Log-polar Coordinate System Research Articles

Superposition of the Similarity Images by Contour

Superposition of the similarity images is implemented by the methodology with divided estimation of parameters. The offsets along the coordinate axes are estimated in the Cartesian coordinate system. The scale and the rotate are estimated in the log-polar coordinate system. The accurate estimation of parameters of similarity models (offsets, scale and rotate) is achieved by the iteration processing. Optimization of the processing time is achieved by contour comparison instead of the image comparison. The test data for experiment is image with the freight car. The decreasing of the processing time for the modified methodology of “contour comparison” was estimated by comparison with the source methodology of “image comparison”.

Real-Time Ship Tracking under Challenges of Scale Variation and Different Visibility Weather Conditions

Visual ship tracking provides crucial kinematic traffic information to maritime traffic participants, which helps to accurately predict ship traveling behaviors in the near future. Traditional ship tracking models obtain a satisfactory performance by exploiting distinct features from maritime images, which may fail when the ship scale varies in image sequences. Moreover, previous frameworks have not paid much attention to weather condition interferences (e.g., visibility). To address this challenge, we propose a scale-adaptive ship tracking framework with the help of a kernelized correlation filter (KCF) and a log-polar transformation operation. First, the proposed ship tracker employs a conventional KCF model to obtain the raw ship position in the current maritime image. Second, both the previous step output and ship training sample are transformed into a log-polar coordinate system, which are further processed with the correlation filter to determine ship scale factor and to suppress the negative influence of the weather conditions. We verify the proposed ship tracker performance on three typical maritime scenarios under typical navigational weather conditions (i.e., sunny, fog). The findings of the study can help traffic participants efficiently obtain maritime situation awareness information from maritime videos, in real time, under different visibility weather conditions.

A New Robust Reference Image Hashing System

The authentication and content protection of multimedia data is a challenging task in the present scenario. One solution is to generate the perceptual hash which essentially authenticates the multimedia data and can also be dealt with image database search problems. In this article, a novel system for generating an image hash is presented. The proposed system utilizes the global and local features in the hash generation process. The local features are obtained from non-linear scale-space based KAZE features. These KAZE features have the ability to capture the most stable point under several content preserving distortions. In contrast, first the input image is converted to a normalized image, it is transformed to the log-polar coordinate system, and then a reference image using the local contrast in the wavelet domain is obtained to extrcat the global features. An intermediate hash sequence is achieved by extracting the significant information from the reference image using the singular value decomposition. The final hash sequence combines both the vectors followed by the randomization process. Extensive experiments are conducted to demonstrate the feasibility and the robustness of the proposed hashing system against a wide range of intentional/unintentional distortions. Further, the comparative analysis with some state-of-the-art techniques validates the better discrimination of the proposed work.

SR-SYBA: A Scale and Rotation Invariant Synthetic Basis Feature Descriptor with Low Memory Usage

Feature description has an important role in image matching and is widely used for a variety of computer vision applications. As an efficient synthetic basis feature descriptor, SYnthetic BAsis (SYBA) requires low computational complexity and provides accurate matching results. However, the number of matched feature points generated by SYBA suffers from large image scaling and rotation variations. In this paper, we improve SYBA’s scale and rotation invariance by adding an efficient pre-processing operation. The proposed algorithm, SR-SYBA, represents the scale of the feature region with the location of maximum gradient response along the radial direction in Log-polar coordinate system. Based on this scale representation, it normalizes all feature regions to the same reference scale to provide scale invariance. The orientation of the feature region is represented as the orientation of the vector from the center of the feature region to its intensity centroid. Based on this orientation representation, all feature regions are rotated to the same reference orientation to provide rotation invariance. The original SYBA descriptor is then applied to the scale and orientation normalized feature regions for description and matching. Experiment results show that SR-SYBA greatly improves SYBA for image matching applications with scaling and rotation variations. SR-SYBA obtains comparable or better performance in terms of matching rate compared to the mainstream algorithms while still maintains its advantages of using much less storage and simpler computations. SR-SYBA is applied to a vision-based measurement application to demonstrate its performance for image matching.

Traffic sign recognition method for intelligent vehicles

Traffic sign recognition is one of the main components of intelligent transportation systems (ITS). It improves safety by informing the driver of the current state of the road, e.g., warnings, prohibitions, restrictions, and other information useful for driving. This paper presents a new road sign recognition method that is achieved in three main steps. The first step maps the input image from the Cartesian coordinate system to the log-polar one. The second step computes the histogram of oriented gradients, local binary pattern, and local self-similarity characteristics from the image represented in the log-polar coordinate system. The third step performs classification on the basis of the random forest classifier and the features computed in the second step. The proposed method has been tested on the German Traffic Sign Recognition Benchmark dataset, and the results obtained are satisfactory when compared to the state-of-the-art approaches.

Authorization Identification by Watermarking in Log-polar Coordinate System

Authorization Identification by Watermarking in Log-polar Coordinate System

基于对数极坐标及对称循环矩阵的形状特征描述

A fundamental requirement in shape retrieval algorithms is that the shape descriptor should be invariant to geometric transformations, such as scaling and rotation. In this paper, the shape boundary is represented in log-polar coordinate system, so that the shape scaling and rotation is translated into translation, which is a much simpler geometric transformation. As the boundary information is related to the starting point, the shape rotation makes the boundary point sequence circulate, which will affect rotational invariance. To eliminate the effect brought by boundary point sequence circulation, we first propose a theorem: for a circulant matrix of odd order, when the generator vector, which forms the first row of the matrix, is shifted circularly, the new formed circulant matrix has the same eigenvector. Based on this theorem, we first get odd number of boundary points using interpolation method, and then construct a corresponding symmetric circulant matrix, whose eigenvectors are used to describe the shape features. Based on the obtained features, we present a new retrieval algorithm that is invariant to translation, scale, and rotation. Experiment results show that the new algorithm is robust for retrieving moving target and non-rigid shapes, and it is also a time saving method and feasible in a real-time system, hence the new algorithm could effetely be applied on target detection and tracking.

Comparison of wave equation migration in logpolar and elliptic coordinates

We extend Riemannian wavefield extrapolation to pre- and post-stack migration using 2D logpolar coordinate system in order to enhance imaging of subsurface structures with imaging of dipping reflectors and turning waves. The logpolar coordinate is a coordinate system adequate for propagating both the source and receiver wavefields. The logpolar extrapolation wavenumber introduces an isotropic slowness model stretch to the single square root operator that enables the use of Cartesian finite-difference extrapolators for propagating wavefields in logpolar meshes. Wavefield extrapolation in this coordinate does not require any ray tracing at all and it can be readily extended to high-order finite-difference schemes since it is an analytic extrapolation operator. Two migration examples illustrate the advantages of the logpolar coordinate for imaging complex geological structures. We compared results of post- and pre-stack depth migration in logpolar and elliptic coordinate systems and we found that steeply dipping events can be better imaged in logpolar coordinate than in elliptic coordinate.

A semi-fragile watermarking algorithm for authenticating 2D CAD engineering graphics based on log-polar transformation

Copyright violation and illegal manipulation of digital data have been acute challenges for many sectors since the very same set of enabling techniques for generating and processing digital data started to emerge. Although traditional protective methods, such as encryption and digital signatures, have been in use for decades, their inability to provide protection after decryption and locating tampering has prompted the development of digital watermarking. In this paper, a semi-fragile watermarking algorithm for authenticating 2D CAD engineering graphics based on log-polar coordinate mapping is proposed. Firstly, the vertices are divided into groups, and for each group, the vertices for carrying a watermark are mapped to the log-polar coordinate system. Then the watermark is embedded in the mantissa of the real-valued log-polar coordinates via bit substitution. Theoretical analysis and experimental results show that the proposed algorithm is not only robust against incidental global operations such as rotation, translation and scaling, but can also detect and locate malicious attacks such as entity modification and entity addition/deletion.

Log-polar height maps for multiple range image registration

We propose a method for coarse registration of multiple range images that uses a log-polar height map (LPHM) as the key for establishing correspondence. The LPHM is a local height map orthogonally mapped on the tangent plane with the log-polar coordinate system. The input range images are roughly represented by signed distance field (SDF) samples. For each SDF sample, an LPHM is generated and is converted to an invariant feature vector. Point correspondence is established by a nearest neighbor search in feature space. The RANSAC algorithm is applied on the corresponding point pairs between each pair of range images, and the pairwise registration of input range images is determined by the extracted inlier point pairs. Finally, the global registration is determined by constructing a view tree, which is the spanning tree that maximizes the total number of inlier point pairs. The result of coarse registration is used as the initial state of the fine registration and modeling. The proposed method was tested on multiple real range image datasets.

Real Coded Genetic Algorithm for Optimal Parameters Selection in Circular Mellin Feature Extractors

Texture is an important clue in region-based segmentation of images. Robust rotation and scale-invariant texture are important for digital image libraries and multimedia databases. Texture feature extraction operators, which comprise linear filtering followed by postprocessing, are considered. The CMF (Circular Mellin Feature) represents the spectral decomposition of the image scene in the polar-log coordinate system and is invariant to both scale and orientation of the target texture pattern. CMFs are used for rotation and scale-invariant texture classification. The image and CMFs are correlated, due to which the unique shift invariance property of the correlator architecture is also coupled. CMFs are based on log polar coordinate system. In this paper we present Real coded Genetic Algorithm (RcGA) for the parameter selection of CMFs. The simple genetic algorithm (GA) is search algorithms based on the mechanics of natural selection and genetics. It involves copying and swapping partial strings of data. A modified genetic algorithm is the RcGA, which basically employs real value vectors for representation of the chromosomes, and is widely applied to many optimization problems.

Real-time restoration of images degraded by uniform motion blur in foveal active vision systems

Foveated, log-polar, or space-variant image architectures provide a high resolution and wide field workspace, while providing a small pixel computation load. These characteristics are ideal for mobile robotic and active vision applications, but have been little used due to the general lack of image processing tools that are applicable to the log-polar coordinate system. Recently, we have described a generalization of the Fourier transform (the fast exponential chirp transform), which allows frame-rate computation of full-field two-dimensional (2-D) frequency transforms directly in log-polar coordinates. In the present work, we show that is possible to achieve full-frame image de-blur at frame rate on a standard "PC" platform, using these methods, we illustrate this idea with a Wiener filter based restoration technique. The main contribution of this note is the implementation of (space-variant) image de-blur directly in log-polar coordinates, using the exponential chirp transform. The results show reasonable quality of de-blur, and suggest that these methods are relevant to applications in mobile image processing platforms in which real-time motion deblur is important, and for which it is not desirable to use extensive or custom fabricated hardware.

A finite difference calculation of forced convective heat transfer from an oscillating cylinder

A finite difference calculation of forced convective heat transfer from an oscillating cylinder is carried out using vorticity, stream function and temperature as the dependent variables. The non-dimensionalized vorticity transport and energy equations in a non-inertial frame attached to the cylinder, are solved in a rectangular grid, based on a log-polar coordinate system. The effects of cylinder oscillation in the in-line and transverse directions, on the time dependent average Nusselt number and the Nusselt number distribution on the cylinder surface are investigated for a Reynolds number of 200. Some of the numerical predictions are compared with experimental data available in the literature. In the case of the stationary cylinder, the average Nusselt number was found to oscillate at twice the natural shedding frequency. The heat transfer rate from the oscillating cylinder increases with the increasing velocity amplitude. In the case of transverse oscillation, the location of maximum local Nusselt number was found to oscillate between the upper and lower surface of the cylinder. Contour maps of vorticity, stream line and isotherms are presented and the physical aspects of the flow field are discussed.

On the advantages of polar and log-polar mapping for direct estimation of time-to-impact from optical flow

The application of an anthropomorphic retina-like visual sensor and the advantages of polar and log-polar mapping for visual navigation are investigated. It is demonstrated that the motion equations that relate the egomotion and/or the motion of the objects in the scene to the optical flow are considerably simplified if the velocity is represented in a polar or log-polar coordinate system, as opposed to a Cartesian representation. The analysis is conducted for tracking egomotion but is then generalized to arbitrary sensor and object motion. The main result stems from the abundance of equations that can be written directly that relate the polar or log-polar optical flow with the time to impact. Experiments performed on images acquired from real scenes are presented. >