The document discusses least square regression with L0, L1, and L2 constraints. It presents the cost functions for each constraint and derives the solutions. For L0 constraint, the solution is a hard threshold determined by comparing the squared value to the regularization parameter. For L1 constraint, the solution is a soft threshold. For L2 constraint, the solution is obtained by setting the derivative of the cost function to zero. It also formulates L0 and L1 constraints as proximal operators.
This document summarizes the Alternating Direction Method of Multipliers (ADMM) algorithm. It discusses how ADMM can be used to solve optimization problems of the form minimize f(x) + g(z) subject to Kx - z = 0, where Kx - z decomposes the problem into separable subproblems for x and z. The algorithm alternates between optimizing the augmented Lagrangian Lρ(x, z, u) with respect to x, z, and their dual variables u. Each subproblem can be solved efficiently using proximal operators, often having closed-form solutions in frequency space.
This document summarizes scattering in computer graphics and computer vision, including:
- Types of scattering such as diffuse reflection, specular reflection, BRDF, subsurface scattering, single scattering, and multiple scattering.
- Models for subsurface scattering including diffuse approximation, plane-parallel approximation, and Donner's empirical BSSRDF model.
- Techniques for measuring scattering properties like BRDF and rendering effects of scattering in participating media and subsurface scattering.
ICASSP2012 Poster Estimating the spin of a table tennis ball using inverse co...Toru Tamaki
Tamaki Toru, Haoming Wang, Bisser Raytchev, Kazufumi Kaneda, Yukihiko Ushiyama: "Estimating the spin of a table tennis ball using inverse compositional image alignment", Proc. of ICASSP 2012 ; 2012 IEEE International Conference on Acoustics, Speech, and Signal Processing,pp. 1457-1460 (2012 03), Kyoto International Conference Center , Kyoto, Japan, March 25-30, 2012.
This document summarizes Toru Tamaki's presentation on scattering in computer graphics (CG) and computer vision (CV). It discusses reflection models including diffuse/specular reflection and bidirectional reflectance distribution functions (BRDFs). It also covers subsurface scattering within materials, models for subsurface scattering including diffuse approximation and plane-parallel approximation, and measuring scattering properties including single and multiple scattering. Examples of subsurface scattering rendering from past CG papers are shown.
The document discusses least square regression with L0, L1, and L2 constraints. It presents the cost functions for each constraint and derives the solutions. For L0 constraint, the solution is a hard threshold determined by comparing the squared value to the regularization parameter. For L1 constraint, the solution is a soft threshold. For L2 constraint, the solution is obtained by setting the derivative of the cost function to zero. It also formulates L0 and L1 constraints as proximal operators.
This document summarizes the Alternating Direction Method of Multipliers (ADMM) algorithm. It discusses how ADMM can be used to solve optimization problems of the form minimize f(x) + g(z) subject to Kx - z = 0, where Kx - z decomposes the problem into separable subproblems for x and z. The algorithm alternates between optimizing the augmented Lagrangian Lρ(x, z, u) with respect to x, z, and their dual variables u. Each subproblem can be solved efficiently using proximal operators, often having closed-form solutions in frequency space.
This document summarizes scattering in computer graphics and computer vision, including:
- Types of scattering such as diffuse reflection, specular reflection, BRDF, subsurface scattering, single scattering, and multiple scattering.
- Models for subsurface scattering including diffuse approximation, plane-parallel approximation, and Donner's empirical BSSRDF model.
- Techniques for measuring scattering properties like BRDF and rendering effects of scattering in participating media and subsurface scattering.
ICASSP2012 Poster Estimating the spin of a table tennis ball using inverse co...Toru Tamaki
Tamaki Toru, Haoming Wang, Bisser Raytchev, Kazufumi Kaneda, Yukihiko Ushiyama: "Estimating the spin of a table tennis ball using inverse compositional image alignment", Proc. of ICASSP 2012 ; 2012 IEEE International Conference on Acoustics, Speech, and Signal Processing,pp. 1457-1460 (2012 03), Kyoto International Conference Center , Kyoto, Japan, March 25-30, 2012.
This document summarizes Toru Tamaki's presentation on scattering in computer graphics (CG) and computer vision (CV). It discusses reflection models including diffuse/specular reflection and bidirectional reflectance distribution functions (BRDFs). It also covers subsurface scattering within materials, models for subsurface scattering including diffuse approximation and plane-parallel approximation, and measuring scattering properties including single and multiple scattering. Examples of subsurface scattering rendering from past CG papers are shown.
The document proposes a new method called Sparse Isotropic Hashing (SIH) to learn compact binary codes for image retrieval. SIH imposes additional constraints of sparsity and isotropic variance on the hash functions to make the learning problem better posed. It formulates SIH as an optimization problem that balances orthogonality, isotropic variance and sparsity, and develops an algorithm to solve it. Experiments on a landmark dataset show SIH achieves comparable retrieval accuracy to the state-of-the-art method while learning hash codes 20 times faster.
The document proposes a new method called Sparse Isotropic Hashing (SIH) to learn compact binary codes for image retrieval. SIH imposes additional constraints of sparsity and isotropic variance on the hash functions to make the learning problem better posed. It formulates SIH as an optimization problem that balances orthogonality, isotropic variance and sparsity, and develops an algorithm to solve it. Experiments on a landmark dataset show SIH achieves comparable retrieval accuracy to the state-of-the-art method while learning hash codes 20 times faster.