We prove several variations on the results in Ricci and Travaglini[RT] concerning L−L ′ bounds for convolution with all rotations of a measure supported by a fixed convex curve in R. Estimates are obtained for averages over higherdimensional convex (nonsmooth) hypersurfaces, smooth k-dimensional surfaces, and nontranslation-invariant families of surfaces. We compare the approach of [RT], based ...

The purpose of this paper is to study the boundedness in the context of Triebel-Lizorkin spaces for some multilinear operators related to certain convolution operators. The operators include Littlewood-Paley operator, Marcinkiewicz integral, and Bochner-Riesz operator. 1. Introduction. Let T be a Calderon-Zygmund operator. A well-known result of Coif-man et al. [6] states that the commutator [b...

Line integral convolution (LIC) has become a well-known and popular method for visualizing vector elds. The method works by convolving a random input texture along the integral curves of the vector eld. In order to accelerate image synthesis signiicantly, an eecient algorithm has been proposed that utilizes pixel coherence in eld line direction. This algorithm, called \fast LIC", originally was...

This paper presents a new visualization technique for flow fields in 2D. It utilizes a physical model of smearing ink over a sheet of paper as an intuitive metaphor for the representation of a dynamical system. This technique is capable of producing images that are comparable to those generated with line integral convolution (LIC), which is a well-known and established visualization technique f...

This paper proposes an extension to the existing automatic pencil drawing generation technique based on Line Integral Convolution (LIC). The original LIC pencil filter utilizes image segmentation and texture direction detection techniques for defining outlines and stroke directions, and the quality of a resulting image depends largely on the result of the white noises and the texture directions...