IMAGE PROCESSING METHOD WITH MODIFIED SAMPLING KANTOROVICH OPERATORS

Abstract

The invention relates to an image processing method based on modified Sampling Kantorovich operators, in which a special transformation function is integrated into the operator structure to reduce structural distortions in digital images, and which are used for processing, resizing, reconstructing, and improving the visual quality of the images.

Description

1 TARIFF MODIFIED SAMPLING WITH KANTOROVICH OPERATORS IMAGE PROCESSING METHOD TECHNICAL AREA 5 The invention involves the processing, resizing, and redesigning of digital images. used for the purpose of structuring and improving visual quality, a special transformation that enables the reduction of structural distortions in the image Modified Sampling where the function is integrated into the operator structure. It is related to an image processing method based on Kantorovich operators. 10 PREVIOUS TECHNIQUE In current technology, resizing, enhancing, and Bilinear, Bicubic, and B-Spline are commonly used in restructuring processes. 15 from classical Sampling Kantorovich operators with interpolation methods These methods are used to process digital images at different resolutions. adapting to the levels and reconstructing missing image data While usable in terms of performance, especially at low sampling rates preserving image quality, maintaining structural details, and reducing processing load. It has various technical shortcomings in terms of reducing it. 20 Acceptable image quality in classic Kantorovich sampling operators. To achieve high quality, the sampling parameter should be selected. is required. In cases where the sampling parameter is kept low, the image... Data loss occurs during the reconstruction process, in the image. Blurring occurs and the edge, texture, and density transitions of the original image are lost. It cannot be preserved with sufficient accuracy. Therefore, under low sampling rates PSNR values ​​are at low levels in the image processing applications performed. and the reconstructed image retains the structural characteristics of the original image sufficiently. It is unable to represent it with precision. In current methods, the sampling frequency needs to be increased to 30 to improve image quality. The need to increase the amount of data to be processed and the calculations accordingly. This increases the workload. This situation makes it difficult to work with high-resolution images. This leads to increased processing time in the systems and live surgical imaging. Real-time processing of satellite imagery, industrial control systems, and similar real-time applications. 2 This increases hardware requirements in time-sensitive applications. Therefore, classic The approaches require higher processing power to improve quality, and low It cannot provide sufficient performance in systems that rely on hardware resources. Current image processing algorithms used in the field of medical imaging, especially in non-contrast computed tomography images, small density differences are 5 Their ability to differentiate is limited. Vascular lumens and vascular structures In most cases, contrast agents are needed to ensure clear visualization. It is heard that this situation necessitates the administration of a chemical agent to the patient. It is an invasive procedure. The use of contrast medium can affect some patients. can lead to allergic reactions, kidney dysfunction, or additional clinical risks. because it can open up existing image processing methods on low-contrast images. The inability to provide adequate separation and remediation is a significant technical shortcoming. It constitutes. Dental volumetric tomography, industrial scanning and similar volumetric applications. Current algorithms in imaging applications reduce noise in the image while 15 It cannot adequately preserve edge and surface information. Therefore, bone, teeth, during the conversion of tissue or industrial part surfaces into three-dimensional models surface roughness, anatomical inconsistencies, or geometric errors occur This is possible. Especially surgical guides, personalized implants, dental models or In industrial prototype production, the accuracy of the model obtained from the image is directly related to 20 Because it affects the reliability of the physical part to be produced, the noise of current methods The technical issue is that it fails to strike an adequate balance between edge protection and removal. This constitutes a problem. Low voltage used in thermographic analysis and building inspection applications In high-resolution thermal images, current interpolation approaches show structure 25 It reveals the boundaries between the elements and the temperature transitions with sufficient precision. This is due to a lack of space in the brick, mortar, insulation, thermal bridge, or damp area. This makes it difficult to separate different structural elements such as thermal insulation. This can lead to inaccurate assessments of performance. Current methods reveal structural details in low-resolution thermal images. 30 inability to improve while protecting, building health monitoring and energy efficiency analyses This constitutes a significant limitation in this regard. In conclusion, the Bilinear, Bicubic, and B-Spline techniques used in the current technology Interpolation methods with classical Sampling Kantorovich operators, low 3 preserving image quality at different sampling rates, preventing structural distortions. reduction, lower processing load, separation in contrast-free medical images enhancing the ability to create smooth-surfaced three-dimensional models from volumetric images obtaining and structural details in low-resolution thermal images It is unable to achieve sufficient technical success in terms of clarification. Therefore, 5 Even at low sampling parameters, the edges, textures, densities, and surfaces in the image are visible. ensuring that information is protected with higher accuracy, without increasing transaction costs. It improves image quality and can be applied in various sensitive imaging fields. A new image processing method of this caliber is needed. THE PURPOSE OF THE INVENTION The purpose of the invention is to resize and recreate digital images. in the processes of structuring and improving, classical Kantorovich Sampling Interpolation methods encountered with operators in Bilinear, Bicubic and B-Spline loss of detail due to low sampling rate, blurring, high computational load and 15 a modified image processing method that reduces structural distortion problems It is about developing. One aim of the invention is to integrate the Sampling Kantorovich operator structure. Thanks to the mathematical 𝜌 transformation function, a low sampling parameter. to make it possible to reconstruct the image even at these values ​​and thus 20 The aim is to achieve higher image quality with fewer data samples. This reduces the processing power, memory usage, and data required in the image processing process. Processing load is reduced, and high sampling is used for high-resolution image production. Dependence on frequency is reduced. Another aim of the invention is to utilize low-resolution, sparsely sampled or 25 Edge, texture, density transition, and structural separation information in degraded images The aim is to ensure its protection. Low sampling rates are used in current interpolation methods. blurring, loss of detail, and Gibbs phenomenon occurring at these ratios. Oscillations are reduced by the modified operator structure used within the scope of the invention; Thus, the fine details in the image are more prominent and more faithful to the original image. 30 It is thus recreated. One of the aims of the invention is to provide contrast-free images in the field of medical imaging. The aim is to make low-density differences more pronounced. The invention, within this scope, relates to the visualization of vascular lumens and vessels in computed tomography images. 4 It contributes to the clearer distinction of structures through image processing and contrast. a technical solution aimed at reducing the need for substance use It provides this. Thus, allergic reactions due to the application of chemical agents to the patient, which helps to reduce clinical risks such as renal dysfunction, Non-invasive image assessment processes are supported. 5 Another purpose of the invention is to enable dental volumetric tomography and similar volumetric applications. surface roughness in three-dimensional models obtained from imaging data The aim is to reduce and preserve anatomical boundaries. Edge protection is included in the invention. With this capability, noise reduction is achieved and the surfaces of bone, teeth or tissue are protected. This allows for more accurate modeling without distortion. Thanks to this, 10 in surgical guidance, implant planning, dental modeling and three-dimensional printing processes Dimensional accuracy and surface quality are improved. One of the aims of the invention is to provide thermographic images, satellite images, and medical images. and flexible, applicable to different image types such as industrial scanning images. The aim is to provide an image processing infrastructure. The parametric structure used in the invention is the ρ transformation 15 based on the image characteristic via the function and the χ kernel It is adaptable, so it is not limited to a single image type, but can display different resolutions. an optimized approach on images with noise and density distributions A processing engine is obtained. Another purpose of the invention is to utilize low 20 in building inspection and thermographic analysis. The aim is to enable the clarification of structural details in high-resolution thermal images. In this context, bricks, mortar, insulation gaps, thermal bridges, or differential temperature transfers can be considered. The aim is to make the distinction between the structural regions clearer. Thus, building health monitoring, thermal insulation performance evaluation, and energy efficiency are carried out. More reliable image-based assessments are possible in the analyses. 25 is happening. The invention offers better performance at lower sampling parameter values ​​compared to existing techniques. By achieving high PSNR values, the image's relation to the original data is improved. It increases loyalty. Comparative analysis is given in Figures 2a-2d and 3a-3d. In the evaluations, 30 samples were taken from Lena's image with a sampling parameter of 𝑤 = 0.2. While a PSNR value of 16.34 was obtained using the classical method, the value used within the scope of the invention Achieving a PSNR of 22.61 with a modified operator, under low data density. This even shows that image quality can be significantly improved. Similarly For fruit images, a PSNR value of 21.21 is obtained using the classical method for a value of 𝑤 = 0.8. While this was being done, achieving a PSNR value of 24.33 within the scope of the invention indicates that the method is suitable for different images. This demonstrates a consistent improvement in the quality of its content. In conclusion, the aim of the invention is to render digital images with low processing power, at a low level. re-designed at varying sampling rates and adaptable to different image types. It enables the creation of edge and texture information, preserving blurring and structural integrity. reducing distortions, medical imaging, dental three-dimensional modeling, thermographic It can be used in analysis, satellite imaging, and industrial image processing. image processing based on modified Sampling Kantorovich operators The goal is to reveal the method. LIST OF FIGURES Figure 1. Flowchart showing the steps of the method described in the invention. Figure 2a. ,𝒦!.# Image generated using ℬ!,&̇𝐼 / : 128 × 128 pixels “Lena”, PSNR: 22.617433 Figure 2b. ,𝒮!.# Image generated using ℬ!𝐼 / : 128 × 128 pixels “Lena”, PSNR: 15 16.347777 Figure 2c. ,𝒦# Image generated using ℬ!,&̇𝐼 / : 128 × 128 pixels “Lena”, PSNR: 22.690266 Figure 2d. ,𝒮# Image generated using ℬ!𝐼 / : 128 × 128 pixels “Lena”, PSNR: 21.669040 20 Figure 3a. ,𝒦!.( Image generated using ℬ!,&̇𝐼 / : 128 × 128 pixels “Fruits”, PSNR: 24.336274 Figure 3b. ,𝒮!.( Image generated using ℬ!𝐼 / : 128 × 128 pixels "Fruits", PSNR: 21.218737 Figure 3c. ,𝒦# Image generated using ℬ!,&̇𝐼 / : 128 × 128 pixels “Fruits”, 25 PSNR: 24.351177 Figure 3d. ,𝒮# Image generated using ℬ!𝐼 / : 128 × 128 pixels “Fruits”, PSNR: 23.382626 The corresponding numbers in the figures are: 30 10: Image Processing Method (General System) 11: Input Image Matrix (I or f) 6 12: Parameter Selection Module (χ, ρ, 𝑤) 13: Modified Transformation Function (ρ) 14: Kernel Function (χ) 15: Sampling Parameter (𝑤) 16: Weighting and Integration Unit 5 17: Reconstructed Output Image (I)) DETAILED DESCRIPTION OF THE INVENTION The method used in the invention is based on the image processing of classic Kantorovich sampling operators. a modified operator structure that improves its use in the processing area 10 It is based on the mathematical representation of the image matrix in this structure. starting with determining the appropriate transformation function, the kernel function selection, definition of sampling parameter, corresponding to each image point applying the resulting integral operation and the resulting reconstructed output There are successive processing steps involved in creating the image. 15 These process steps work together to achieve a low sampling parameter. Even at these values, the structural integrity of the image is preserved, blurring is minimized. reduction, preservation of edge continuity, and the original output image This allows the image to be rendered with higher fidelity. The technical impact of the invention is the inclusion of the modified transformation function into the operator structure. This transformation function is obtained by measuring the intensity in the image. a transformed processing space that represents its changes more precisely It creates and, together with the core function, assigns each pixel value to the environmental data. It redefines the relationship. Thus, the method redefines the classical Bilinear, Bicubic, B-Spline 25 in interpolation approaches and classical Sampling Kantorovich operators Data loss, anti-aliasing, and image distortion observed due to low sampling rate. against turbidity, oscillation-induced distortions, and high processing load problems. It offers a technical solution. The working principle of the invention is based on the flowchart shown in Figure 1. The method (10) is detailed below. An input image taken from a digital environment 30 It starts with matrix (11). This matrix is ​​defined in the space 𝐿*(ℝ#) (1 ≤ 𝑝 < ∞) and is compact. It is modeled as a step function with support. Input image matrix (11), Each pixel's (i, i) coordinates represent the grayscale level (a+,). 7 The most critical stage of the method is within the parameter selection module (12). This is happening. Here, unlike classical methods, a modification is applied to the system. The transformation function (13) is defined. The modified transformation function (13) is two For each coordinate component of the three-dimensional image matrix, 𝜌(𝑥-, 𝑥#) = is defined separately. ,𝜌-(𝑥-), 𝜌#(𝑥#) / is a transformation function applied in this form. The 𝜌- and 𝜌# are 5. functions defined on the set of real numbers, continuous, strictly increasing, 𝜌+(0) = 0 defined such that for every x → ±∞, 𝜌+(x) → ±∞ satisfies the condition, and for every x value These are functions whose derivative 𝜌+.(𝑥) > 1. Thanks to these properties, modified transformations are possible. function (13) creates an invertible coordinate transformation and the input image Sampling the matrix in the transformed coordinate space with the Kantorovich operator 10 It enables processing. In preferred configurations 𝜌+(𝑥) = 𝑥 + The functions 𝑡𝑎𝑛ℎ(𝑥), ρ+(𝑥) = 𝑥 / + 𝑥 or 𝜌+(𝑥) = 𝑥 + 1 / 2𝑎𝑟𝑐𝑡𝑎𝑛(𝑥) can be used. Simultaneously, the kernel to be used in the sampling process The function (14) is selected. The mentioned sampling process selects the input image matrix. (11) The pixel values ​​that make up the pixels are not directly based on point values, but 15 calculated on the intervals determined by the sampling parameter (15) Evaluation based on average / integral values ​​and modification of these values The kernel in the transformed coordinate space created by the transformation function. weighting via the function and corresponding to each image point The new pixel value obtained as a result of this weighted sum and integration process is 20. It is based on the principle of being made. Within the scope of the invention, this core function (14), B- Like spline or Jackson-type cores, which satisfy specific moment conditions and have 𝑀0 &(χ) These are functions with a finite absolute moment, expressed as . The precision of the operation The determining sampling parameter (15), namely the value of 𝑤, is the value required by the user. The resolution is determined according to the rate of increase. The parameter 𝑤 goes to infinity at 25. In this case, the input function approaches the function itself under the operator. Therefore, the larger the input image 𝑤 is chosen, the closer it will be to the original image. will achieve the resolution. However, increasing this parameter requires more hardware and time. This significantly increases costs. The technical advantage of the invention is sampling. Although the parameter (15) was chosen much lower than the classical methods, 30 (e.g., 𝑤 = 0.2) indicates a high success rate. Here, the sampling parameter is... (15) low selection, classic Sampling during image reconstruction The need for higher sampling density is used in Kantorovich operators. 8 without being heard, fewer sampling points and consequently lower processing capacity. This means performing calculations with the load. Data processing process, weighting and integration unit (16) This is implemented. This unit uses the following mathematical relationship for each pixel: (Formula 1) applies: χ is a suitable kernel function, 𝑥 ∈ ℝ#, 𝑤 > 0 and 𝑓 ∘5 Let ρ1-: ℝ# → ℝ be an integrable function. ,𝒦2 3,&𝑓 / (𝑥) = T χ(𝑤ρ(𝑥) − 𝑘)𝑤#W(𝑓 ∘ ρ1-)(𝑢)𝑑𝑢 45∈ℤ" . Here, the operation uses a modified transformation function for each point in coordinates (x-, x#). (13) weighted kernel function (14) in the transformed space It is a summation and integration process. This formulation is schematized in Figures 2a-2d and 3a-3d. recalculating the generated pixel matrix while preserving edge continuity This ensures that the "Gibbs phenomenon" or "time-jitter" errors seen in classical methods, This is minimized thanks to this modified structure. In the final stage, the newly calculated pixel values ​​are combined to reconstruct the image. The resulting output image (17) is created. In the results in Figure 2 and Figure 3, 15 As can be seen, the generated output image (17) is obtained by classical methods. It has a higher Peak Signal-to-Noise Ratio (PSNR) value compared to other images. For example, in a particular test image, the classical method remains at 16.34 dB, The method in question (10) reached a level of 22.61 dB with the same parameters. He has mathematically proven the visual clarity. 20 The invention is an input image matrix, particularly in the field of medical imaging (CT, MRI). (11) noise removal and without the need for contrast agent It offers a technical solution for highlighting vascular structures. 30

Claims

9 REQUESTS 1. Sampling Kantorovich for the reconstruction of digital images. It is an operator-based image processing method, characterized by its ability to process images from a digital environment. 5 corresponding to the coordinates of each pixel of an input image matrix (11) mathematically representing the incoming grayscale levels modeling; for the input image matrix (11), each coordinate continuous, definitely increasing, reversible and derivative, to be applied separately to its components (13) parameter selection module of a positive modified transformation function (12) identification through; specific 10 to be used in the sampling process a core that satisfies the moment conditions and has a finite absolute moment Selection of function (14) determines the reconstruction accuracy of the image. Determining a sampling parameter (15) such as the input image matrix (11) the pixel values ​​that make up the sampling instead of point values The integral values ​​calculated over the intervals determined by parameter (15) are 15 its evaluation through; created with the modified transformation function (13) In the transformed coordinate space, each image point corresponds to weighting of the pixel value through the kernel function (14) and Calculation by the unit of integration (16) with weighting; calculated The new pixel values ​​were combined to maintain edge continuity, and the blur level was increased to 20. reduced and high-fidelity reconstructed output compared to the original image. It is characterized by including the steps involved in creating the image (17). 30

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