = f[vid];
+            ++col;
+        }
+    }
+    return A;
+}
+
+}

include/cinolib/HKS.h

@@ -0,0 +1,61 @@
+/********************************************************************************
+*  This file is part of CinoLib                                                 *
+*  Copyright(C) 2025: Marco Livesu                                              *
+*                                                                               *
+*  The MIT License                                                              *
+*                                                                               *
+*  Permission is hereby granted, free of charge, to any person obtaining a      *
+*  copy of this software and associated documentation files (the "Software"),   *
+*  to deal in the Software without restriction, including without limitation    *
+*  the rights to use, copy, modify, merge, publish, distribute, sublicense,     *
+*  and/or sell copies of the Software, and to permit persons to whom the        *
+*  Software is furnished to do so, subject to the following conditions:         *
+*                                                                               *
+*  The above copyright notice and this permission notice shall be included in   *
+*  all copies or substantial portions of the Software.                          *
+*                                                                               *
+*  THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR   *
+*  IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,     *
+*  FITNESS FOR A PARTICULAR PURPOSE AND NON INFRINGEMENT. IN NO EVENT SHALL THE *
+*  AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER       *
+*  LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING      *
+*  FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS *
+*  IN THE SOFTWARE.                                                             *
+*                                                                               *
+*  Author(s):                                                                   *
+*                                                                               *
+*     Marco Livesu ([email protected])                                     *
+*     http://pers.ge.imati.cnr.it/livesu/                                       *
+*                                                                               *
+*     Italian National Research Council (CNR)                                   *
+*     Institute for Applied Mathematics and Information Technologies (IMATI)    *
+*     Via de Marini, 6                                                          *
+*     16149 Genoa,                                                              *
+*     Italy                                                                     *
+*********************************************************************************/
+#ifndef CINO_HKS_H
+#define CINO_HKS_H
+
+#include <cinolib/meshes/abstract_mesh.h>
+#include <Eigen/Dense>
+
+namespace cinolib
+{
+
+// Heat Kernel Signature
+
+template<class M, class V, class E, class P>
+CINO_INLINE
+Eigen::MatrixXd HKS(      AbstractMesh<M,V,E,P> & m,
+                    const std::vector<uint>     & landmarks,
+                    const uint                    n_timesteps,
+                    const bool                    normalize_mesh = false,
+                    const bool                    normalize_columns = false,
+                    const bool                    verbose = false);
+}
+
+#ifndef  CINO_STATIC_LIB
+#include "HKS.cpp"
+#endif
+
+#endif // CINO_HKS_H