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Zernike moments

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Zernike moments are a set of orthogonal polynomials defined on the unit disk, used in image analysis and pattern recognition. They provide a robust method for representing shapes and capturing geometric features, allowing for invariant descriptions under rotation, translation, and scaling.
lightbulbAbout this topic
Zernike moments are a set of orthogonal polynomials defined on the unit disk, used in image analysis and pattern recognition. They provide a robust method for representing shapes and capturing geometric features, allowing for invariant descriptions under rotation, translation, and scaling.

Key research themes

1. How can Zernike moments be effectively utilized for rotation-, scale-, and translation-invariant feature extraction in image-based pattern recognition tasks?

This research theme focuses on the application of Zernike moments and related orthogonal moment variants to extract robust features invariant under geometric transformations such as rotation, scaling, and translation for image analysis, particularly in face recognition, head pose estimation, and cosmic ray detection. The invariant and orthogonal properties of Zernike moments make them powerful tools for constructing compact, discriminative feature representations that improve classification and recognition performance while handling noise and varied image conditions.

Key finding: Demonstrated the use of orthogonal Zernike geometrical moments as robust feature vectors providing rotation, scale, and translation invariance in a forward-backpropagation neural network to localize faces in images. The... Read more
Key finding: Combined pseudo Zernike moments with Fisher's Linear Discriminant to achieve enhanced discriminative feature extraction that maximizes between-class variation while minimizing within-class variation in face recognition.... Read more
Key finding: Proposed a hybrid framework that integrates Zernike moments for extracting rotation-, scale-, and illumination-invariant local and global features used in real-time head pose and gaze estimation. Experiments on standard... Read more
Key finding: Applied Zernike moments as morphological feature carriers to classify cosmic ray candidate hits into categories such as spots, tracks, worms, and artifacts. Feature-based statistical classifiers using Zernike moments achieved... Read more
Key finding: Developed a fast and accurate method to compute pseudo Zernike moments based on linear combinations of exact geometric and radial geometric moments computed by integration over image pixels. The method preserved moment... Read more

2. What are the computational challenges and solutions for accurately and efficiently calculating Zernike and pseudo Zernike moments in practical applications?

Substantial research investigates algorithmic advances to reduce the high computational cost and numerical instability inherent in calculating traditional Zernike and pseudo Zernike moments, especially for high order moments or large images. Solutions include recursive algorithms, linear combinations with geometric moments, and integral image-based methods to accelerate computations while preserving numerical precision and orthogonality. Addressing computational efficiency and numerical errors is key for enabling real-time and large-scale applications of these moments in imaging.

Key finding: Identified that binomial expansions in complex-valued integral image computations of Zernike moments introduce numerical instability and precision loss. Proposed piecewise integral images and a numerically safer formula... Read more
Key finding: Introduced a novel accurate and efficient approach to compute pseudo Zernike moments by expressing them as linear combinations of exactly computed geometric and radial geometric moments via integration, overcoming... Read more
Key finding: Leveraged Bell's polynomials and their generalizations for systematic and efficient computation of moments of nested composite functions, including generalized Gaussian distributions. Presented explicit formulae and... Read more

3. How do Zernike moments and their variants integrate with machine learning methods to enhance classification and recognition tasks?

Integrating Zernike moment-based feature extraction with machine learning classifiers, including neural networks and discriminant analysis, has been shown effective for improving pattern recognition in images. Research explores novel hybrid descriptors combining Zernike moments with other statistical features, recursive and discriminant feature selection methods, and uses of orthogonal moments to produce compact, discriminative representations facilitating improved predictive accuracy in domains like face recognition and biomedical image classification.

Key finding: Showcased that vectors of orthogonal Zernike moments fed into a forward backpropagation neural network can effectively learn face localization boundaries, supporting a robust classification framework by leveraging rotation-... Read more
Key finding: Combined pseudo Zernike moments with Fisher's Linear Discriminant Analysis to extract discriminative moment-based features, resulting in significantly improved face recognition performance and stable classification even with... Read more
Key finding: Proposed a new hybrid shape descriptor combining Fourier coefficients with scalar parameters (Euler number and object count) derived from binary images representing Arabic handprints. Comparative studies with Zernike moments... Read more
Key finding: Demonstrated the effective use of Zernike moments in a hybrid framework combined with conventional discriminant classifiers to extract invariant features for real-time head pose and gaze estimation with improved accuracy,... Read more

All papers in Zernike moments

In the paper we present an approach to Introduce automation of brain CT image analysis Because CT Scan method that used especially for the diagnosis of stroke and can detect bleeding in stroke due to a blocked artery, of course Images... more
Floating-point arithmetics may lead to numerical errors when numbers involved in an algorithm vary strongly in their orders of magnitude. In the paper we study numerical stability of Zernike invariants computed via complex-valued integral... more
There are just too many trademarks out there so that a good automated retrieval system is required to help to protect them from possible infringements. However, it is from people, i.e., the general consumers' viewpoint how similar or... more
In this paper a method for extraction of mid-level semantics from sign language videos is proposed, by employing high level domain knowledge. The semantics concern labeling of the depicted objects of the head and the right/left hand as... more
The importance of the plant for the human being and the environment led to deeply been studied and classified in detail. The advancement of the technology is the main factor in finding many ways for plant identification process. Some kind... more
Most of Content Based Image Retrieval (CBIR) system use global texture features for representing and retrieving images. If local texture features are ignored during the initial stage of image processing, the performance will be affected.... more
Today, the number of registered trademarks is huge and is increasing rapidly. Thus, the job of identifying infringement of trademarks by solely using manual inspection is tiring, laborious and time consuming. To cope with the tremendous... more
The matching and retrieval of the 2D shapes are challenging issues in object recognition and computer vision. The principal idea in this paper focus to propose an robust descriptor for indexing and retrieval Arabic hand print character.... more
This paper represents a new approach for face recognition that incorporates Prewitt edge detection, Gabor filter and Zernike moments to transform the image into a unified domain. On this joint domain, five distance metrics are constructed... more
This paper reports the results of experiments in improving performance of leaf identification system using Principal Component Analysis (PCA). The system involved combination of features derived from shape, vein, color, and texture of... more
There are situations where it is not possible to capture a large document with a given imaging media such as scanner or copying machine in a single stretch because of their inherent limitations. This results in capturing a large document... more
The study presents a plant recognition system that uses image and data processing techniques for recognition. A lot of research has been going on to identify plants by their leaves and one of the features that is used is the shape of the... more
The study presents a plant recognition system that uses image and data processing techniques for recognition. A lot of research has been going on to identify plants by their leaves and one of the features that is used is the shape of the... more
Background and Objective: According to the World Health Organization, breast cancer is the main cause of cancer death among adult women in the world. Although breast cancer occurs indiscriminately in countries with several degrees of... more
Background and Objective: Every second, on average, 8 (eight) new malware are created. So, our goal is to propose an antivirus, endowed with artificial intelligence, able of identifying malwares through models based on fast training and... more
This paper represents a new approach for face recognition that incorporates Prewitt edge detection, Gabor filter and Zernike moments to transform the image into a unified domain. On this joint domain, five distance metrics are constructed... more
Handwritten signature is broadly utilized as personal verification in financial institutions ensures the necessity for a robust automatic signature verification tool. This tool aims to reduce fraud in all related financial transactions'... more
One of important components in an image retrieval system is selecting a distance measure to compute rank between two objects. In this paper, several distance measures were researched to implement a foliage plant retrieval system. Sixty... more
For finger-vein recognition, many successful methods, such as Line Tracking (LT), Maximum Curvature (MC) and Wide Line Detector (WL), have been proposed. Among these, LT has a very slow matching and featureextraction phase, and LT, MC and... more
For finger-vein recognition, many successful methods, such as Line Tracking (LT), Maximum Curvature (MC) and Wide Line Detector (WL), have been proposed. Among these, LT has a very slow matching and featureextraction phase, and LT, MC and... more
Floating-point arithmetics may lead to numerical errors when numbers involved in an algorithm vary strongly in their orders of magnitude. In the paper we study numerical stability of Zernike invariants computed via complex-valued integral... more
This paper describes an approach based on Zernike moments and Delaunay triangulation for localization of handwritten text in machine printed text documents. The Zernike moments of the image are first evaluated and we classify the text as... more
The last few years witnessed great and increasing use in the field of medical image analysis. These tools helped the Radiologists and Doctors to consult while making a particular diagnosis. In this study, we used the relationship between... more
One of important components in an image retrieval system is selecting a distance measure to compute rank between two objects. In this paper, several distance measures were researched to implement a foliage plant retrieval system. Sixty... more
Content based information retrieval is now a widely investigated issue that aims at allowing users of multimedia information systems to retrieve images coherent with a sample image. A way to achieve this goal is the automatic computation... more
One of important components in an image retrieval system is selecting a distance measure to compute rank between two objects. In this paper, several distance measures were researched to implement a foliage plant retrieval system. Sixty... more
Image edge is the most basic feature of image. Most of the classical edge detection methods are sensitive to noise, poor anti-interference performance.To overcome the limitations of the earlier work a new approach has been proposed for... more
In the paper, an effective method for reducing Geometrical Error (G.E) and Numerical Error (N.E) of Zernike moments is proposed. By running MATLAB for the proposed Zernike's algorithm, the results of our proposed methods have shown a... more
One of important components in an image retrieval system is selecting a distance measure to compute rank between two objects. In this paper, several distance measures were researched to implement a foliage plant retrieval system. Sixty... more
Leaf identification is a challenging research. So far, many approaches have been proposed. In this paper, an approach that combines Fourier descriptors with other shape features was investigated to identify 100 hundred kinds of leaves.... more
The paper proposes a new approach as a combination of the multiscale analysis and the Zernike moment based for detecting tampered image with the formation of copy – move forgeries. Although the traditional Zernike moment based technique... more
This paper presents a new method to classify facial expressions from frontal pose images. In our method, first Pseudo Zernike Moment Invariant (PZMI) was used to extract features from the global information of the images and then Radial... more
Center Symmetric Local Binary Pattern (CSLBP) is widely used in texture and object detection, but its utilization in image hashing is still limited. Image hashing is a powerful technique to identify whether image content is changed or... more
The rapid growth of digital imaging techniques and versatility among the images has motivated the development of Content Based Image Retrieval (CBIR). CBIR is the application of computer vision techniques which uses the visual contents to... more
The purpose of this project was to do a comparative study for content based image retrieval using DCT, DWT, LBP and curvelet transform texture descriptor. The aim is to investigate an efficient and effective technique for content based... more
Signature recognition is the process of verifying a writer’s identity by checking the signature against samples previously stored in the database. Several techniques such as the distance-based and statistical classifiers used for feature... more
This research focuses on image recognition of beef and pork. Beef as an example of halal food, while pork as haram food, especially for Muslims. This study used PNN classification and feature extraction methods. These images show some... more
So far, plant identification has challenges for several researchers. Various methods and features have been proposed. However, there are still many approaches could be investigated to develop robust plant identification systems. This... more
Purpose: Breast cancer is among the leading causes of cancer death among women. The occurrence of breast cancer is similar both in developed countries and in underdeveloped and developing nations, although mortality is higher in... more
Weapon detection is a vital need in dual-energy X-ray luggage inspection systems at security of airport and strategic places. In this paper, a novel weapon detection framework in high- energy images of X-ray dual-energy images based on... more
One of important components in an image retrieval system is selecting a distance measure to compute rank between two objects. In this paper, several distance measures were researched to implement a foliage plant retrieval system. Sixty... more
Recently, many approaches have been introduced by several researchers to identify plants. Now, applications of texture, shape, color and vein features are common practices. However, there are many possibilities of methods can be developed... more
So far, plant identification has challenges for several researchers. Various methods and features have been proposed. However, there are still many approaches could be investigated to develop robust plant identification systems. This... more
Several researches in leaf identification did not include color information as features. The main reason is caused by a fact that they used green colored leaves as samples. However, for foliage plants-plants with colorful leaves, fancy... more
Problem statement : One challenging research area nowadays is pattern recognition. Many applications lay under the field of pattern recognition such as face and iris recognition, speech recognition, texture discrimination and optical... more
The retrieval and classification of shape-based objects employing three descriptors-generic Fourier descriptor (GFD), Legendre moment descriptor (LMD), and wavelet Zernike moment descriptor (WZMD) are described. All three descriptors have... more
In most of classic plant identification methods a dichotomous or multi-access key is used to compare characteristics of leaves. Some questions about if the analyzed leaves are lobed, unlobed, simple or compound need to be answered to... more
This paper represents a new approach for face recognition that incorporates Prewitt edge detection, Gabor filter and Zernike moments to transform the image into a unified domain. On this joint domain, five distance metrics are constructed... more
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