We show that by extending the Laplacian formalism, which was first introduced
in the Graphics community to regularize 3D meshes, we can turn the monocular 3D
shape reconstruction of a deformable surface given correspondences with a
reference image into a much better-posed problem. This allows us to quickly and
reliably eliminate outliers by simply solving a linear least squares problem.
This yields an initial 3D shape estimate, which is not necessarily accurate,
but whose 2D projections are. The initial shape is then refined by a
constrained optimization problem to output the final surface reconstruction.
Our approach allows us to reduce the dimensionality of the surface
reconstruction problem without sacrificing accuracy, thus allowing for
real-time implementations.

通过扩展 Laplacian formalism，我们可以将单目 3D 形状重建转化为更好处理的问题，通过简单地解决线性最小二乘问题可以快速可靠地消除异常值。这使我们能够实时地降低表面重建问题的维度而不会损失准确性。

使用拉普拉斯网格的基于模板的单目三维形状恢复

Template-based Monocular 3D Shape Recovery using Laplacian Meshes

Sparse coding is an unsupervised learning algorithm that learns a succinct
high-level representation of the inputs given only unlabeled data; it
represents each input as a sparse linear combination of a set of basis
functions. Originally applied to modeling the human visual cortex, sparse
coding has also been shown to be useful for self-taught learning, in which the
goal is to solve a supervised classification task given access to additional
unlabeled data drawn from different classes than that in the supervised
learning problem. Shift-invariant sparse coding (SISC) is an extension of
sparse coding which reconstructs a (usually time-series) input using all of the
basis functions in all possible shifts. In this paper, we present an efficient
algorithm for learning SISC bases. Our method is based on iteratively solving
two large convex optimization problems: The first, which computes the linear
coefficients, is an L1-regularized linear least squares problem with
potentially hundreds of thousands of variables. Existing methods typically use
a heuristic to select a small subset of the variables to optimize, but we
present a way to efficiently compute the exact solution. The second, which
solves for bases, is a constrained linear least squares problem. By optimizing
over complex-valued variables in the Fourier domain, we reduce the coupling
between the different variables, allowing the problem to be solved efficiently.
We show that SISC's learned high-level representations of speech and music
provide useful features for classification tasks within those domains. When
applied to classification, under certain conditions the learned features
outperform state of the art spectral and cepstral features.

本文研究了一种名为 SISC 的移不变稀疏编码学习算法，通过迭代求解两个大型凸优化问题，其能够在给定无监督数据的情况下，通过将每个输出表示为一组基函数的稀疏线性组合，学习输入的简洁高级表示。研究发现，使用 SISC 算法学习到的高级表示对语音和音乐分类任务具有良好的分类性能。