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Mathematics
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Mathematical Approaches to Image Processing with Applications
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Mathematical Approaches to Image Processing with Applications

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Engineering Mathematics".

Deadline for manuscript submissions: closed (20 December 2021) | Viewed by 28994

Special Issue Editor

Prof. Dr. Javier Martínez

E-Mail Website
Guest Editor
Department of Applied Mathematics I, University of Vigo, Vigo, Spain
Interests: machine learning techniques: applications and new algorithms; functional statistics: outliers detection and quality control; image processing;
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Image processing is a set of techniques that have been developed over the last 30 years in such a way that they are increasingly more complex and their applications more diverse.

Several authors include the acquisition of the image within image processing as an important phase with an important mathematical load due to the models of calibration that intervene, which needs to be more effective and efficient every time. Thus, the mathematical modeling of each application and the algorithms designed ad-hoc for the extraction of characteristics or simply for the measurement of some parameters of the image are of special interest to the scientific community. In addition, it is not only important to extract characteristics, but all possible classification or regression models, once the characteristics have been extracted, which can establish decision patterns. This is where machine learning and/or deep learning models come in.

For all these reasons, this Special Issue will collect works of special relevance in the different phases of image processing, with special emphasis on the different mathematical approaches addressed.

Prof. Dr. Javier Martínez
Guest Editor

Manuscript Submission Information

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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. Mathematics is an international peer-reviewed open access semimonthly 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 2600 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
  • Mathematical algorithm
  • Image acquisition
  • Machine learning

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Published Papers (8 papers)

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Research

20 pages, 5119 KiB  
Article
Modeling of Hyperparameter Tuned Deep Learning Model for Automated Image Captioning
by Mohamed Omri, Sayed Abdel-Khalek, Eied M. Khalil, Jamel Bouslimi and Gyanendra Prasad Joshi
Mathematics 2022, 10(3), 288; https://doi.org/10.3390/math10030288 - 18 Jan 2022
Cited by 13 | Viewed by 2305
Abstract
Image processing remains a hot research topic among research communities due to its applicability in several areas. An important application of image processing is the automatic image captioning technique, which intends to generate a proper description of an image in a natural language [...] Read more.
Image processing remains a hot research topic among research communities due to its applicability in several areas. An important application of image processing is the automatic image captioning technique, which intends to generate a proper description of an image in a natural language automated. Image captioning is a recently developed hot research topic, and it started to receive significant attention in the field of computer vision and natural language processing (NLP). Since image captioning is considered a challenging task, the recently developed deep learning (DL) models have attained significant performance with increased complexity and computational cost. Keeping these issues in mind, in this paper, a novel hyperparameter tuned DL for automated image captioning (HPTDL-AIC) technique is proposed. The HPTDL-AIC technique encompasses two major parts, namely encoder and decoder. The encoder part utilizes Faster SqueezNet with the RMSProp model to generate an effective depiction of the input image via insertion into a predefined length vector. At the same time, the decoder unit employs a bird swarm algorithm (BSA) with long short-term memory (LSTM) model to concentrate on the generation of description sentences. The design of RMSProp and BSA for the hyperparameter tuning process of the Faster SqueezeNet and LSTM models for image captioning shows the novelty of the work, which helps to accomplish enhanced image captioning performance. The experimental validation of the HPTDL-AIC technique is carried out against two benchmark datasets, and the extensive comparative study pointed out the improved performance of the HPTDL-AIC technique over recent approaches. Full article
(This article belongs to the Special Issue Mathematical Approaches to Image Processing with Applications)
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17 pages, 3105 KiB  
Article
Unified Mathematical Formulation of Monogenic Phase Congruency
by Manuel G. Forero and Carlos A. Jacanamejoy
Mathematics 2021, 9(23), 3080; https://doi.org/10.3390/math9233080 - 30 Nov 2021
Cited by 5 | Viewed by 2251
Abstract
Phase congruency is a technique that has been used for edge, corner and symmetry detection. Its implementation through the use of monogenic filters has improved its computational cost. For this purpose, different methods of implementation have been published, but they do not use [...] Read more.
Phase congruency is a technique that has been used for edge, corner and symmetry detection. Its implementation through the use of monogenic filters has improved its computational cost. For this purpose, different methods of implementation have been published, but they do not use a common notation, which makes it difficult to understand. Therefore, this paper presents a unified mathematical formulation that allows a general understanding of the Monogenic phase congruency concepts and establishes criteria for its use. A new protocol for parameter tuning is also described, allowing better practical results to be obtained with this technique. Some examples are presented allowing one to observe the changes produced in the parameter tuning, evidencing the validity of the proposed criteria. Full article
(This article belongs to the Special Issue Mathematical Approaches to Image Processing with Applications)
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13 pages, 5353 KiB  
Article
Automatic Image Characterization of Psoriasis Lesions
by Javier Martínez-Torres, Alicia Silva Piñeiro, Álvaro Alesanco, Ignacio Pérez-Rey and José García
Mathematics 2021, 9(22), 2974; https://doi.org/10.3390/math9222974 - 22 Nov 2021
Viewed by 2311
Abstract
Psoriasis is a chronic skin disease that affects 125 million people worldwide and, particularly, 2% of the Spanish population, characterized by the appearance of skin lesions due to a growth of the epidermis that is seven times larger than usual. Its diagnosis and [...] Read more.
Psoriasis is a chronic skin disease that affects 125 million people worldwide and, particularly, 2% of the Spanish population, characterized by the appearance of skin lesions due to a growth of the epidermis that is seven times larger than usual. Its diagnosis and monitoring are based on the use of methodologies for measuring the severity and extent of these spots, and this includes a large subjective component. For this reason, this paper presents an automatic method for characterizing psoriasis images that is divided into four parts: image preparation or pre-processing, feature extraction, classification of the lesions, and the obtaining of parameters. The methodology proposed in this work covers different digital-image processing techniques, namely, marker-based image delimitation, hair removal, nipple detection, lesion contour detection, areal-measurement-based lesion classification, as well as lesion characterization by means of red and white intensity. The results obtained were also endorsed by a professional dermatologist. This methodology provides professionals with a common software tool for monitoring the different existing typologies, which proved satisfactory in the cases analyzed for a set of 20 images corresponding to different types of lesions. Full article
(This article belongs to the Special Issue Mathematical Approaches to Image Processing with Applications)
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18 pages, 5547 KiB  
Article
A High Fidelity Authentication Scheme for AMBTC Compressed Image Using Reference Table Encoding
by Tungshou Chen, Xiaoyu Zhou, Rongchang Chen, Wien Hong and Kiasheng Chen
Mathematics 2021, 9(20), 2610; https://doi.org/10.3390/math9202610 - 16 Oct 2021
Cited by 4 | Viewed by 1712
Abstract
In this paper, we propose a high-quality image authentication method based on absolute moment block truncation coding (AMBTC) compressed images. The existing AMBTC authentication methods may not be able to detect certain malicious tampering due to the way that the authentication codes are [...] Read more.
In this paper, we propose a high-quality image authentication method based on absolute moment block truncation coding (AMBTC) compressed images. The existing AMBTC authentication methods may not be able to detect certain malicious tampering due to the way that the authentication codes are generated. In addition, these methods also suffer from their embedding technique, which limits the improvement of marked image quality. In our method, each block is classified as either a smooth block or a complex one based on its smoothness. To enhance the image quality, we toggle bits in bitmap of smooth block to generate a set of authentication codes. The pixel pair matching (PPM) technique is used to embed the code that causes the least error into the quantization values. To reduce the computation cost, we only use the original and flipped bitmaps to generate authentication codes for complex blocks, and select the one that causes the least error for embedment. The experimental results show that the proposed method not only obtains higher marked image quality but also achieves better detection performance compared with prior works. Full article
(This article belongs to the Special Issue Mathematical Approaches to Image Processing with Applications)
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22 pages, 4870 KiB  
Article
A Method of Image Quality Assessment for Text Recognition on Camera-Captured and Projectively Distorted Documents
by Julia Shemiakina, Elena Limonova, Natalya Skoryukina, Vladimir V. Arlazarov and Dmitry P. Nikolaev
Mathematics 2021, 9(17), 2155; https://doi.org/10.3390/math9172155 - 3 Sep 2021
Cited by 6 | Viewed by 3583
Abstract
In this paper, we consider the problem of identity document recognition in images captured with a mobile device camera. A high level of projective distortion leads to poor quality of the restored text images and, hence, to unreliable recognition results. We propose a [...] Read more.
In this paper, we consider the problem of identity document recognition in images captured with a mobile device camera. A high level of projective distortion leads to poor quality of the restored text images and, hence, to unreliable recognition results. We propose a novel, theoretically based method for estimating the projective distortion level at a restored image point. On this basis, we suggest a new method of binary quality estimation of projectively restored field images. The method analyzes the projective homography only and does not depend on the image size. The text font and height of an evaluated field are assumed to be predefined in the document template. This information is used to estimate the maximum level of distortion acceptable for recognition. The method was tested on a dataset of synthetically distorted field images. Synthetic images were created based on document template images from the publicly available dataset MIDV-2019. In the experiments, the method shows stable predictive values for different strings of one font and height. When used as a pre-recognition rejection method, it demonstrates a positive predictive value of 86.7% and a negative predictive value of 64.1% on the synthetic dataset. A comparison with other geometric quality assessment methods shows the superiority of our approach. Full article
(This article belongs to the Special Issue Mathematical Approaches to Image Processing with Applications)
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13 pages, 5185 KiB  
Article
Digital Image Processing Method for Characterization of Fractures, Fragments, and Particles of Soil/Rock-Like Materials
by Zizi Pi, Zilong Zhou, Xibing Li and Shaofeng Wang
Mathematics 2021, 9(8), 815; https://doi.org/10.3390/math9080815 - 9 Apr 2021
Cited by 15 | Viewed by 3551
Abstract
Natural soil and rock materials and the associated artificial materials have cracks, fractures, or contacts and possibly produce rock fragments or particles during geological, environmental, and stress conditions. Based on color gradient distribution, a digital image processing method was proposed to automatically recognize [...] Read more.
Natural soil and rock materials and the associated artificial materials have cracks, fractures, or contacts and possibly produce rock fragments or particles during geological, environmental, and stress conditions. Based on color gradient distribution, a digital image processing method was proposed to automatically recognize the outlines of fractures, fragments, and particles. Then, the fracture network, block size distribution, and particle size distribution were quantitatively characterized by calculating the fractal dimension and equivalent diameter distribution curve. The proposed approach includes the following steps: production of an image matrix; calculation of the gradient magnitude matrix; recognition of the outlines of fractures, fragments, or particles; and characterization of the distribution of fractures, fragments, or particles. Case studies show that the fractal dimensions of cracks in the dry mud layer, ceramic panel, and natural rock mass are 1.4332, 1.3642, and 1.5991, respectively. The equivalent diameters of fragments of red sandstone, granite, and marble produced in quasi-static compression failures are mainly distributed in the ranges of 20–40 mm, 25–65 mm, and 10–35 mm, respectively. The fractal dimension of contacts between mineral particles and the distribution of the equivalent diameters of particles in rock are 1.6381 and 0.8–3.6 mm, respectively. The proposed approach provides a computerized method to characterize quantitatively and automatically the structure characteristics of soil/rock or soil/rock-like materials. By this approach, the remote sensing for characterization can be achieved. Full article
(This article belongs to the Special Issue Mathematical Approaches to Image Processing with Applications)
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17 pages, 3248 KiB  
Article
Auto-Colorization of Historical Images Using Deep Convolutional Neural Networks
by Madhab Raj Joshi, Lewis Nkenyereye, Gyanendra Prasad Joshi, S. M. Riazul Islam, Mohammad Abdullah-Al-Wadud and Surendra Shrestha
Mathematics 2020, 8(12), 2258; https://doi.org/10.3390/math8122258 - 21 Dec 2020
Cited by 22 | Viewed by 6189
Abstract
Enhancement of Cultural Heritage such as historical images is very crucial to safeguard the diversity of cultures. Automated colorization of black and white images has been subject to extensive research through computer vision and machine learning techniques. Our research addresses the problem of [...] Read more.
Enhancement of Cultural Heritage such as historical images is very crucial to safeguard the diversity of cultures. Automated colorization of black and white images has been subject to extensive research through computer vision and machine learning techniques. Our research addresses the problem of generating a plausible colored photograph of ancient, historically black, and white images of Nepal using deep learning techniques without direct human intervention. Motivated by the recent success of deep learning techniques in image processing, a feed-forward, deep Convolutional Neural Network (CNN) in combination with Inception- ResnetV2 is being trained by sets of sample images using back-propagation to recognize the pattern in RGB and grayscale values. The trained neural network is then used to predict two a* and b* chroma channels given grayscale, L channel of test images. CNN vividly colorizes images with the help of the fusion layer accounting for local features as well as global features. Two objective functions, namely, Mean Squared Error (MSE) and Peak Signal-to-Noise Ratio (PSNR), are employed for objective quality assessment between the estimated color image and its ground truth. The model is trained on the dataset created by ourselves with 1.2 K historical images comprised of old and ancient photographs of Nepal, each having 256 × 256 resolution. The loss i.e., MSE, PSNR, and accuracy of the model are found to be 6.08%, 34.65 dB, and 75.23%, respectively. Other than presenting the training results, the public acceptance or subjective validation of the generated images is assessed by means of a user study where the model shows 41.71% of naturalness while evaluating colorization results. Full article
(This article belongs to the Special Issue Mathematical Approaches to Image Processing with Applications)
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13 pages, 3626 KiB  
Article
A Fast Image Restoration Algorithm Based on a Fixed Point and Optimization Method
by Adisak Hanjing and Suthep Suantai
Mathematics 2020, 8(3), 378; https://doi.org/10.3390/math8030378 - 8 Mar 2020
Cited by 61 | Viewed by 4749
Abstract
In this paper, a new accelerated fixed point algorithm for solving a common fixed point of a family of nonexpansive operators is introduced and studied, and then a weak convergence result and the convergence behavior of the proposed method is proven and discussed. [...] Read more.
In this paper, a new accelerated fixed point algorithm for solving a common fixed point of a family of nonexpansive operators is introduced and studied, and then a weak convergence result and the convergence behavior of the proposed method is proven and discussed. Using our main result, we obtain a new accelerated image restoration algorithm, called the forward-backward modified W-algorithm (FBMWA), for solving a minimization problem in the form of the sum of two proper lower semi-continuous and convex functions. As applications, we apply the FBMWA algorithm to solving image restoration problems. We analyze and compare convergence behavior of our method with the others for deblurring the image. We found that our algorithm has a higher efficiency than the others in the literature. Full article
(This article belongs to the Special Issue Mathematical Approaches to Image Processing with Applications)
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