  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 (available under
http://optlang.org), for writing these objective functions over image- or
graph-structured unknowns concisely and at a high level. Our compiler
automatically transforms these specifications into state-of-the-art GPU solvers
based on Gauss-Newton or Levenberg-Marquardt methods. Opt can generate
different variations of the solver, so users can easily explore tradeoffs in
numerical precision, matrix-free methods, and solver approaches. In our
results, we implement a variety of real-world graphics and vision applications.
Their energy functions are expressible in tens of lines of code, and produce
highly-optimized GPU solver implementations. These solver have performance
competitive with the best published hand-tuned, application-specific GPU
solvers, and orders of magnitude beyond a general-purpose auto-generated
solver.
