Energy-Based Optimization for Video Shot Assembly

• The paper introduces a hybrid optimization framework combining genetic algorithms and Langevin-like methods to minimize a global energy function for shot sequencing.
• It decomposes the energy function into shot-size, camera-motion, and semantic alignment terms, aligning automated shot assembly with human cinematic principles.
• Empirical evaluations show that the method outperforms conventional approaches in replicating narrative coherence and stylistic continuity in video editing.

Energy-based optimization for video shot assembly defines a theoretical and practical foundation for automated sequencing of shots in cinematic video editing, leveraging energy models to encode both stylistic and semantic constraints. This approach replaces exclusively manual shot arrangement with computational methods that formalize editing syntax, narrative alignment, and artistic reference, optimizing for both human-like continuity and narrative logic.

1. Problem Definition and Theoretical Framework

Energy-based optimization for shot assembly formalizes the task as the selection and sequencing of $K$ shots $S = (s_1,\ldots,s_K)$ from a repository $V$ of $N$ total candidate shots ($s_k$ drawn without replacement). The objective is to assemble $S$ that minimizes a global energy function capturing both filmic syntax and semantic alignment.

This methodology models essential cinematic properties—such as shot-size and camera-motion syntax, as well as semantic correspondence to a textual script—as distinct energy terms. The overall energy is given as a weighted sum:

$$E^J(S) = \alpha\,E^G(S) + \beta\,E^M(S) + \gamma\,E^{Se}(S)$$

where $E^G$ encodes shot-size syntax, $E^M$ encodes camera-motion syntax, and $E^{Se}$ encodes semantic alignment, with $\alpha, \beta, \gamma \geq 0$ and typically $\alpha+\beta+\gamma=1$ or set by cross-validation (Chen et al., 4 Nov 2025).

Selection constraints are imposed to guarantee that each position in the output is filled exactly once by a unique shot.

2. Component Energy Functions and Cinematic Syntax

2.1 Shot-Size Syntax Energy

Each shot is categorized into one of $M=5$ types: $$\{ \texttt{ELS}, \texttt{LS}, \texttt{MS}, \texttt{CU}, \texttt{ECU} \}$$. The transition dynamics of shot size are described by a learned or hand-designed transition score matrix $G \in \mathbb{R}^{M \times M}$, where $G_{ij}$ quantifies the preference for transitioning from size $i$ to $j$. The total syntax score over a sequence $S$ is:

$$\text{Score}^G(S) = \sum_{k=1}^{K-1} G_{t_{s_k}, t_{s_{k+1}}}$$

The corresponding energy is defined as $E^G(S) = -\text{Score}^G(S)$.

2.2 Camera-Motion Syntax Energy

Analogous to shot size, each shot has a motion label in $$\{\texttt{Stable}, \texttt{Up}, \texttt{Down}, \texttt{Left}, \texttt{Right}, \texttt{Out}, \texttt{In}\}$$. With a motion transition matrix $M \in \mathbb{R}^{L \times L}$, the energy is similarly defined:

$$\text{Score}^M(S) = \sum_{k=1}^{K-1} M_{m_{s_k}, m_{s_{k+1}}}$$

$E^M(S) = -\text{Score}^M(S)$

2.3 Semantic-Alignment Energy

A LLM-generated script $T_\text{text}$ defines the narrative intent. Each shot $s_k$ receives a caption $d_k$ (via automatic image captioning or manual annotation). Using CLIP text encoders, we compute:

$E^{Se}(S) = -\cos\_\text{sim}( D,\,T_\text{text} )$

where $D = (d_1, ..., d_K)$ and $\cos_\text{sim}$ is cosine similarity in embedding space. This term anchors shot selection to semantic script relevance.

2.4 Joint Energy and Constraints

The three energy terms are linearly combined, and a binary matrix $X \in \{0,1\}^{N \times K}$ encodes assignment of library shots to sequence positions, subject to:

$$\sum_{i=1}^N X_{i,k} = 1 \ \forall k;\qquad \sum_{k=1}^K X_{i,k} \leq 1 \ \forall i$$

3. Optimization Algorithms: Hybrid Discrete Approaches

The joint minimization $S^* = \arg\min_S E^J(S)$ is a combinatorial problem (over all $K$-permutations of $N$). To address both local minima and discrete assignment, the solution employs a hybrid of genetic algorithms (GA) and discrete Langevin-like methods.

Hybrid Algorithm Structure

• Population Initialization: Randomly generate $P$ candidate sequences.
• Langevin-like Local Refinement: For each candidate, propose local swaps and accept moves by deterministic improvement or stochastically (with probability $\exp(-\Delta E/(\epsilon T))$ for energy-increasing moves).
• GA Operations: Fitness is defined as $F(S) = -E^J(S)$. Parenting via softmax selection, followed by crossover and mutation, forms the new population.
• Convergence: The algorithm typically converges within $\sim100$–$200$ iterations for $N \leq 50$, $K \leq 7$, with each iteration costing $O(P K^2)$ (Chen et al., 4 Nov 2025).

Comparative Optimization Results

Ablation experiments demonstrate that the hybrid ("Langevin+GA") approach achieves 100% global optimum recovery for "10 choose 7" shot selection cases, outperforming pure Beam Search, pure GA, or continuous relaxations ($<$60% for the latter).

4. Instance Preparation: Visual-Semantic Matching and Label Extraction

4.1 Script and Candidate Shot Retrieval

• Script Generation: An LLM (e.g., GPT-3.5) produces a narrative script.
• Visual Embedding: All repository shots $v_i$ are embedded with CLIP.
• Candidate Pooling: Compute similarity between shot captions or visual features and script, select top $K_c$ candidates, forming the pool $R$.

4.2 Shot Segmentation and Labeling

• Segmentation: Reference videos are segmented by detecting hard cuts through histogram-difference thresholding and dissolves.
• Shot Attributes:
  • Shot size by CNN classification across frames; majority class forms shot label.
  • Camera motion via optical-flow heuristics or ResNet classifier.
  • Semantic captioning with image-captioning models (e.g., BLIP).
• Transition Statistics: For reference videos, empirical transition matrices $G$, $M$ are built by counting shot-size and -motion transitions.

5. Cinematic Editing Syntax and Integration into the Energy Model

Cinematic editing is governed by continuity principles:

• Large shot-size jumps (e.g., ELS$\to$ECU) are avoided (zero or strongly penalized).
• Gradual shot progression (e.g., LS$\to$MS$\to$CU) is preferred.
• Camera motion transitions maintain directional continuity.

These are injected as high values or zeros in $G$, $M$ matrices and thus directly determine the energy surface—infeasible transitions acquire maximal energy and are minimized against.

No further hard constraints are imposed beyond unique selection, but illegal transitions automatically have low probability due to their impact on $E^J(S)$.

6. Experimental Evaluation and Comparative Analysis

Subjective and objective evaluations benchmark energy-based shot assembly against four baselines:

6.1 Subjective Evaluations

Thirty expert graders evaluated outputs on two reference videos (sitcom, food clip) on:

• Semantic Matching Score (SMC)
• Camera Motion Similarity (CMS)
• Shot Size Similarity (SSS)
• Overall Style Similarity (OSS)

Method	Ref1: SMC	CMS	SSS	OSS	Ref2: SMC	CMS	SSS	OSS
ESA (Ours)	3.52	3.10	2.48	2.62	3.29	3.38	3.10	3.10
MoneyPrinterTurbo	3.19	2.57	2.05	2.19	1.62	2.17	2.29	1.91
MoneyPrinterTurboClip	3.38	2.91	2.19	2.38	2.62	2.81	2.67	2.57
CapCut	2.33	2.29	1.95	1.95	2.81	2.64	2.86	2.67
JichuangAI	2.52	2.43	1.95	2.00	1.71	2.74	2.62	2.43

ESA attains the highest mean scores, indicating closer style emulation and semantic coherence.

6.2 Objective Measures

Objective metrics are provided by transition-matrix mean-squared error (MSE) against the reference's ground-truth transitions:

Method	Ref1 M_MSE	S_MSE	Ref2 M_MSE	S_MSE
ESA (Ours)	0.048	0.055	0.021	0.079
MoneyPrinterTurbo	0.059	0.174	0.066	0.101
CapCut	0.064	0.201	0.031	0.105
JichuangAI	0.055	0.121	0.029	0.123

ESA offers the lowest transition-matrix errors, confirming objective replication of editing pace and visual grammar.

6.3 Optimization Convergence

Empirical convergence is rapid: for libraries up to $N=50$, $K=7$, hybrid optimization reaches the global minimum typically within 100–200 iterations.

7. Distinctions from Other Energy-based Video Optimization Methods

While energy-based optimization for shot assembly in ESA (Chen et al., 4 Nov 2025) is primarily oriented toward narrative- and style-coherent assembly from heterogeneous shot libraries, related methods (e.g., EditIQ (Girmaji et al., 4 Feb 2025), GAZED (Moorthy et al., 2020), ILS-SUMM (Shemer et al., 2019)) address somewhat different instantiations by varying the definitions of unary and pairwise energies, candidate space construction, and constraints. For example:

• EditIQ and GAZED employ dynamic programming over framewise shot choices in virtually generated rushes for static-camera stage recordings, using dialogue, saliency, or gaze cues.
• ILS-SUMM frames video summarization as a constrained $k$-median/knapsack energy minimization.

The shared core across these methods is the decomposition of global energy into interpretable unary (shot or synopsis potential) and pairwise (transition, rhythm, overlap) terms, enabling direct modeling of cinematic conventions and semantic objectives.

8. Significance, Limitations, and Practical Implications

Energy-based optimization for shot assembly realizes the capacity to reassemble video in a manner both semantically faithful and stylistically aligned with human-edited references. It enables creators, regardless of domain expertise, to synthesize visually and narratively coherent video from found footage or heterogeneous source libraries.

Key implications:

• Modular energy terms allow for extension to new syntax conventions or domain-specific constraints.
• Demonstrated superiority in both subjective human evaluation and objective style-matching versus LLM-driven or template-based alternatives.
• The discrete, hybrid optimization is empirically necessary; relaxation-based solvers fail on high-dimensional permutation constraints.
• Practical runtimes and empirical convergence support application in editorial pipelines for short-to-medium-length video with moderate shot library sizes.

A plausible implication is that this paradigm can substantially lower the barrier to high-quality, stylistically controlled video editing, while remaining modifiable for future inclusion of further syntactic or semantic rules. However, the approach relies on the availability and quality of labeled reference material and the validity of automated captioning and embedding techniques. Misalignment or biases in these upstream modules may constrain output expressivity or style fidelity.