Lattice Identification and Separation: Theory and Algorithm

Abstract

Motivated by lattice mixture identification and grain boundary detection, we present a framework for lattice pattern representation and comparison, and propose an efficient algorithm for lattice separation. We define new scale and shape descriptors, which helps to reduce the size of equivalence classes of lattice bases considerably. These finitely many equivalence relations are fully characterized by modular group theory. We construct the lattice space L based on the equivalent descriptors and define a metric d L to accurately quantify the visual similarities and differences between lattices. Furthermore, we introduce the Lattice Identification and Separation Algorithm (LISA), which identifies each lattice patterns from superposed lattices. LISA finds lattice candidates from the high responses in the image spectrum, then sequentially extracts different layers of lattice patterns one by one. Analyzing the frequency components, we reveal the intricate dependency of LISA's performances on particle radius, lattice density, and relative translations. Various numerical experiments are designed to show LISA's robustness against a large number of lattice layers, moiré patterns and missing particles.

Pattern‐driven color pattern recognition for printed fabric motif design

“…The fourth and fifth column is the element detection results and the representative design elements T A B L E 1 The average consumption time of the main computational algorithms and the processed image size patterns from real-world design images as a spatial, multitarget tracking, classification, segmentation and association problem using a recently published, efficient color feature description method. 20,27 Compared to existing work, our approach has multiple advantages, including: (a) detecting different unit tiling methods of multicolored printed fabric motif image by using highly plausible lattice points and efficient Belief Propagation algorithms; (b) coupling color feature dimension reduction with grayscale color difference maximization, where the scale invariant color pattern features are grouped and classified by SURF algorithms in an iteration mode; (c) achieving efficient and effective performance than state-of the-art algorithms for fabric color pattern detection, and making full use of fast numerical algorithms and artificial intelligence technologies, such as fuzzy region competition models and convolutional neural networks, to identify the color pattern elements in the fabric motif image and index the similar elements in database; and (d) incorporating higher order color pattern features from the existing design image and generating highly practical element image layers to use the retrieved similar elements from database to synthesize new motif design unit with the same design theme that can be directly used in actual production. These advantages are demonstrated by quantitative experimental results on printed fabric designs.…”

“…The proposed detection method can be used for real‐world fabric images with rotation and deformation conditions. The potential lattice 20 to represent the motif unit is given by: where E is a normalized error function to describe the similarity of the lattice units. ‖⋅‖ 2 is a L 2 norm regularization term.…”

“…The proposed detection method can be used for realworld fabric images with rotation and deformation conditions. The potential lattice 20 to represent the motif unit is given by:…”