Laplacian Coordinates: Theory and Methods for Seeded Image Segmentation

Autor(es)

Casaca, Wallace ^[1] ; Gois, Joao Paulo ^[2] ; Batagelo, Harlen Costa ^[2] ; Taubin, Gabriel ^[3] ; Nonato, Luis Gustavo ^[4]

Afiliação do(s) autor(es)

^[1] Sao Paulo State Univ UNESP, Dept Energy Engn, BR-01049010 Rosana - Brazil

^[2] Fed Univ ABC UFABC, Ctr Math Comp & Cognit, BR-09210580 Santo Andr e - Brazil

^[3] Brown Univ, Sch Engn, Providence, RI 02912 - USA

^[4] Univ Sao Paulo, ICMC, BR-13566590 Sao Carlos - Brazil

• Tipo de documento: Artigo Científico
• Fonte: IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE; v. 43, n. 8, p. 2665-2681, AUG 1 2021.
• Citações Web of Science: 2

Resumo

Seeded segmentation methods have gained a lot of attention due to their good performance in fragmenting complex images, easy usability and synergism with graph-based representations. These methods usually rely on sophisticated computational tools whose performance strongly depends on how good the training data reflect a sought image pattern. Moreover, poor adherence to the image contours, lack of unique solution, and high computational cost are other common issues present in most seeded segmentation methods. In this work we introduce Laplacian Coordinates, a quadratic energy minimization framework that tackles the issues above in an effective and mathematically sound manner. The proposed formulation builds upon graph Laplacian operators, quadratic energy functions, and fast minimization schemes to produce highly accurate segmentations. Moreover, the presented energy functions are not prone to local minima, i.e., the solution is guaranteed to be globally optimal, a trait not present in most image segmentation methods. Another key property is that the minimization procedure leads to a constrained sparse linear system of equations, enabling the segmentation of high-resolution images at interactive rates. The effectiveness of Laplacian Coordinates is attested by a comprehensive set of comparisons involving nine state-of-the-art methods and several benchmarks extensively used in the image segmentation literature. (AU)

• Processo FAPESP: 13/07375-0 - CeMEAI - Centro de Ciências Matemáticas Aplicadas à Indústria
• Beneficiário: Francisco Louzada Neto
• Modalidade de apoio: Auxílio à Pesquisa - Centros de Pesquisa, Inovação e Difusão - CEPIDs
• Processo FAPESP: 14/16857-0 - Segmentação interativa de imagens digitais e rearranjo de layouts visuais via minimização de funcionais de energia em grafos
• Beneficiário: Wallace Correa de Oliveira Casaca
• Modalidade de apoio: Bolsas no Brasil - Pós-Doutorado
• Processo FAPESP: 16/04391-2 - Operadores de morfologia matemática para a análise visual de dados urbanos
• Beneficiário: Fábio Augusto Salve Dias
• Modalidade de apoio: Bolsas no Exterior - Estágio de Pesquisa - Pós-Doutorado