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Seongchan Kim

Publications and source records attributed to Seongchan Kim.

At least 19 recordsLinked to original sources
arXiv2025

MATRIX: Mask Track Alignment for Interaction-aware Video Generation

Video DiTs have advanced video generation, yet they still struggle to model multi-instance or subject-object interactions. This raises a key question: How do these models internally represent interactions? To answer this, we curate MATRIX-11K, a video dataset with interaction-aware captions and multi-instance mask tracks. Using this dataset, we conduct a systematic analysis that formalizes two perspectives of video DiTs: semantic grounding, via video-to-text attention, which evaluates whether noun and verb tokens capture instances and their relations; and semantic propagation, via video-to-video attention, which assesses whether instance bindings persist across frames. We find both effects concentrate in a small subset of interaction-dominant layers. Motivated by this, we introduce MATRIX, a simple and effective regularization that aligns attention in specific layers of video DiTs with multi-instance mask tracks from the MATRIX-11K dataset, enhancing both grounding and propagation. We further propose InterGenEval, an evaluation protocol for interaction-aware video generation. In experiments, MATRIX improves both interaction fidelity and semantic alignment while reducing drift and hallucination. Extensive ablations validate our design choices. Codes and weights will be released.

cs.CV↗
arXiv2025

Spatial Stark-Zeeman Systems and Their Regularizations

In this article, we study spatial Stark-Zeeman systems which describe the dynamics of a charged particle moving in three-dimensional space under the influence of a Coulomb potential, a magnetic field, and an electric field, possibly time-dependent. Such systems are modeled by Hamiltonian flows on the cotangent bundle of an open subset of $\mathbb{R}^3, $ equipped with a twisted symplectic structure. The presence of the Coulomb singularity leads to the study of collision orbits, and hence understanding the regularization of these orbits is essential for global dynamical properties. We investigate regularization techniques for spatial Stark-Zeeman systems, both in time-independent and time-dependent cases. In particular, in the time-dependent case, following a new regularization method developed by Barutello, Ortega, and Verzini, we formulate the corresponding regularized variational principles and carefully analyze the effects of magnetic and electric terms under the Kustaanheimo-Stiefel transformation. The resulting regularized action functional yields a variational characterization of collision orbits and facilitates further analysis of periodic solutions. Our results provide a general scheme for regularizing spatial Stark-Zeeman systems, opening the door for further applications in symplectic geometry, Floer theory, and celestial mechanics.

math.DS↗
arXiv2025

A variational approach to time-dependent planar two-center Stark-Zeeman systems

We study periodic orbits in a time-dependent two-center Stark-Zeeman system, which models the motion of a charged particle attracted by two fixed Coulomb centers and subject to external magnetic and time-dependent electric fields. A motivating example is provided by the bicircular restricted four-body problem which investigates the motion of a massless particle, influenced by the Newtonian gravitational attraction of the earth, moon and periodically moving sun. Due to singularities at the Coulomb centers, standard local variational approaches fail. To overcome this, we employ the Birkhoff regularization map and construct a non-local regularized action functional on a blown-up loop space, following a recent method due to Barutello-Ortega-Vernizi \cite{BOV21}. We show that the critical points of this regularized action functional satisfy a certain second-order delay differential equation and correspond to periodic solutions of the original system, including collisions. Additionally, we examine the symmetric structure of the regularized functional.

math.SG↗
arXiv2025

InterRVOS: Interaction-aware Referring Video Object Segmentation

Referring video object segmentation (RVOS) aims to segment objects in a video described by a natural language expression. However, most existing approaches focus on segmenting only the referred object (typically the actor), even when the expression clearly describes an interaction involving multiple objects with distinct roles. For instance, "A throwing B" implies a directional interaction, but standard RVOS segments only the actor (A), neglecting other involved target objects (B). In this paper, we introduce Interaction-aware Referring Video Object Segmentation (InterRVOS), a novel task that focuses on the modeling of interactions. It requires the model to segment the actor and target objects separately, reflecting their asymmetric roles in an interaction. This task formulation enables fine-grained understanding of object relationships, as many video events are defined by such relationships rather than individual objects. To support this task, we propose a new evaluation protocol that separately evaluates actor and target segmentation, enabling more accurate assessment of the model's ability to distinguish and segment actor and target roles. We also present InterRVOS-127K, a large-scale dataset with over 127K automatically annotated expressions, including interaction expressions annotated with distinct masks for actor and target objects. Furthermore, we develop ReVIOSa, an MLLM-based architecture that introduces interaction-aware special tokens and leverages an attention mask loss to enhance role-specific segmentation. Extensive experiments show that ReVIOSa not only outperforms existing baselines on our proposed InterRVOS-127K evaluation set, but also achieves strong performance on standard RVOS benchmarks. Our project page is available at: https://cvlab-kaist.github.io/InterRVOS.

cs.CV↗
arXiv2024

Referring Video Object Segmentation via Language-aligned Track Selection

Referring video object segmentation (RVOS) requires tracking and segmenting an object throughout a video according to a given natural language expression, demanding both complex motion understanding and the alignment of visual representations with language descriptions. Given these challenges, the recently proposed Segment Anything Model 2 (SAM2) emerges as a potential candidate due to its ability to generate coherent segmentation mask tracks across video frames, and provide an inherent spatio-temporal objectness in its object token representations. In this paper, we introduce SOLA (Selection by Object Language Alignment), a novel framework that leverages SAM2 object tokens as compact video-level object representations, which are aligned with language features through a lightweight track selection module. To effectively facilitate this alignment, we propose an IoU-based pseudo-labeling strategy, which bridges the modality gap between SAM2 representations with language features. Extensive experiments show that SOLA achieves state-of-the-art performance on the MeViS dataset and demonstrate that SOLA offers an effective solution for RVOS. Our project page is available at: https://cvlab-kaist.github.io/SOLA.

cs.CV↗
arXiv2024

Multi-Granularity Video Object Segmentation

Current benchmarks for video segmentation are limited to annotating only salient objects (i.e., foreground instances). Despite their impressive architectural designs, previous works trained on these benchmarks have struggled to adapt to real-world scenarios. Thus, developing a new video segmentation dataset aimed at tracking multi-granularity segmentation target in the video scene is necessary. In this work, we aim to generate multi-granularity video segmentation dataset that is annotated for both salient and non-salient masks. To achieve this, we propose a large-scale, densely annotated multi-granularity video object segmentation (MUG-VOS) dataset that includes various types and granularities of mask annotations. We automatically collected a training set that assists in tracking both salient and non-salient objects, and we also curated a human-annotated test set for reliable evaluation. In addition, we present memory-based mask propagation model (MMPM), trained and evaluated on MUG-VOS dataset, which leads to the best performance among the existing video object segmentation methods and Segment SAM-based video segmentation methods. Project page is available at https://cvlab-kaist.github.io/MUG-VOS.

cs.CV↗
arXiv2024

Transverse foliations for two-degree-of-freedom mechanical systems

We investigate the dynamics of a two-degree-of-freedom mechanical system for energies slightly above a critical value. The critical set of the potential function is assumed to contain a finite number of saddle points. As the energy increases across the critical value, a disk-like component of the Hill region gets connected to other components precisely at the saddles. Under certain convexity assumptions on the critical set, we show the existence of a weakly convex foliation in the region of the energy surface where the interesting dynamics takes place. The binding of the foliation is formed by the index-$2$ Lyapunov orbits in the neck region about the rest points and a particular index-$3$ orbit. Among other dynamical implications, the transverse foliation forces the existence of periodic orbits, homoclinics, and heteroclinics to the Lyapunov orbits. We apply the results to the H\'enon-Heiles potential for energies slightly above $1/6$. We also discuss the existence of transverse foliations for decoupled mechanical systems, including the frozen Hill's lunar problem with centrifugal force, the Stark problem, the Euler problem of two centers, and the potential of a chemical reaction.

math.DS↗
arXiv2024

Genus zero transverse foliations for weakly convex Reeb flows on the tight $3$-sphere

A contact form on the tight $3$-sphere $(S^3,ξ_0)$ is called weakly convex if the Conley-Zehnder index of every Reeb orbit is at least $2$. In this article, we study Reeb flows of weakly convex contact forms on $(S^3,ξ_0)$ admitting a prescribed finite set of index-$2$ Reeb orbits, which are all hyperbolic and mutually unlinked. We present conditions so that these index-$2$ orbits are binding orbits of a genus zero transverse foliation whose additional binding orbits have index $3$. In addition, we show in the real-analytic case that the topological entropy of the Reeb flow is positive if the branches of the stable/unstable manifolds of the index-$2$ orbits are mutually non-coincident.

math.SG↗
arXiv2024

Transverse foliations in the rotating Kepler problem

We construct finite energy foliations and transverse foliations of neighbourhoods of the circular orbits in the rotating Kepler problem for all negative energies. This paper would be a first step towards our ultimate goal that is to recover and refine McGehee's results on homoclinics and to establish a theoretical foundation to the numerical demonstration of the existence of a homoclinic-heteroclinic chain in the planar circular restricted three-body problem, using pseudoholomorphic curves.

math.DS↗
arXiv2023

Self-Evolving Neural Radiance Fields

Recently, neural radiance field (NeRF) has shown remarkable performance in novel view synthesis and 3D reconstruction. However, it still requires abundant high-quality images, limiting its applicability in real-world scenarios. To overcome this limitation, recent works have focused on training NeRF only with sparse viewpoints by giving additional regularizations, often called few-shot NeRF. We observe that due to the under-constrained nature of the task, solely using additional regularization is not enough to prevent the model from overfitting to sparse viewpoints. In this paper, we propose a novel framework, dubbed Self-Evolving Neural Radiance Fields (SE-NeRF), that applies a self-training framework to NeRF to address these problems. We formulate few-shot NeRF into a teacher-student framework to guide the network to learn a more robust representation of the scene by training the student with additional pseudo labels generated from the teacher. By distilling ray-level pseudo labels using distinct distillation schemes for reliable and unreliable rays obtained with our novel reliability estimation method, we enable NeRF to learn a more accurate and robust geometry of the 3D scene. We show and evaluate that applying our self-training framework to existing models improves the quality of the rendered images and achieves state-of-the-art performance in multiple settings.

cs.CV↗
arXiv2021

Symmetric periodic orbits and invariant disk-like global surfaces of section on the three-sphere

We study Reeb dynamics on the three-sphere equipped with a tight contact form and an anti-contact involution. We prove the existence of a symmetric periodic orbit and provide necessary and sufficient conditions for it to bound an invariant disk-like global surface of section. We also study the same questions under the presence of additional symmetry and obtain similar results in this case. The proofs make use of pseudoholomorphic curves in symplectizations. As applications, we study Birkhoff's conjecture on disk-like global surfaces of section in the planar circular restricted three-body problem and the existence of symmetric closed Finsler geodesics on the two-sphere. We also present applications to some classical Hamiltonian systems.

math.DS↗
arXiv2021

Equivariant wrapped Floer homology and symmetric periodic Reeb orbits

The aim of this article is to apply a Floer theory to study symmetric periodic Reeb orbits. We define positive equivariant wrapped Floer homology using a (anti-)symplectic involution on a Liouville domain and investigate its algebraic properties. By a careful analysis of index iterations, we obtain a non-trivial lower bound on the minimal number of geometrically distinct symmetric periodic Reeb orbits on a certain class of real contact manifolds. This includes non-degenerate real dynamically convex starshaped hypersurfaces in $\mathbb{R}^{2n}$ which are invariant under complex conjugation. As a result, we give a partial answer to the Seifert conjecture on brake orbits in the contact setting.

math.SG↗
arXiv2020

Remarks on the systoles of symmetric convex hypersurfaces and symplectic capacities

In this note we study the systoles of convex hypersurfaces in $\mathbb{R}^{2n}$ invariant under an anti-symplectic involution. We investigate a uniform upper bound of the ratio between the systole and the symmetric systole of the hypersurfaces using symplectic capacities from Floer theory. We discuss various concrete examples in which the ratio can be understood explicitly.

math.SG↗
arXiv2020

Bifurcations of symmetric periodic orbits via Floer homology

We give criteria for the existence of bifurcations of symmetric periodic orbits in reversible Hamiltonian systems in terms of local equivariant Lagrangian Rabinowitz Floer homology. As an example, we consider the family of the direct circular orbits in the rotating Kepler problem and observe bifurcations of torus-type orbits. Our setup is motivated by numerical work of Hénon on Hill's lunar problem.

math.DS↗
arXiv2019

On families of periodic orbits in the restricted three-body problem

Since Poincaré, periodic orbits have been one of the most important objects in dynamical systems. However, searching them is in general quite difficult. A common way to find them is to construct families of periodic orbits which start at obvious periodic orbits. On the other hand, given two periodic orbits one might ask if they are connected by an orbit cylinder, i.e., by a one-parameter family of periodic orbits. In this article we study this question for a certain class of periodic orbits in the planar circular restricted three-body problem. Our strategy is to compare the Cieliebak-Frauenfelder-van Koert invariants which are obstructions to the existence of an orbit cylinder.

math.DS↗