Benjamin W. Wah

AAAI Conference 2026 Conference Paper

Video Mirror Detection with the Motion-in-Depth Cue

• Alex Warren
• Ke Xu
• Xin Tian
• Gary K. L. Tam
• Benjamin W. Wah
• Rynson W. H. Lau

Detecting mirror regions in RGB videos is essential for scene understanding in applications such as scene reconstruction and robotic navigation. Existing video mirror detectors typically rely on cues like inside-outside mirror correspondences and 2D motion inconsistencies. However, these methods often yield noisy or incomplete predictions when confronted with complex real-world video scenes, especially in areas with occlusion or limited visual features and motions. We observe that human perceive and navigate 3D occluded environments with remarkable ease, owing to Motion-in-Depth (MiD) perception. MiD integrates information from visual appearance (image colors and textures), the way objects move around us in 3D space (3D motions), and their relative distance from us (depth) to determine if something is approaching or receding and to support navigation. Motivated by this neuroscience mechanism, we introduce MiD-VMD, the first approach to explicitly model MiD for video mirror detection. MiD-VMD jointly utilizes contrastive 3D motion, depth, and image features through two novel modules based on a combinational QKV transformer architecture. The Motion-in-Depth Attention Learning (MiD-AL) module captures complementary relationships across these modalities with combinatorial attention and enforces a compact encoding to represent global 3D transformations, resulting in more accurate mirror detection and reduced motion artifacts. The Motion-in-Depth Boundary Detection (MiD-BD) module further sharpens mirror boundaries by leveraging cross-modal attention on 3D motion and depth features. Extensive experiments show that MiD-VMD outperforms current SOTAs.

IJCAI Conference 2007 Conference Paper

• Chih-Wei Hsu
• Benjamin W. Wah
• Ruoyun Huang
• Yixin Chen.

The PDDL3 specifications include soft goals and trajectory constraints for distinguishing high-quality plans among the many feasible plans in a solution space. To reduce the complexity of solving a large PDDL3 planning problem, constraint partitioning can be used to decompose its constraints into subproblems of much lower complexity. However, constraint locality due to soft goals and trajectory constraints cannot be effectively exploited by existing subgoal-partitioning techniques developed for solving PDDL2. 2 problems. In this paper, we present an improved partition-and-resolve strategy for supporting the new features in PDDL3. We evaluate techniques for resolving violated global constraints, optimizing goal preferences, and achieving subgoals in a multi-valued representation. Empirical results on the 5-th International Planning Competition (IPC5) benchmarks show that our approach is effective and significantly outperforms other competing planners.

AIJ Journal 2006 Journal Article

Constraint partitioning in penalty formulations for solving temporal planning problems

• Benjamin W. Wah
• Yixin Chen

In this paper, we study the partitioning of constraints in temporal planning problems formulated as mixed-integer nonlinear programming (MINLP) problems. Constraint partitioning is attractive because it leads to much easier subproblems, where each is a significant relaxation of the original problem. Moreover, each subproblem is very similar to the original problem and can be solved by any existing solver with little or no modification. Constraint partitioning, however, introduces global constraints that may be violated when subproblems are evaluated independently. To reduce the overhead in resolving such global constraints, we develop in this paper new conditions and algorithms for limiting the search space to be backtracked in each subproblem. Using a penalty formulation of a MINLP where the constraint functions of the MINLP are transformed into non-negative functions, we present a necessary and sufficient extended saddle-point condition (ESPC) for constrained local minimization. When the penalties are larger than some thresholds, our theory shows a one-to-one correspondence between a constrained local minimum of the MINLP and an extended saddle point of the penalty function. Hence, one way to find a constrained local minimum is to increase gradually the penalties of those violated constraints and to look for a local minimum of the penalty function using any existing algorithm until a solution to the constrained model is found. Next, we extend the ESPC to constraint-partitioned MINLPs and propose a partition-and-resolve strategy for resolving violated global constraints across subproblems. Using the discrete-space ASPEN and the mixed-space MIPS planners to solve subproblems, we show significant improvements on some planning benchmarks, both in terms of the quality of the plans generated and the execution times to find them.

ICAPS Conference 2003 Conference Paper

Automated Planning and Scheduling using Calculus of Variations in Discrete Space

• Yixin Chen 0001
• Benjamin W. Wah

In this paper, we propose new dominance relations that can speed up significantly the solution process of planning problems formulated as nonlinear constrained dynamic optimization in discrete time and space. We first show that path dominance in dynamic programming cannot be applied when there are general constraints that span across multiple stages, and that node dominance, in the form of Euler-Lagrange conditions developed in optimal control theory in continuous space, cannot be extended to that in discrete space. This paper is the first to propose efficient node-dominance relations, in the form of local saddle-point conditions in each stage of a discrete-space planning problem, for pruning states that will not lead to locally optimal paths. By utilizing these dominance relations, we present efficient search algorithms whose complexity, despite exponential, has a much smaller base as compared to that without using the relations. Finally, we demonstrate the performance of our approach by integrating it in the ASPEN planner and show significant improvements in CPU time and solution quality on some spacecraft scheduling and planning benchmarks.

AAAI Conference 1999 Conference Paper

Trap Escaping Strategies in Discrete Lagrangian Methods for Solving Hard Satisfiability and Maximum Satisfiability Problems

• Zhe Wu
• Benjamin W. Wah
• University of Illinois
• Urbana Champaign

In this paper, wepresent efficient trap-escapingstrategies in a search based on discrete Lagrangemultipliers to solve difficult SAT problems. Althougha basic discrete Lagrangian method(DLM) can solve most the satisfiable DIMACS SAT benchmarksefficiently, a few of the large benchmarkshave eluded solutions by any local-search methodstoday. Thesedifficult benchmarks generally have manytraps that attract localsearch trajectories. Tothis end, we identify the existence of traps whenany change to a variable wilt cause the resulting Lagrangianvalue to increase. Using the hanoi4and par16-1benchmarks, weillustrate that someunsatisfied clauses are trapped moreoften than others. Since it is too difficult to remember explicitly all the traps encountered, we proposeto remember these traps implicitly by giving larger increases to Lagrange multipliers of unsatisfied clauses that are trapped moreoften. Weillustrate the merit of this new update strategy by solving someof mostdifficult but satisfiable SATbenchmarks in the DIMACS archive (hanoi4, hanoi4-simple ~ par16-1to par16-5, ]2000, and par32-1-c to par32-3-c). Finally, weapply the same algorithm to improveon the solutions of somebenchmark MAX-SAT problems that we solved before.