Graph-based approaches have recently seen a spike of interest in the image processing and computer vision communities, and many classical problems are finding new solutions thanks to these techniques. The Graph Fourier Transform (GFT), the equivalent of the Fourier transform for graph signals, is used in many domains to analyze and process data modeled by a graph. In this thesis we present some classical image processing problems that can be solved through the use of GFT. We'll focus our attention on two main research area: the first is image compression, where the use of the GFT is finding its way in recent literature; we'll propose two novel ways to deal with the problem of graph weight encoding. We'll also propose approaches to reduce overhead costs of shape-adaptive compression methods. The second research field is image anomaly detection, GFT has never been proposed to this date to solve this class of problems; we'll discuss here a novel technique and we'll test its application on hyperspectral and medical images. We'll show how graph approaches can be used to generalize and improve performance of the widely popular RX Detector, by reducing its computational complexity while at the same time fixing the well known problem of its dependency from covariance matrix estimation and inversion. All our experiments confirm that graph-based approaches leveraging on the GFT can be a viable option to solve tasks in multiple image processing domains.

The use of Graph Fourier Transform in image processing: A new solution to classical problems

VERDOJA, FRANCESCO
2017

Abstract

Graph-based approaches have recently seen a spike of interest in the image processing and computer vision communities, and many classical problems are finding new solutions thanks to these techniques. The Graph Fourier Transform (GFT), the equivalent of the Fourier transform for graph signals, is used in many domains to analyze and process data modeled by a graph. In this thesis we present some classical image processing problems that can be solved through the use of GFT. We'll focus our attention on two main research area: the first is image compression, where the use of the GFT is finding its way in recent literature; we'll propose two novel ways to deal with the problem of graph weight encoding. We'll also propose approaches to reduce overhead costs of shape-adaptive compression methods. The second research field is image anomaly detection, GFT has never been proposed to this date to solve this class of problems; we'll discuss here a novel technique and we'll test its application on hyperspectral and medical images. We'll show how graph approaches can be used to generalize and improve performance of the widely popular RX Detector, by reducing its computational complexity while at the same time fixing the well known problem of its dependency from covariance matrix estimation and inversion. All our experiments confirm that graph-based approaches leveraging on the GFT can be a viable option to solve tasks in multiple image processing domains.
https://www.researchgate.net/publication/317662348_The_use_of_Graph_Fourier_Transform_in_image_processing_a_new_solution_to_classical_problems
Verdoja, Francesco
File in questo prodotto:
File Dimensione Formato  
PhdThesis_Verdoja.pdf

Accesso aperto

Tipo di file: POSTPRINT (VERSIONE FINALE DELL’AUTORE)
Dimensione 8.98 MB
Formato Adobe PDF
8.98 MB Adobe PDF Visualizza/Apri

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2318/1645345
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus ND
  • ???jsp.display-item.citation.isi??? ND
social impact