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1. Frame Field Operators

   https://doi.org/10.1111/cgf.14370  

   Palmer, D.; Stein, O.; Solomon, J. (August 2021, Computer Graphics Forum)

   Abstract Differential operators are widely used in geometry processing for problem domains like spectral shape analysis, data interpolation, parametrization and mapping, and meshing. In addition to the ubiquitous cotangent Laplacian, anisotropic second‐order operators, as well as higher‐order operators such as the Bilaplacian, have been discretized for specialized applications. In this paper, we study a class of operators that generalizes the fourth‐order Bilaplacian to support anisotropic behavior. The anisotropy is parametrized by asymmetric frame field, first studied in connection with quadrilateral and hexahedral meshing, which allows for fine‐grained control of local directions of variation. We discretize these operators using a mixed finite element scheme, verify convergence of the discretization, study the behavior of the operator under pullback, and present potential applications. 

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2. Progress-Aware Video Frame Captioning

   Xue, Z; An, J; Yang, X; Grauman, K (March 2025, https://doi.org/10.48550/arXiv.2412.02071)

   While image captioning provides isolated descriptions for individual images, and video captioning offers one single narrative for an entire video clip, our work explores an important middle ground: progress-aware video captioning at the frame level. This novel task aims to generate temporally fine-grained captions that not only accurately describe each frame but also capture the subtle progression of actions throughout a video sequence. Despite the strong capabilities of existing leading vision language models, they often struggle to discern the nuances of frame-wise differences. To address this, we propose ProgressCaptioner, a captioning model designed to capture the fine-grained temporal dynamics within an action sequence. Alongside, we develop the FrameCap dataset to support training and the FrameCapEval benchmark to assess caption quality. The results demonstrate that ProgressCaptioner significantly surpasses leading captioning models, producing precise captions that accurately capture action progression and set a new standard for temporal precision in video captioning. Finally, we showcase practical applications of our approach, specifically in aiding keyframe selection and advancing video understanding, highlighting its broad utility. 

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3. Frame Spectral Pairs and Exponential Bases

   https://doi.org/10.1007/s00041-021-09872-9  

   Frederick, Christina; Mayeli, Azita (October 2021, Journal of Fourier Analysis and Applications)

   null (Ed.)
4. Discretizing L norms and frame theory

   https://doi.org/10.1016/j.jmaa.2022.126846  

   Freeman, Daniel; Ghoreishi, Dorsa (March 2023, Journal of Mathematical Analysis and Applications)
5. Frame dimension functions and phase retrievability

   https://doi.org/10.1007/s43036-024-00331-y  

   Han, Deguang; Liu, Kai (April 2024, Advances in Operator Theory)