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
this http URL), 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.

该研究展示了一个可用于图像和视觉数据非线性最小二乘目标函数最优化的新语言 Opt，其数学描述非常简洁，但在实现过程中需要考虑到现代 GPU 在交互式应用中实时性能的优化。该语言生成的 GPU 求解器在精度、矩阵无关方法和求解器方法中均具有良好的折衷、性能优异，经实验证明，它们的性能竞争力可以与已发布的手动调优、应用特定的 GPU 求解器相媲美。