Numerical Analysis of Diagonal-Preserving, Ripple-Minimizing and Low-Pass Image Resampling Methods

Chantal Racette

Home/Archive/arXiv

arXiv · 1204.4734

Numerical Analysis of Diagonal-Preserving, Ripple-Minimizing and Low-Pass Image Resampling Methods

Chantal Racette

View original source ↗Read source document ↗Export metadata ↓

Abstract

Image resampling is a necessary component of any operation that changes the size of an image or its geometry. Methods tuned for natural image upsampling (roughly speaking, image enlargement) are analyzed and developed with a focus on their ability to preserve diagonal features and suppress overshoots. Monotone, locally bounded and almost monotone "direct" interpolation and filtering methods, as well as face split and vertex split surface subdivision methods, alone or in combination, are studied. Key properties are established by way of proofs and counterexamples as well as numerical experiments involving 1D curve and 2D diagonal data resampling. In addition, the Remez minimax method for the computation of low-cost polynomial approximations of low-pass filter kernels tuned for natural image downsampling (roughly speaking, image reduction) is refactored for relative error minimization in the presence of roots in the interior of the interval of approximation and so that even and odd functions are approximated with like polynomials. The accuracy and frequency response of the approximations are tabulated and plotted against the original, establishing their rapid convergence.

Explore related subjects

cs.GR

Keep this discovery

BibTeX RIS

Chantal Racette. 2012-04-20. Numerical Analysis of Diagonal-Preserving, Ripple-Minimizing and Low-Pass Image Resampling Methods. https://arxiv.org/abs/1204.4734

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

KEEP EXPLORING

Related papers

arXiv2026

ReCHOIR: Contact-guided Human Object Interaction Retargeting to Diverse Characters

We present ReCHOIR, a novel contact-guided motion retargeting method for transferring human object interaction (HOI) motions across diverse humanoid characters. Unlike prior motion retargeting methods that primarily focus on transferring human motion alone, our goal is to preserve not only the semantics of the original body movement but also consistent interaction between the character and the manipulated object, while jointly producing aligned target human and object motions. Given source HOI motion, object geometry, and contact cues extracted from the source interaction, ReCHOIR retargets an HOI sequence to target characters with different skeletal configurations while maintaining both motion semantics and contact-consistent interaction patterns. Our method builds on a Part-Aware Motion Embedding (PAME) autoencoder, which encodes full-body motion into a shared body-part-wise latent space. This representation enables generalization across heterogeneous skeletons while preserving local motion semantics beneficial for part-aware adaptation in HOI retargeting. On top of this representation, we introduce a contact-guided retargeting module and an object motion decoder for HOI retargeting. The contact-guided retargeting module treats the source object interaction as a condition for refining target character motion: object- and contact-related signals are encoded into a body-part-aligned latent representation and injected into decoding through a residual control branch, enabling stronger adaptation in interaction-relevant body regions without discarding the underlying motion prior. In parallel, the object motion decoder predicts a target object motion aligned with the refined target character motion, ensuring that the object trajectory remains consistent with how the interaction is realized by the target character.

cs.GR↗

arXiv2026

Gaussian Light Transport

We present a novel method for computing global illumination by expressing the solution to the light transport equation as a 13D Gaussian mixture model over positions, directions, surface normals, and material properties. We show that including scene properties in the Gaussian representation drastically reduces the number of functions and speeds up evaluation. As opposed to traditional light transport methods based on Neumann series, the parameters of our model are directly estimated by minimizing the residual of the rendering equation. While both optimization and rendering require repeated evaluations of a linear combination of high-dimensional Gaussian functions, we introduce an efficient culling strategy to keep the optimization tractable and produce renderings in real time. Our representation enables to render fast, view-independent solutions to the light transport equation, achieving rendering times on the order of milliseconds, with a fraction of the memory requirements of conventional neural rendering approaches.

cs.GR↗

arXiv2026

Hologram Representation via Quadratic Phase Gaussian Splatting

We introduce Complex-Valued Quadratic Phase Gaussian (CVQPG), a novel hologram representation method that replaces standard 2D Gaussian representations used in 2D Gaussian Splatting with 2D quadratic phase functions. CVQPG incorporates additional learnable parameters to control the curvature of these bases. We evaluate our approach against state-of-the-art methods, exceeding the visual quality by +0.19 dB (RGB) and +0.33 dB (grayscale) on average in holographic reconstructions. Specifically, our equal parameter count evaluations show that modulating the primitive's wavefront is an effective and lightweight enhancement for hologram representations. In addition, our frequency domain analysis illustrates that CVQPG has successfully preserved the mid-to-high frequency band of natural images.

cs.GR↗