Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · 2201.00877

Gaussian-Hermite Moment Invariants of General Multi-Channel Functions

Hanlin Mo·Hua Li·Guoying Zhao
View original source ↗Read source document ↗Export metadata ↓

Abstract

With the development of data acquisition technology, large amounts of multi-channel data are collected and widely used in many fields. Most of them, such as RGB images and vector fields, can be expressed as different types of multi-channel functions. Feature extraction of multi-channel data for identifying interest patterns is a critical but challenging task. This paper focuses on constructing moment-based features of general multi-channel functions. Specifically, we define two transform models, rotation-affine transform and total rotation transform, to describe real deformations of multi-channel data. Then, we design a structural framework to generate Gaussian-Hermite moment invariants for these two transform models systematically. It is the first time that a unified framework has been proposed in the literature to construct orthogonal moment invariants of general multi-channel functions. Given a specific type of multi-channel data, we demonstrate how to utilize the new method to derive all possible invariants and eliminate dependences among them. We obtain independent sets of invariants with low orders and low degrees for RGB images, 2D vector fields and color volume data. Based on synthetic and real multi-channel data, we conduct extensive experiments to evaluate the stability and discriminability of these invariants and their robustness to noise. The results show that new moment invariants significantly outperform previous moment invariants of multi-channel data in RGB image classification and vortex detection in 2D vector fields.

Explore related subjects

cs.CV

Keep this discovery

BibTeXRIS

Hanlin Mo, Hua Li, Guoying Zhao. 2022-01-03. Gaussian-Hermite Moment Invariants of General Multi-Channel Functions. https://arxiv.org/abs/2201.00877

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

HiPerViT: A Hierarchical Perceiver-Vision Transformer Architecture for Multi-Scale Texture Recognition

Texture recognition remains challenging for modern vision models because discriminative evidence is often carried by higher-order spatial statistics rather than by object shape alone. While Vision Transformers provide strong long-range modeling capacity, their standard object-centric representations do not explicitly expose such statistical structure, which limits texture sensitivity in fine-grained recognition settings. We present HiPerViT, a compact vision-only architecture that injects an explicit second-order statistical prior into a transformer-based recognition pipeline. The method combines global and local image views with a compact bilinear descriptor encoded as a statistical token, and integrates this token with first-order spatial representations through Perceiver-style latent distillation. This design enables direct interaction between spatial tokens and second-order feature co-occurrence statistics, providing the model with explicit access to texture-relevant information without requiring multimodal pretraining or ensemble construction. Across six texture recognition benchmarks, HiPerViT achieves consistent improvements over strong vision-only baselines under the reported evaluation protocols, including gains of +3.05 percentage points on DTD, +10.48 on GTOS-Mobile, and +10.10 on 1200Tex. Beyond benchmark performance, our analyses show that these gains are largely invariant to the backbone depth used to extract second-order statistics and to the ordering of interaction and distillation stages. This pattern suggests that the primary source of improvement is not a specific fusion topology, but the explicit availability of second-order statistical information as a first-class representational signal. These results support explicit statistical tokenization as an effective and robust design principle for texture-centric visual recognition.

cs.CV↗
arXiv2026

CamPilot: A Multi-Agent Cinematic Assistant for Camera-Controlled Movie Generation

The integration of large language models (LLMs) into video generation has enabled rapid text-to-video creation and improved visual quality. However, it still falls short of professional filmmaking, where cinematographic language is less refined than human-crafted camera work and multi-shot continuity remains challenging. To address these limitations, we introduce CamPilot, a multi-agent framework that integrates cinematographic planning and camera-work control to produce more coherent, logically structured, and human-aesthetic movies. CamPilot adopts a GRPO-based learning paradigm to learn camera work planning from 14K real-world professional movies, internalizing motion patterns and composition principles that support reasoning over shooting techniques (e.g., camera angle, motion, and focal behavior) and cross-shot relationships for controllable camera-viewpoint generation. Multiple agents further collaborate and evolve to improve overall output quality. To support this work and further studies in this domain, we establish CamEval, a benchmark for evaluating camera work quality and cinematic engagement. Empirical results show that CamPilot outperforms state-of-the-art text-to-movie generation methods on cinematographic control and quality, highlighting the impact of professional camera design on movie generation.

cs.CV↗
arXiv2026

New Evidence, Same Choice: Testing Physical Experiment Selection in Vision Language Models

A model first sees an image from one physical measurement experiment, such as how far a block coasted, and must answer a question about a new trial, such as whether the block will pass a target after a fixed push. The initial experiment may provide enough information to answer, or the model may need another measurement, such as the object's mass, friction, restitution, or spring stiffness. We study whether vision language models can decide when to answer immediately and, when more evidence is needed, which experiment to perform. Current physical reasoning benchmarks usually evaluate only the final answer, so they do not directly measure this decision-making ability. We introduce a controlled evaluation where each problem provides one measurement image and four possible physical worlds created by combining two possible masses and two possible values of another relevant property. The model must either stop and answer or select the cheapest additional experiment that can resolve the question. We construct matched problem pairs where changing either the observed measurement or the question changes the optimal action. Since all possible worlds and experiment costs are known, we can explicitly determine the optimal choice. Across six open models and 144 physical parameter sets, direct responses repeat the same action for 95.1% to 100% of image pairs even when the correct action changes. Brief reasoning improves action switching, but the best model makes both decisions correctly for only 5.9% of image pairs. Additional analysis reveals failures in measurement interpretation, physical reasoning, and response formatting. By evaluating evidence selection separately from final answers, our benchmark reveals limitations in physical reasoning that conventional answer accuracy can overlook.

cs.CV↗