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J. Imaging
Special Issues
Mathematical and Computational Methods in Image Processing
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Mathematical and Computational Methods in Image Processing

A special issue of Journal of Imaging (ISSN 2313-433X).

Deadline for manuscript submissions: closed (25 January 2019)

Special Issue Editor

Prof. Dr. Vasudevan (Vengu) Lakshminarayanan

E-Mail Website
Guest Editor
Theoretical and Experimental Epistemology Laboratory, University of Waterloo, Waterloo, ON N2J 4A8, Canada
Interests: vision science; physics; ECE and systems design engineering; optics and photonics; including mathematical methods; waveguides and fiber optics; image processing; biomedical optics; deep learning/machine learning in ophthalmic diagnosis
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

There have been tremendous advances in image processing algorithms over the past few years.  New mathematical and computational techniques have been employed to analyze and process images in a form suitable for analysis. Some of these techniques include graph theoretical methods, dynamic programming for optimization, fuzzy set theory, super resolution methods, and so on. These techniques have found a myriad of applications, especially in the area of biomedical imaging. In addition, an emerging area is the development of deep learning/neural network methods (especially unsupervised learning techniques) for biomedical image analysis and classification. This Special Issue welcomes submissions in all areas of image processing with a special emphasis on innovative mathematical/computational methods and algorithms.

Prof. Vasudevan Lakshminarayanan
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Journal of Imaging is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 1800 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • Image processing
  • Deep learning
  • Biomedical images
  • Image segmentation
  • Noise reduction
  • Optimization
  • Mathematical methods

Published Papers (2 papers)

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Research

16 pages, 1187 KiB  
Article
PixelBNN: Augmenting the PixelCNN with Batch Normalization and the Presentation of a Fast Architecture for Retinal Vessel Segmentation
by Henry A. Leopold, Jeff Orchard, John S. Zelek and Vasudevan Lakshminarayanan
J. Imaging 2019, 5(2), 26; https://0-doi-org.brum.beds.ac.uk/10.3390/jimaging5020026 - 02 Feb 2019
Cited by 47 | Viewed by 7352
Abstract
Analysis of retinal fundus images is essential for eye-care physicians in the diagnosis, care and treatment of patients. Accurate fundus and/or retinal vessel maps give rise to longitudinal studies able to utilize multimedia image registration and disease/condition status measurements, as well as applications [...] Read more.
Analysis of retinal fundus images is essential for eye-care physicians in the diagnosis, care and treatment of patients. Accurate fundus and/or retinal vessel maps give rise to longitudinal studies able to utilize multimedia image registration and disease/condition status measurements, as well as applications in surgery preparation and biometrics. The segmentation of retinal morphology has numerous applications in assessing ophthalmologic and cardiovascular disease pathologies. Computer-aided segmentation of the vasculature has proven to be a challenge, mainly due to inconsistencies such as noise and variations in hue and brightness that can greatly reduce the quality of fundus images. The goal of this work is to collate different key performance indicators (KPIs) and state-of-the-art methods applied to this task, frame computational efficiency–performance trade-offs under varying degrees of information loss using common datasets, and introduce PixelBNN, a highly efficient deep method for automating the segmentation of fundus morphologies. The model was trained, tested and cross tested on the DRIVE, STARE and CHASE_DB1 retinal vessel segmentation datasets. Performance was evaluated using G-mean, Mathews Correlation Coefficient and F1-score, with the main success measure being computation speed. The network was 8.5× faster than the current state-of-the-art at test time and performed comparatively well, considering a 5× to 19× reduction in information from resizing images during preprocessing. Full article
(This article belongs to the Special Issue Mathematical and Computational Methods in Image Processing)
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18 pages, 468 KiB  
Article
Two-Dimensional Orthonormal Tree-Structured Haar Transform for Fast Block Matching
by Izumi Ito and Karen Egiazarian
J. Imaging 2018, 4(11), 131; https://0-doi-org.brum.beds.ac.uk/10.3390/jimaging4110131 - 07 Nov 2018
Cited by 3 | Viewed by 3867
Abstract
The goal of block matching (BM) is to locate small patches of an image that are similar to a given patch or template. This can be done either in the spatial domain or, more efficiently, in a transform domain. Full search (FS) BM [...] Read more.
The goal of block matching (BM) is to locate small patches of an image that are similar to a given patch or template. This can be done either in the spatial domain or, more efficiently, in a transform domain. Full search (FS) BM is an accurate, but computationally expensive procedure. Recently introduced orthogonal Haar transform (OHT)-based BM method significantly reduces the computational complexity of FS method. However, it cannot be used in applications where the patch size is not a power of two. In this paper, we generalize OHT-based BM to an arbitrary patch size, introducing a new BM algorithm based on a 2D orthonormal tree-structured Haar transform (OTSHT). Basis images of OHT are uniquely determined from the full balanced binary tree, whereas various OTSHTs can be constructed from any binary tree. Computational complexity of BM depends on a specific design of OTSHT. We compare BM based on OTSHTs to FS and OHT (for restricted patch sizes) within the framework of image denoising, using WNNM as a denoiser. Experimental results on eight grayscale test images corrupted by additive white Gaussian noise with five noise levels demonstrate that WNNM with OTSHT-based BM outperforms other methods both computationally and qualitatively. Full article
(This article belongs to the Special Issue Mathematical and Computational Methods in Image Processing)
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