A simple toolbox to illustrate how graph wedgelets can be used to sparsely approximate and compress images
Version: 0.3 (01.07.2025)
Written by Wolfgang Erb
This package contains a Matlab implementation for the illustration of graph-based wedgelets in image approximation, compression and segmentation.
Graph wedgelets are a tool for lossy data compression based on the approximation of graph signals by piecewise constant functions on adaptively generated binary wedge partitioning trees (BWP trees) on a graph. Graph wedgelets are discrete variants of continuous wedgelets and binary space partitionings known from image processing. Wedgelet representations of graph signals can be encoded in a simple way by a set of graph nodes and applied easily to the compression and segmentation of graph signals and images. A detailed description of the encoding and decoding of graph signals with wedgelets is given in [1]. An application to image segmentation is presented in [2].
The package contains three main parts
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The main folder contains six example scripts on how to calculate and apply the wedgelet decomposition for images. The package works for RGB images as well as for gray-scale images. In the various examples it is illustrated how graph wedgelets can be used for image approximation and segmentation.
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The subfolder ./core contains the core code of the package for wedgelet encoding and decoding of images.
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The subfolder ./data contains two example images from the BSDS500 dataset and one example from Kaggle.
This code is written for educational purposes and is not optimized for speed nor for optimal data storage.
This code was written by Wolfgang Erb at the Dipartimento di Matematica ''Tullio Levi-Civita'', University of Padova. The corresponding theory related to graph wedgelets and data compression can be found in
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[1] Erb, W.
Graph Wedgelets: Adaptive Data Compression on Graphs based on Binary Wedge Partitioning Trees and Geometric Wavelets. IEEE Trans. Signal Inf. Process. Netw. 9 (2023), 24-34 -
[2] Erb, W.
Split-and-Merge Segmentation of Biomedical Images Using Graph Wedgelet Decompositions. In: Gervasi, O., et al. Computational Science and Its Applications - ICCSA 2025 Workshops, ICCSA 2025, Istanbul, Turkey. Lecture Notes in Computer Science, vol 15899. Springer, Cham (2026), 252-263
Sources for the original images: Berkeley Segmentation Data Set and Benchmarks 500 (BSDS500), Kaggle (https://www.kaggle.com/sartajbhuvaji/brain-tumor-classification-mri/).
This project is funded by the Università degli Studi di Padova - Dipartimento di Matematica under the project SID BIRD 2023 entitled "ALISIA-ALgorithms for Immersive Stereoscopic Imaging with Applications to the Daedalus camera system", and by the European Union-NextGenerationEU under the National Recovery and Resilience Plan (NRRP), Mission 4 Component 2 Investment 1.1-Call PRIN 2022 No. 104 of February 2, 2022 of Italian Ministry of University and Research; Project 2022FHCNY3 (subject area: PE-Physical Sciences and Engineering) "Computational mEthods for Medical Imaging (CEMI)".
Copyright (C) 2021, 2025 Wolfgang Erb
GraphWedgelets is free software: you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version.
This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.
You should have received a copy of the GNU General Public License along with this program. If not, see http://www.gnu.org/licenses/.