Title: “FlowVid: A Consistent Video-to-Video Synthesis Framework with Spatial Conditions

Title: “FlowVid: A Consistent Video-to-Video Synthesis Framework with Spatial Conditions

Diffusion models have transformed the image-to-image (I2I) synthesis and are
now permeating into videos. However, the advancement of video-to-video (V2V)
synthesis has been hampered by the challenge of maintaining temporal
consistency across video frames. This paper proposes a consistent V2V synthesis
framework by jointly leveraging spatial conditions and temporal optical flow
clues within the source video. Contrary to prior methods that strictly adhere
to optical flow, our approach harnesses its benefits while handling the
imperfection in flow estimation. We encode the optical flow via warping from
the first frame and serve it as a supplementary reference in the diffusion
model. This enables our model for video synthesis by editing the first frame
with any prevalent I2I models and then propagating edits to successive frames.
Our V2V model, FlowVid, demonstrates remarkable properties: (1) Flexibility:
FlowVid works seamlessly with existing I2I models, facilitating various
modifications, including stylization, object swaps, and local edits. (2)
Efficiency: Generation of a 4-second video with 30 FPS and 512×512 resolution
takes only 1.5 minutes, which is 3.1x, 7.2x, and 10.5x faster than CoDeF,
Rerender, and TokenFlow, respectively. (3) High-quality: In user studies, our
FlowVid is preferred 45.7% of the time, outperforming CoDeF (3.5%), Rerender
(10.2%), and TokenFlow (40.4%).

Analysis of Video-to-Video Synthesis Framework

The content discusses the challenges in video-to-video (V2V) synthesis and introduces a novel framework called FlowVid that addresses these challenges. The key issue in V2V synthesis is maintaining temporal consistency across video frames, which is crucial for creating realistic and coherent videos.

FlowVid tackles this challenge by leveraging both spatial conditions and temporal optical flow clues within the source video. Unlike previous methods that rely solely on optical flow, FlowVid takes into account the imperfection in flow estimation and encodes the optical flow by warping from the first frame. This encoded flow serves as a supplementary reference in the diffusion model, enabling the synthesis of videos by propagating edits made to the first frame to successive frames.

One notable aspect of FlowVid is its multi-disciplinary nature, as it combines concepts from various fields including computer vision, image synthesis, and machine learning. The framework integrates techniques from image-to-image (I2I) synthesis and extends them to videos, showcasing the potential synergy between these subfields of multimedia information systems.

In the wider field of multimedia information systems, video synthesis plays a critical role in applications such as visual effects, virtual reality, and video editing. FlowVid’s ability to seamlessly work with existing I2I models allows for various modifications, including stylization, object swaps, and local edits. This makes it a valuable tool for artists, filmmakers, and content creators who rely on video editing and manipulation techniques to achieve their desired visual results.

Furthermore, FlowVid demonstrates efficiency in video generation, with a 4-second video at 30 frames per second and 512×512 resolution taking only 1.5 minutes. This speed is significantly faster compared to existing methods such as CoDeF, Rerender, and TokenFlow, highlighting the potential impact of FlowVid in accelerating video synthesis workflows.

The high-quality results achieved by FlowVid, as evidenced by user studies where it was preferred 45.7% of the time over competing methods, validate the effectiveness of the proposed framework. This indicates that FlowVid successfully addresses the challenge of maintaining temporal consistency in V2V synthesis, resulting in visually pleasing and realistic videos.

In conclusion, the video-to-video synthesis framework presented in the content, FlowVid, brings together concepts from various disciplines to overcome the challenge of temporal consistency. Its integration of spatial conditions and optical flow clues demonstrates the potential for advancing video synthesis techniques. Additionally, its relevance to multimedia information systems, animations, artificial reality, augmented reality, and virtual realities highlights its applicability in diverse industries and creative endeavors.

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Exploring Combinatorial Problems with Wires and Swaps

Exploring Combinatorial Problems with Wires and Swaps

Introduction: Exploring the Complexity of Combinatorial Problems with Wires and Swaps

In this article, we delve into the intricacies of a combinatorial problem involving y-monotone wires. The problem revolves around the concept of a tangle, which determines the order of wires on different horizontal layers. The orders can only differ through swaps of neighboring wires. Our main focus is on two related problems: List-Feasibility and Tangle-Height Minimization.

List-Feasibility seeks to find a tangle that realizes a given list of swaps, while Tangle-Height Minimization looks to minimize the number of layers used by the tangle. These problems have been proven to be NP-hard, making them highly challenging to solve.

However, our research takes a step further by showing that List-Feasibility remains NP-hard even when each pair of wires swaps only a constant number of times. On a positive note, we present an algorithm for Tangle-Height Minimization that calculates an optimal tangle for $n$ wires and a given list of swaps in efficient time.

By leveraging this algorithm, we are able to derive a simplified and faster version to solve List-Feasibility. In addition, we demonstrate that List-Feasibility is in NP and fixed-parameter tractable with respect to the number of wires.

We also tackle a specific type of list called “simple” lists, where each swap occurs at most once. For such lists, we showcase an algorithm that solves Tangle-Height Minimization in faster time.

Abstract:We study the following combinatorial problem. Given a set of $n$ y-monotone emph{wires}, a emph{tangle} determines the order of the wires on a number of horizontal emph{layers} such that the orders of the wires on any two consecutive layers differ only in swaps of neighboring wires. Given a multiset~$L$ of emph{swaps} (that is, unordered pairs of wires) and an initial order of the wires, a tangle emph{realizes}~$L$ if each pair of wires changes its order exactly as many times as specified by~$L$. textsc{List-Feasibility} is the problem of finding a tangle that realizes a given list~$L$ if such a tangle exists. textsc{Tangle-Height Minimization} is the problem of finding a tangle that realizes a given list and additionally uses the minimum number of layers. textsc{List-Feasibility} (and therefore textsc{Tangle-Height Minimization}) is NP-hard [Yamanaka, Horiyama, Uno, Wasa; CCCG 2018].

We prove that textsc{List-Feasibility} remains NP-hard if every pair of wires swaps only a constant number of times. On the positive side, we present an algorithm for textsc{Tangle-Height Minimization} that computes an optimal tangle for $n$ wires and a given list~$L$ of swaps in $O((2|L|/n^2+1)^{n^2/2} cdot varphi^n cdot n)$ time, where $varphi approx 1.618$ is the golden ratio and $|L|$ is the total number of swaps in~$L$. From this algorithm, we derive a simpler and faster version to solve textsc{List-Feasibility}. We also use the algorithm to show that textsc{List-Feasibility} is in NP and fixed-parameter tractable with respect to the number of wires. For emph{simple} lists, where every swap occurs at most once, we show how to solve textsc{Tangle-Height Minimization} in $O(n!varphi^n)$ time.

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