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Many graphics and vision problems can be expressed as non-linear leastsquares optimizations of objective functions over visual data, such as imagesand meshes. The mathematical descriptions of these functions are extremelyconcise, but their implementation in real code is tedious, especially whenoptimized for real-time performance on modern GPUs in interactive applications.In this work, we propose a new language, Opt (available underhttp://optlang.org), for writing these objective functions over image- orgraph-structured unknowns concisely and at a high level. Our compilerautomatically transforms these specifications into state-of-the-art GPU solversbased on Gauss-Newton or Levenberg-Marquardt methods. Opt can generatedifferent variations of the solver, so users can easily explore tradeoffs innumerical precision, matrix-free methods, and solver approaches. In ourresults, we implement a variety of real-world graphics and vision applications.Their energy functions are expressible in tens of lines of code, and producehighly-optimized GPU solver implementations. These solver have performancecompetitive with the best published hand-tuned, application-specific GPUsolvers, and orders of magnitude beyond a general-purpose auto-generatedsolver.

Opt: A Domain Specific Language for Non-linear Least Squares Optimization in Graphics and Imaging