Log-polar Coordinate Research Articles

All-optical geometric image transformations enabled by ultrathin metasurfaces

Image processing plays a vital role in artificial visual systems, which have diverse applications in areas such as biomedical imaging and machine vision. In particular, optical analog image processing is of great interest because of its parallel processing capability and low power consumption. Here, we present ultra-compact metasurfaces performing all-optical geometric image transformations, which are essential for image processing to correct image distortions, create special image effects, and morph one image into another. We show that our metasurfaces can realize binary image transformations by modifying the spatial relationship between pixels and converting binary images from Cartesian to log-polar coordinates with unparalleled advantages for scale- and rotation-invariant image preprocessing. Furthermore, we extend our approach to grayscale image transformations and convert an image with Gaussian intensity profile into another image with flat-top intensity profile. Our technique will potentially unlock new opportunities for various applications such as target tracking and laser manufacturing.

A global optimization generation method of stitching dental panorama with anti-perspective transformation.

To address the limitation of narrow field-of-view in local oral cavity images that fail to capture large-area targets at once, this paper designs a method for generating natural dental panoramas based on oral endoscopic imaging that consists of two main stages: the anti-perspective transformation feature extraction and the coarse-to-fine global optimization matching. In the first stage, we increase the number of matched pairs and improve the robustness of the algorithm to viewpoint transformation by normalizing the anti-affine transformation region extracted from the Gaussian scale space and using log-polar coordinates to compute the gradient histogram of the octagonal region to obtain the set of perspective transformation resistant feature points. In the second stage, we design a coarse-to-fine global optimization matching strategy. Initially, we incorporate motion smoothing constraints and improve the Fast Library for Approximate Nearest Neighbors (FLANN) algorithm by utilizing neighborhood information for coarse matching. Then, we eliminate mismatches via homography-guided Random Sample Consensus (RANSAC) and further refine the matching using the Levenberg-Marquardt (L-M) algorithm to reduce cumulative errors and achieve global optimization. Finally, multi-band blending is used to eliminate the ghosting due to unalignment and make the image transition more natural. Experiments show that the visual effect of dental panoramas generated by the proposed method is significantly better than that of other methods, addressing the problems of sparse splicing discontinuities caused by sparse keypoints, ghosting due to parallax, and distortion caused by the accumulation of errors in multi-image splicing in oral endoscopic image stitching.

Novel angular velocity estimation technique for plasma filaments.

Magnetic field aligned filaments such as blobs and edge localized mode filaments carry significant amounts of heat and particles to the plasma facing components and they decrease their lifetime. The dynamics of these filaments determine at least a part of the heat and particle loads. These dynamics can be characterized by their translation and rotation. In this paper, we present an analysis method novel for fusion plasmas, which can estimate the angular velocity of the filaments on frame-by-frame time resolution. After pre-processing, the frames are two-dimensional (2D) Fourier-transformed, then the resulting 2D Fourier magnitude spectra are transformed to log-polar coordinates, and finally the 2D cross-correlation coefficient function (CCCF) is calculated between the consecutive frames. The displacement of the CCCF's peak along the angular coordinate estimates the angle of rotation of the most intense structure in the frame. The proposed angular velocity estimation method is tested and validated for its accuracy and robustness by applying it to rotating Gaussian-structures. The method is also applied to gas-puff imaging measurements of filaments in National Spherical Torus Experiment plasmas.

Theoretical study of vortex beam generation based on geometric coordinate transformation

By performing a conformal optical mapping of an input beam from Cartesian to log-polar coordinates, we propose a method to generate vortex beam. By tilting the incident beam, a phase gradient is attached and evolves into a vortex phase due to the optical transformation. Thus, the topological charge of the generated vortex beam is continuously adjustable. With this method, vortex beams with integer and fractional orders are generated. The purity of the generated vortex beam is theoretically analyzed, as well as the possible effects of phase misalignment on the output vortex. The continuously tunable vortex beam achieved by this method is expected to be used in information processing and optical routing in optical communications.

Mapping spatial frequency preferences across human primary visual cortex.

Neurons in primate visual cortex (area V1) are tuned for spatial frequency, in a manner that depends on their position in the visual field. Several studies have examined this dependency using functional magnetic resonance imaging (fMRI), reporting preferred spatial frequencies (tuning curve peaks) of V1 voxels as a function of eccentricity, but their results differ by as much as two octaves, presumably owing to differences in stimuli, measurements, and analysis methodology. Here, we characterize spatial frequency tuning at a millimeter resolution within the human primary visual cortex, across stimulus orientation and visual field locations. We measured fMRI responses to a novel set of stimuli, constructed as sinusoidal gratings in log-polar coordinates, which include circular, radial, and spiral geometries. For each individual stimulus, the local spatial frequency varies inversely with eccentricity, and for any given location in the visual field, the full set of stimuli span a broad range of spatial frequencies and orientations. Over the measured range of eccentricities, the preferred spatial frequency is well-fit by a function that varies as the inverse of the eccentricity plus a small constant. We also find small but systematic effects of local stimulus orientation, defined in both absolute coordinates and relative to visual field location. Specifically, peak spatial frequency is higher for pinwheel than annular stimuli and for horizontal than vertical stimuli.

Rotation-aware correlation filters for robust visual tracking

Recent years have witnessed several modified discriminative correlation filter (DCF) models exhibiting excellent performance in visual tracking. A fundamental drawback to these methods is that rotation of the target is not well addressed which leads to model deterioration. In this paper, we propose a novel rotation-aware correlation filter to address the issue. Specifically, samples used for training of the modified DCF model are rectified when rotation occurs, rotation angle is effectively calculated using phase correlation after transforming the search patch from Cartesian coordinates to the Log-polar coordinates, and an adaptive selection mechanism is further adopted to choose between a rectified target patch and a rectangular patch. Moreover, we extend the proposed approach for robust tracking by introducing a simple yet effective Kalman filter prediction strategy. Extensive experiments on five standard benchmarks show that the proposed method achieves superior performance against state-of-the-art methods while running in real-time on single CPU.

A novel enhanced quantum image representation based on bit-planes for log-polar coordinates

Quantum image representation has a significant impact in quantum image processing. In this paper, a bit-plane representation for log-polar quantum images (BRLQI) is proposed, which utilizes $(n+4)$ or $(n+6)$ qubits to store and process a grayscale or RGB color image of $2^n$ pixels. Compared to a quantum log-polar image (QUALPI), the storage capacity of BRLQI improves 16 times. Moreover, several quantum operations based on BRLQI are proposed, including color information complement operation, bit-planes reversing operation, bit-planes translation operation and conditional exchange operations between bit-planes. Combining the above operations, we designed an image scrambling circuit suitable for the BRLQI model. Furthermore, comparison results of the scrambling circuits indicate that those operations based on BRLQI have a lower quantum cost than QUALPI. In addition, simulation experiments illustrate that the proposed scrambling algorithm is effective and efficient.

LPNet: Retina Inspired Neural Network for Object Detection and Recognition

The detection of rotated objects is a meaningful and challenging research work. Although the state-of-the-art deep learning models have feature invariance, especially convolutional neural networks (CNNs), their architectures did not specifically design for rotation invariance. They only slightly compensate for this feature through pooling layers. In this study, we propose a novel network, named LPNet, to solve the problem of object rotation. LPNet improves the detection accuracy by combining retina-like log-polar transformation. Furthermore, LPNet is a plug-and-play architecture for object detection and recognition. It consists of two parts, which we name as encoder and decoder. An encoder extracts images which feature in log-polar coordinates while a decoder eliminates image noise in cartesian coordinates. Moreover, according to the movement of center points, LPNet has stable and sliding modes. LPNet takes the single-shot multibox detector (SSD) network as the baseline network and the visual geometry group (VGG16) as the feature extraction backbone network. The experiment results show that, compared with conventional SSD networks, the mean average precision (mAP) of LPNet increased by 3.4% for regular objects and by 17.6% for rotated objects.

Quantum Representations and Scaling Up Algorithms of Adaptive Sampled-Data in Log-Polar Coordinates.

In log-polar coordinates, the conventional data sampling method is to sample uniformly in the log-polar radius and polar angle directions, which makes the sample at the fovea of the data denser than that of the peripheral. The central oversampling phenomenon of the conventional sampling method gives no more efficient information and results in computational waste. Fortunately, the adaptive sampling method is a powerful tool to solve this problem in practice, so the paper introduces it to quantum data processing. In the paper, the quantum representation model of adaptive sampled data is proposed first, in which the upper limit of the sampling number of the polar angles is related to the log-polar radius. Owing to this characteristic, its preparation process has become relatively complicated. Then, in order to demonstrate the practicality of the model given in the paper, the scaling up algorithm with an integer scaling ratio based on biarcuate interpolation and its circuit implementation of quantum adaptive sampled data is given. However, due to the special properties of the adaptive sampling method in log-polar coordinates, the interpolation process of adaptive sampled data becomes quite complicated as well. At the end of this paper, the feasibility of the algorithm is verified by a numerical example.

An Object Tracking Algorithm with Channel Reliability and Target Response Adaptation

In order to solve the problems of lower precision of target location in short-term occlusion and inaccurate of scale estimation of target in rotation by Spatial-Temporal Regularized Correlation Filters (STRCF), an object tracking algorithm with channel reliability and target response adaptation is proposed in this paper. In this algorithm, target response regularization is added to train target model. By updating the ideal target response function in the process of solving model, the target can be tracked again after being occluded for a short time. The reliability of each feature channel is evaluated by coefficient of channel reliability, which can improves the model's expression of the target. Scale filters can be trained in log-polar coordinates to improve the accuracy of scale estimation when target is rotating. The experimental results show that the proposed algorithm reduces 28.54 pixels in the average center position error and improves the average overlap rate by 22.8% compared with STRCF.

Image analysis by log-polar Exponent-Fourier moments

Moments, as a popular class of the global invariant image descriptors, have been widely used in image analysis, pattern recognition and computer vision applications. Exponent-Fourier moments (EFMs) are a new set of orthogonal moments based on exponential functions, which are suitable for image analysis and rotation invariant pattern recognition. However, EFMs lack natively the scaling-invariant property. In addition, they always suffer from high time complexity, numerical instability, and reconstruction error, especially for higher order of moments. In this paper, we introduce a class of scaling and rotation-invariant orthogonal moments, named Log-Polar Exponent-Fourier moments (LPEFMs), by extending the classical EFMs to the log-polar coordinates. Firstly, we redefined the EFMs’ basis functions in log-polar domain instead of Cartesian/polar coordinate domain in order to obtain the scaling-invariant property. Then, we develop a new framework for computing the LPEFMs by using pseudo-polar Fourier transform and frequency domain interpolation, which result in better image representation capability, numerical stability, and computational speed. Compared with the classical EFMs, the proposed LPEFMs have four advantages, scaling invariance, speed, accuracy and stability. Theoretical analysis and simulation results are provided to validate the proposed image moment and to compare its performance with previous works.

Robust Estimation of Similarity Transformation for Visual Object Tracking

Most of existing correlation filter-based tracking approaches only estimate simple axis-aligned bounding boxes, and very few of them is capable of recovering the underlying similarity transformation. To tackle this challenging problem, in this paper, we propose a new correlation filter-based tracker with a novel robust estimation of similarity transformation on the large displacements. In order to efficiently search in such a large 4-DoF space in real-time, we formulate the problem into two 2-DoF sub-problems and apply an efficient Block Coordinates Descent solver to optimize the estimation result. Specifically, we employ an efficient phase correlation scheme to deal with both scale and rotation changes simultaneously in log-polar coordinates. Moreover, a variant of correlation filter is used to predict the translational motion individually. Our experimental results demonstrate that the proposed tracker achieves very promising prediction performance compared with the state-of-the-art visual object tracking methods while still retaining the advantages of high efficiency and simplicity in conventional correlation filter-based tracking methods.

Logarithmically discretized model of bounce averaged gyrokinetics and its implications on tokamak turbulence

A logarithmically discretized model, which consists of writing the system in log polar coordinates in wave-number domain and reducing the nonlinear interactions to a sum over neighboring scales that satisfy the triad conditions, is proposed for bounce averaged gyrokinetics, where the energy dependence is kept over a semi-regular grid that allows quadrature calculations in order to guarantee quasi-neutrality. The resulting model is a cheaper implementation of nonlinear multi-scale physics involving trapped electron modes, trapped ion modes, and zonal flows, which can handle anisotropy. The resulting wave-number spectrum is anisotropic at large scales, where the energy injection is clearly anisotropic, but is isotropised rapidly, leading generally towards an isotropic k−4 spectrum for spectral potential energy density for fully kinetic system and a k−5 spectrum for the system with one adiabatic species. Zonal flow damping, which is necessary for reaching a steady state in this model, plays an important role along with electron adiabaticity. Interesting dynamics akin to predator-prey evolution is observed among zonal flows and similarly large scale but radially elongated structures.

The research of prediction model on intelligent vehicle based on driver’s perception

In the field of self-driving technology, the stability and comfort of the intelligent vehicle are the focus of attention. The paper applies cognitive psychology theory to the research of driving behavior and analyzes the behavior mechanism about the driver’s operation. Through applying the theory of hierarchical analysis, we take the safety and comfort of intelligent vehicle as the breakthrough point. And then we took the data of human drivers’ perception behavior as the training set and did regression analysis using the method of regression analysis of machine learning according to the charts of the vehicle speed and the visual field, the vehicle speed and the gaze point as well as the vehicle speed and the dynamic vision. At last we established linear and nonlinear regression models (including the logarithmic model) for the training set. The change in thinking is the first novelty of this paper. Last but not least important, we verified the accuracy of the model through the comparison of different regression analysis. Eventually, it turned out that using logarithmic relationship to express the relationship between the vehicle speed and the visual field, the vehicle speed and the gaze point as well as the vehicle speed and the dynamic vision is better than other models. In the aspect of application, we adopted the technology of multi-sensor fusion and transformed the acquired data from radar, navigation and image to log-polar coordinates, which makes us greatly simplify information when dealing with massive data problems from different sensors. This approach can not only reduce the complexity of the server’s processing but also drives the development of intelligent vehicle in information computing. We also make this model applied in the intelligent driver’s cognitive interactive debugging program, which can better explain and understand the intelligent driving behavior and improved the safety of intelligent vehicle to some extent.

Fast hyperbolic Radon transform represented as convolutions in log-polar coordinates

The hyperbolic Radon transform is a commonly used tool in seismic processing, for instance in seismic velocity analysis, data interpolation and for multiple removal. A direct implementation by summation of traces with different moveouts is computationally expensive for large data sets. In this paper we present a new method for fast computation of the hyperbolic Radon transforms. It is based on using a log-polar sampling with which the main computational parts reduce to computing convolutions. This allows for fast implementations by means of FFT. In addition to the FFT operations, interpolation procedures are required for switching between coordinates in the time-offset; Radon; and log-polar domains. Graphical Processor Units (GPUs) are suitable to use as a computational platform for this purpose, due to the hardware supported interpolation routines as well as optimized routines for FFT. Performance tests show large speed-ups of the proposed algorithm. Hence, it is suitable to use in iterative methods, and we provide examples for data interpolation and multiple removal using this approach.

Efficient Local Image Descriptors

We consider descriptors in polar and log-polar coordinates that produce compact description of the image near interest points. These descriptors may be used to establish one-to-one correspondence between points in two images. Algorithms to compute these descriptors are described and the results of a numerical experiment comparing them with SIFT and SURF descriptors are reported. The numerical experiment suggests that the proposed descriptors are highly efficient for finding conjugate points in two images.

Fast Algorithms and Efficient GPU Implementations for the Radon Transform and the Back-Projection Operator Represented as Convolution Operators

The Radon transform and its adjoint, the back-projection operator, can both be expressed as convolutions in log-polar coordinates. Hence, fast algorithms for the application of these operators can be constructed by using the FFT, if data is resampled at log-polar coordinates. Radon data is typically measured on an equally spaced grid in polar coordinates, and reconstructions are represented (as images) in Cartesian coordinates. Therefore, in addition to FFT, several steps of interpolation have to be conducted in order to apply the Radon transform and the back-projection operator by means of convolutions. However, in comparison to the interpolation conducted in Fourier-based gridding methods, the interpolation performed in the Radon and image domains will typically deal with functions that are substantially less oscillatory. Reasonable reconstruction results can thus be expected using interpolation schemes of moderate order. The approach also provides better control over the artifacts that can appear due t...

Image rotation-elimination based on a retina-like sensor

The pixels of a retina-like sensor are arranged in concentric rings, and the output image is given in log-polar coordinates. Thus, additional residual errors will not be produced when the output image is rotated. Therefore, retina-like sensors have obvious advantages and many prospects for applications in the fields of image rotation and rapid image rotation-elimination. In this study, a theory concerning the image rotation of a retina-like sensor is proposed, and a solution based on the theory is presented and realized for eliminating image rotation caused by camera rotation. The camera rotation angle is obtained using a microelectromechanical systems digital accelerometer and gyroscope; only the readout sequence of each row from static random-access memory must be changed to achieve image rotation-elimination. Several image rotation-elimination experiments have been performed which show that the proposed solution is simple, accurate, and rapid. This rapid image rotation-elimination method can be used in fields that require higher image rotation-elimination processing speeds.

A video zero-watermarking algorithm based on LPM

To resist geometrical attacks, the video zero watermarking algorithm based on log-polar transform presented in this paper. In our method, an original image transformed in log-polar coordinate after transformation of 2D DWT and 3D DCT. In experiment, the proposed method was evaluated the performance of resistance against attacks such as noise attack, rotation attack, compression attack and frame attack. The experiment results show that this algorithm can effectively resist against geometric attacks, and it has high robustness to the noise, filtering, compression and other common attacks. The bit error rate of the proposed algorithm is less than 0.06 for all tested attacks.

Mutual information optimization based dynamic log-polar image registration

Log-polar transformation (LPT) is widely used in image registration due to its scale and rotation invariant properties. Through LPT, rotation and scale transformation can be made into translation displacement in log-polar coordinates, and phase correlation technique can be used to get the displacement. In LPT based image registration, constant samples in digitalization processing produce less precise and effective results. Thus, dynamic log-polar transformation (DLPT) is used in this paper. DLPT is a method that generates several sample sets in axes to produce several results and only the effective results are used to get the final results by using statistical approach. Therefore, DLPT can get more precise and effective transformation results than the conventional LPT. Mutual information (MI) is a similarity measure to align two images and has been used in image registration for a long time. An optimal transform for image registration can be obtained by maximizing MI between the two images. Image registration based on MI is robust in noisy, occlusion and illumination changing circumstance. In this paper, we study image registration using MI and DLPT. Experiments with digitalizing images and with real image datasets are performed, and the experimental results show that the combination of MI with DLPT is an effective and precise method for image registration.