Image decomposition offers deep insights into the imaging factors of visual data and significantly enhances various advanced computer vision tasks. In this work, we introduce a novel approach to low-light image enhancement based on decomposed physics-informed priors. Existing methods that directly map low-light to normal-light images in the sRGB color space suffer from inconsistent color predictions and high sensitivity to spectral power distribution (SPD) variations, resulting in unstable performance under diverse lighting conditions. To address these challenges, we introduce a Physics-informed Color-aware Transform (PiCat), a learning-based framework that converts low-light images from the sRGB color space into deep illumination-invariant descriptors via our proposed Color-aware Transform (CAT). This transformation enables robust handling of complex lighting and SPD variations. Complementing this, we propose the Content-Noise Decomposition Network (CNDN), which refines the descriptor distributions to better align with well-lit conditions by mitigating noise and other distortions, thereby effectively restoring content representations to low-light images. The CAT and the CNDN collectively act as a physical prior, guiding the transformation process from low-light to normal-light domains. Our proposed PiCat framework demonstrates superior performance compared to state-of-the-art methods across five benchmark datasets.

Picat [27] is a Prolog-like language that takes many features from other languages, including patternmatching rules, functions, list/array comprehensions, loops, assignments, tabling for dynamic programming and planning, and constraint programming. These features make Picat a convenient modeling language for combinatorial problems, on a par with AMPL [8], OPL [9], and MiniZinc [17]. As a logic language, Picat can often offer solutions that are as concise and elegant as the ones in ASP [5]. Picat supports constraint solving using different solvers, including CP (constraint programming), SAT (satisfiability), MIP (mixed integer programming), and SMT (SAT Modulo Theories). The last two decades have witnessed dramatic enhancement in SAT solvers' performance, thanks to inventions of techniques, from conflict-driven clause learning, backjumping, variable and value selection heuristics, to random restarts [2, 4, 16]. With findings of effective encodings [12, 13, 15, 19, 21, 23, 26], SAT has become a strong contendant for solving a wide range of constraint satisfaction and optimization problems (CSP). Many CSPs involve synthesizing subgraphs that satisfy certain reachability constraints, including the constraint that ensures a cycle connecting all the vertices, as in the Hamiltonian cycle problem (HCP), and the constraint that ensures a strongly connected component. For that reason, CP systems provide graph constraints for easing the modeling and solving of these problems [1, 20].

This paper describes Picat's planner, its implementation, and planning models for several domains used in International Planning Competition (IPC) 2014. Picat's planner is implemented by use of tabling. During search, every state encountered is tabled, and tabled states are used to effectively perform resource-bounded search. In Picat, structured data can be used to avoid enumerating all possible permutations of objects, and term sharing is used to avoid duplication of common state data. This paper presents several modeling techniques through the example models, ranging from designing state representations to facilitate data sharing and symmetry breaking, encoding actions with operations for efficient precondition checking and state updating, to incorporating domain knowledge and heuristics. Broadly, this paper demonstrates the effectiveness of tabled logic programming for planning, and argues the importance of modeling despite recent significant progress in domain-independent PDDL planners.