Unified Mathematical Formulation of Monogenic Phase Congruency

Forero, Manuel G.; Jacanamejoy, Carlos A.

doi:10.3390/math9233080

Cited by 4 publications

(4 citation statements)

References 20 publications

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“…However, when the scale of the image changes, such as in multiresolution analysis (MRA), the position of the edge may not be consistent, or completely different problems may occur [25]. Kovesi introduced the PC principle to identify regions where considerable changes are in phase at the point of the step in a high-variation square wave [30,31]. Morrone and Owens mathematically defined PC by extending the Fourier series for position x as follows [31,32]:…”

Section: Methodsmentioning

confidence: 99%

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A Multiscale Deep Encoder–Decoder with Phase Congruency Algorithm Based on Deep Learning for Improving Diagnostic Ultrasound Image Quality

Kim,

Lee

2023

Applied Sciences

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Ultrasound imaging is widely used as a noninvasive lesion detection method in diagnostic medicine. Improving the quality of these ultrasound images is very important for accurate diagnosis, and deep learning-based algorithms have gained significant attention. This study proposes a multiscale deep encoder–decoder with phase congruency (MSDEPC) algorithm based on deep learning to improve the quality of diagnostic ultrasound images. The MSDEPC algorithm included low-resolution (LR) images and edges as inputs and constructed a multiscale convolution and deconvolution network. Simulations were conducted using the Field 2 program, and data from real experimental research were obtained using five clinical datasets containing images of the carotid artery, liver hemangiomas, breast malignancy, thyroid carcinomas, and obstetric nuchal translucency. LR images, bicubic interpolation, and super-resolution convolutional neural networks (SRCNNs) were modeled as comparison groups. Through visual assessment, the image processed using the MSDEPC was the clearest, and the lesions were clearly distinguished. The structural similarity index metric (SSIM) value of the simulated ultrasound image using the MSDEPC algorithm improved by approximately 38.84% compared to LR. In addition, the peak signal-to-noise ratio (PSNR) and SSIM values of clinical ultrasound images using the MSDEPC algorithm improved by approximately 2.33 times and 88.58%, respectively, compared to LR. In conclusion, the MSDEPC algorithm is expected to significantly improve the spatial resolution of ultrasound images.

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Section: Methodsmentioning

confidence: 99%

“…Kovesi introduced the PC principle to identify regions where considerable changes are in phase at the point of the step in a high-variation square wave [30,31]. Morrone and Owens mathematically defined PC by extending the Fourier series for position x as follows [31,32]:…”

Section: Methodsmentioning

confidence: 99%

A Multiscale Deep Encoder–Decoder with Phase Congruency Algorithm Based on Deep Learning for Improving Diagnostic Ultrasound Image Quality

Kim,

Lee

2023

Applied Sciences

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“…For analytical purposes, it can be decomposed into three components that signify frequency distribution weighting, phase congruency quantization, and noise compensation. This trichotomy not only facilitates comprehensive examination but also enables the consolidation of various technique variations through the utilization of the equation [14]…”

Section: Monogenic Phase Congruencymentioning

confidence: 99%

“…Phase congruency is another technique used for edge detection, although it is less well-known. Despite several recent works utilizing this method, such as its integration into pipelines for image registration or edge detection in various applications [11][12][13], there have been no new developments concerning the principles of this technique, except those produced by the authors themselves [14].…”

Section: Introductionmentioning

confidence: 99%

Generalized Quantification Function of Monogenic Phase Congruency

Forero,

Jacanamejoy,

Machado

et al. 2023

Mathematics

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Edge detection is a technique in digital image processing that detects the contours of objects based on changes in brightness. Edges can be used to determine the size, orientation, and properties of the object of interest within an image. There are different techniques employed for edge detection, one of them being phase congruency, a recently developed but still relatively unknown technique due to its mathematical and computational complexity compared to more popular methods. Additionally, it requires the adjustment of a greater number of parameters than traditional techniques. Recently, a unique formulation was proposed for the mathematical description of phase congruency, leading to a better understanding of the technique. This formulation consists of three factors, including a quantification function, which, depending on its characteristics, allows for improved edge detection. However, a detailed study of the characteristics had not been conducted. Therefore, this article proposes the development of a generalized function for quantifying phase congruency, based on the family of functions that, according to a previous study, yielded the best results in edge detection.

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Biological Basis and Computer Vision Applications of Image Phase Congruency: A Comprehensive Survey

Tian,

Wen,

et al. 2024

Biomimetics

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The concept of Image Phase Congruency (IPC) is deeply rooted in the way the human visual system interprets and processes spatial frequency information. It plays an important role in visual perception, influencing our capacity to identify objects, recognize textures, and decipher spatial relationships in our environments. IPC is robust to changes in lighting, contrast, and other variables that might modify the amplitude of light waves yet leave their relative phase unchanged. This characteristic is vital for perceptual tasks as it ensures the consistent detection of features regardless of fluctuations in illumination or other environmental factors. It can also impact cognitive and emotional responses; cohesive phase information across elements fosters a perception of unity or harmony, while inconsistencies can engender a sense of discord or tension. In this survey, we begin by examining the evidence from biological vision studies suggesting that IPC is employed by the human perceptual system. We proceed to outline the typical mathematical representation and different computational approaches to IPC. We then summarize the extensive applications of IPC in computer vision, including denoise, image quality assessment, feature detection and description, image segmentation, image registration, image fusion, and object detection, among other uses, and illustrate its advantages with a number of examples. Finally, we discuss the current challenges associated with the practical applications of IPC and potential avenues for enhancement.

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Unified Mathematical Formulation of Monogenic Phase Congruency

Cited by 4 publications

References 20 publications

A Multiscale Deep Encoder–Decoder with Phase Congruency Algorithm Based on Deep Learning for Improving Diagnostic Ultrasound Image Quality

A Multiscale Deep Encoder–Decoder with Phase Congruency Algorithm Based on Deep Learning for Improving Diagnostic Ultrasound Image Quality

Generalized Quantification Function of Monogenic Phase Congruency

Biological Basis and Computer Vision Applications of Image Phase Congruency: A Comprehensive Survey

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