author={Zach DeVito and Michael Mara and Michael Zollh{\"o}fer and Gilbert Louis Bernstein and Jonathan Ragan-Kelley and Christian Theobalt and Pat Hanrahan and Matthew Fisher and Matthias Nie{\ss}ner},
  journal={ACM Transactions on Graphics (TOG)},
  pages={1 - 27}
Many graphics and vision problems can be expressed as non-linear least squares optimizations of objective functions over visual data, such as images and meshes. The mathematical descriptions of these functions are extremely concise, but their implementation in real code is tedious, especially when optimized for real-time performance on modern GPUs in interactive applications. In this work, we propose a new language, Opt,1 for writing these objective functions over image- or graph-structured… Expand
Thallo - Scheduling for High-Performance Large-Scale Non-Linear Least-Squares Solvers
Large-scale optimization problems at the core of many graphics, vision, and imaging applications are often implemented by hand in tedious and error-prone processes in order to achieve highExpand
Differentiable programming for image processing and deep learning in halide
This work extends the image processing language Halide with general reverse-mode automatic differentiation (AD), and the ability to automatically optimize the implementation of gradient computations, and shows how differentiable programming enables dramatically improving the quality of even traditional, feed-forward image processing algorithms, blurring the distinction between classical and deep methods. Expand
An Efficient Solution to Structured Optimization Problems using Recursive Matrices
This work presents a linear algebra framework for structured matrices and general optimization problems that yields a speedup of 3–5 compared to other optimization frameworks and defines mixed matrices, which allow every element to be of a different type. Expand
Fast Nonlinear Least Squares Optimization of Large‐Scale Semi‐Sparse Problems
A novel iterative solver is introduced for nonlinear least squares optimization of large‐scale semi‐sparse problems using the nonlinear Levenberg‐Marquardt method, and results are obtained up to one order of magnitude faster than other existing solvers, without sacrificing the generality and the accuracy of the model. Expand
Massively parallel data processing for quantitative total flow imaging with optical coherence microscopy and tomography
An application of massively parallel processing of quantitative flow measurements data acquired using spectral optical coherence microscopy and achieved a 150 fold reduction in processing time when compared to a former CPU implementation. Expand
Optimization of freeform surfaces using intelligent deformation techniques for LED applications
This research addresses two important issues: the selection of appropriate vertices of the cubical grid and the surfaces created by them are not always feasible to manufacture, which is the same problem faced in any optimization technique while creating freeform surfaces. Expand
Freeform surface descriptions. Part II: Application benchmark
Recommendations for the right choice of freeform surface representations for practical issues in the optimization of optical systems can be given under restrictions of the benchmark assumptions. Expand
Symmetric moving frames
A fundamentally new representation of 3D cross fields based on Cartan's method of moving frames is introduced, finding that cross fields and ordinary frame fields are locally characterized by identical conditions on their Darboux derivative, and applies this representation to compute 3DCross fields that are as smooth as possible everywhere but on a prescribed network of singular curves. Expand
"First time right" - calculating imaging systems from scratch -INVITED
Freeform optics can be used to greatly extend the functionalities, improve performance, and reduce the volume and weight of optical systems. Today, the design of imaging systems largely relies onExpand
SHARP: a distributed, GPU-based ptychographic solver
A set of algorithmic and computational methodologies used at the Advanced Light Source, and DOE light sources packaged as a CUDA based software environment named SHARP is introduced, aimed at providing state-of-the-art high-throughput ptychography reconstructions for the coming era of diffraction limited light sources. Expand


Limit Theorems for Stochastic Processes
I. The General Theory of Stochastic Processes, Semimartingales and Stochastic Integrals.- II. Characteristics of Semimartingales and Processes with Independent Increments.- III. Martingale ProblemsExpand
Asymptotic arbitrage in large financial markets
The suggested theory can be considered as a natural extension of Arbirage Pricing Theory covering the continuous as well as the discrete time case. Expand
On the range of options prices
This paper considers the valuation of an option with time to expiration and pay-off function which is a convex function, and constant interest rate, and finds that, for “most” such models, the range of the values of the option is the interval, this interval being the biggest interval in which the values must lie, whatever model is used. Expand
Robustness of the Black and Scholes Formula
Consider an option on a stock whose volatility is unknown and stochastic. An agent assumes this volatility to be a specific function of time and the stock price, knowing that this assumption mayExpand
Dynamic Programming and Pricing of Contingent Claims in an Incomplete Market
The problem of pricing contingent claims or options from the price dynamics of certain securities is well understood in the context of a complete financial market. This paper studies the same problemExpand
Equivalent martingale measures and no-arbitrage in stochastic securities market models
We characterize those vector-valued stochastic processes (with a finite index set and defined on an arbitrarystochasic base) which can become a martingale under an equivalent change of measure.ThisExpand
Processes of normal inverse Gaussian type
A number of stochastic processes with normal inverse Gaussian marginals and various types of dependence structures are discussed, including Ornstein-Uhlenbeck type processes, superpositions of such processes and Stochastic volatility models in one and more dimensions. Expand
The second part of this study deals with criteria for the absolute continuity of measures for various classes of random processes, starting out from the general results in Part I. We considerExpand
Optional decomposition of supermartingales and hedging in incomplete security markets
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Probabilité et Potentiel
  • Hermann, Paris,
  • 1976