Projection Distortion Research Articles

The Influence of Cognitive Distortions on the Administration of Justice in Civil and Economic Cases

Subjects of evidentiary activity when assessing evidence in civil and economic disputes, like any person, are faced with certain biases (distortions). One of these biases is cognitive distortions. Purpose of the work: based on the analysis of doctrinal sources in the field of psychology and law, to identify what distortions the subjects of procedural relations encounter and how they influence the legal decision made. Brief conclusions. The author identified the following ten cognitive distortions that influence the decisions made by participants in the process: “confirmation bias”, “extreme decision aversion”, “black and white thinking”, “projective distortion”, “framing”, “priming effect”, “anchor heuristic”, “planning fallacy”, “availability heuristic”, “hindsight”. Accordingly, when assessing evidence and exercising procedural rights, you should analyze your actions and the activities of other entities for the impact of the indicated distortions on them. This will lead to improvement of the procedure for adopting a legal and justified judicial act.

Unfolder: fast localization and image rectification of a document with a crease from folding in half

Presentation of folded documents is not an uncommon case in modern society. Digitizing such documents by capturing them with a smartphone camera can be tricky since a crease can divide the document contents into separate planes. To unfold the document, one could hold the edges potentially obscuring it in a captured image. While there are many geometrical rectification methods, they were usually developed for arbitrary bends and folds. We consider such algorithms and propose a novel approach Unfolder developed specifically for images of documents with a crease from folding in half. Unfolder is robust to projective distortions of the document image and does not fragment the image in the vicinity of a crease after rectification. A new Folded Document Images dataset was created to investigate the rectification accuracy of folded (2, 3, 4, and 8 folds) documents. The dataset includes 1600 images captured when document placed on a table and when held in hand. The Unfolder algorithm allowed for a recognition error rate of 0.33, which is better than the advanced neural network methods DocTr (0.44) and DewarpNet (0.57). The average runtime for Unfolder was only 0.25 s/image on an iPhone XR.

Integration of GNSS, Total Station, and Grid Controls: An Analysis of Combined Effect of Elevation of Topography and Map Projection Distortion to Solve the Distance Discrepancy

Heterogeneous measurements from various surveying methods need to be integrated to accomplish any survey project. The use of Global Navigation Satellite System (GNSS) and Total Station (TS) to establish a control framework along with utilizing existing national grid controls, for any survey project has been the standard practice. However, the successful integration of GNSS, TS, and existing grid controls could be challenging at times. Both survey professionals, and surveying stakeholders would benefit from the successful augmentation of heterogeneous measurements from GNSS, TS, and existing grid controls in order to provide a control framework for their survey project. In the past, the distance discrepancy/mismatch of GNSS-derived distance which is obtained from indirect measurements from GNSS survey and TS distance which is ground-based direct measurements, has created confusion. Herein, we have analyzed in detail, the combined effect of elevation of topography and map projection's distortion on the distance; demonstrate the magnitude of combined effect by numerical examples; tested this formulation with real-world GNSS and TS measurements. This way we proposed a solution to solve distance discrepancy/mismatch between various survey methods. The magnitude of the combined effect would be substantial with higher elevations and longer distances and could cross the threshold of specified/required accuracy. The effect would be more pronounced in mountainous regions suggesting combined effect should be properly taken into account. Taking combined effect into consideration brings the compatibility and comparability of GNSS, TS, and existing grid controls together. Thus, allowing both survey professionals and surveying stakeholders to utilize the mix of GNSS, TS, and existing grid controls to achieve required precision and accuracy in an economical, timely, and easy manner.

Dynamic Projection Method of Electronic Navigational Charts for Polar Navigation

Electronic navigational charts (ENCs) are geospatial databases compiled in strict accordance with the technical specifications of the International Hydrographic Organization (IHO). Electronic Chart Display and Information System (ECDIS) is a Geographic Information System (GIS) operated by ENCs for real-time navigation at sea, which is one of the key technologies for intelligent ships to realize autonomous navigation, intelligent decision-making, and other functions. Facing the urgent demand for high-precision and real-time nautical chart products for polar navigation under the new situation, the projection of ENCs for polar navigation is systematically analyzed in this paper. Based on the theory of complex functions, we derive direct transformations of Mercator projection, polar Gauss-Krüger projection, and polar stereographic projection. A rational set of dynamic projection options oriented towards polar navigation is proposed with reference to existing specifications for the compilation of the ENCs. From the perspective of nautical users, rather than the GIS expert or professional cartographer, an ENCs visualization idea based on multithread-double buffering is integrated into Polar Region Electronic Navigational Charts software, which effectively solves the problem of large projection distortion in polar navigation applications. Taking the CGCS2000 reference ellipsoid as an example, the numerical analysis shows that the length distortion of the Mercator projection is less than 10% in the region up to 74°, but it is more than 80% at very high latitudes. The maximum distortion of the polar Gauss-Krüger projection does not exceed 10%. The degree of distortion of the polar stereographic projection is less than 1% above 79°. In addition, the computational errors of the direct conversion formulas do not exceed 10−9 m throughout the Arctic range. From the point of view of the computational efficiency of the direct conversion model, it takes no more than 0.1 s to compute nearly 8 million points at 1′×1′ resolution, which fully meets the demand for real-time nautical chart products under information technology conditions.

Projection Distortion Effects Caused by Tip-Tilt of Fast Steering Mirror in Space Telescopes

Projection Distortion Effects Caused by Tip-Tilt of Fast Steering Mirror in Space Telescopes

Online measurement method for dimensions of disk parts based on machine vision.

Online measurement of disk part dimensions by the standard industrial camera features low cost, high efficiency and good universality, but the impact of projection distortion and end face chamfer on measurement is needed to overcome. Present work presents a measurement method to resolve above issues based on machine vision. To improve the measurement accuracy, lower end face of a disk part is determined as calibration plane and the upper end face is measurement plane. To reduce the impact of projection distortion and chamfer on measurement, the measurement points are reconstructed on the measurement plane by re-projection. Then, the inner and outer diameters of disk parts are measured by circle geometric fitting, and the thickness is calculated by the measurement plane position. The experimental results show that the method can online measure disk part dimensions just by a single image, and accuracy meets the requirements of universal grade disk parts.

Computational Quantification of Map Projection Distortion by Fractal Dimension of Coastlines

Computational Quantification of Map Projection Distortion by Fractal Dimension of Coastlines

On the Definition of Standard Parallels in Map Projections

The article belongs to the field of theoretical research on map projections. It is observed that there is no unique and generally accepted definition of standard parallels in the cartographic literature. For some authors, a standard line is a line along which there is no distortion, and for others, it is a line along which there is no distortion of length. At the same time, it is forgotten that the length distortions at any point generally change and depend on the direction. The main goal of this article is very simple: the sentence “linear deformation is zero in all directions” is expressed using a mathematical formula. Besides that, the paper introduces equidistance in a broader sense. This is a novelty in the theory of map projections. Equidistance is defined at a point, along a line and in an area, especially in the direction of the parallels and especially in the direction of the meridian. This enables an unambiguous definition of standard parallels. Theoretical considerations are illustrated with examples of cylindrical projections. The practical value of the proposed approach is manifested in the possibility of a better understanding of the distribution of distortions in any map projection used.

Modular CSI Quantization for FDD Massive MIMO Communication

We consider high-dimensional MIMO transmissions in frequency division duplexing (FDD) systems. For precoding, the frequency selective channel has to be measured, quantized and fed back to the base station by the users. When the number of antennas is very high this typically leads to prohibitively high quantization complexity and large feedback. In 5G New Radio (NR), a modular quantization approach has been applied for this, where first a low-dimensional subspace is identified for the whole frequency selective channel, and then subband channels are linearly mapped to this subspace and quantized. We analyze how the components in such a modular scheme contribute to the overall quantization distortion. Based on this analysis we improve the technology components in the modular approach and propose an orthonormalized wideband precoding scheme and a sequential wideband precoding approach which provide considerable gains over the conventional method. We compare the performance of the developed quantization schemes to prior art by simulations in terms of the projection distortion, overall distortion and spectral efficiency, in a scenario with a realistic spatial channel model.

Visual perception-oriented quality assessment for high dynamic range stereoscopic omnidirectional video system

High dynamic range stereoscopic omnidirectional video (HSOV) system provides users with an immersive visual experience, but the distortions generated in the process of visual content generation, coding, and visualization also brings challenges to visual quality assessment. This paper proposes a visual perception-oriented quality metric for HSOV system. Considering the computational efficiency, for frames within each second, several key frames are selected so that features reflecting distortions can be extracted from the viewports and equi-angular cubemap (EAC) projection surfaces of these frames. In viewport feature extraction module, the sum and difference maps of the left and right views of the key frames are used to simulate the binocular perception. Considering that distortions will affect the structure, color and statistical properties of the image, the gradient, local binary pattern and statistical features are extracted, respectively. To reduce projection distortion, EAC projection is used to instead of other projections normally used in quality assessment, and the Sigma domain feature extraction and color feature extraction are performed on EAC projection map. In temporal feature extraction module, wavelet decomposition is used to perform temporal domain bandpass filtering on partial continuous frames to calculate the naturalness features. Finally, the above features of the frames at different scales are pooled through random forest model to predicate the quality score of HSOV. Experimental results on the NBU-HSOVD dataset show that the proposed metric is superior to some blind image/video quality assessment metrics and has higher consistency with the human visual perception.

Crystal Analyzer Based Multispectral Microtomography Using CCD-Sensor.

To solve the problems of spectral tomography, an X-ray optical scheme was proposed, using a crystal analyzer in Laue geometry between the sample and the detector, which allowed for the selection of predetermined pairs of wavelengths from the incident polychromatic radiation to obtain projection images. On a laboratory X-ray microtomography setup, an experiment was carried out for the first time where a mixture of micro-granules of sodium chloride NaCl, silver behenate AgC22H43O2, and lithium niobate LiNbO3 was used as a test sample to identify their spatial arrangement. The elements were chosen based on the presence of absorption edges in two of the elements in the energy range of the polychromatic spectrum of the probing radiation. The method of projection distortion correction was used to preprocess the obtained projections. To interpret the obtained reconstruction results, the segmentation method based on the analysis of joint histograms was used. This allowed us to identify each of the three substances. To compare the results obtained, additional "reference" tomographic measurements were performed: one in polychromatic and two in monochromatic (MoKα-, MoKβ-lines) modes. It took three times less time for the tomographic experiment with the crystal analyzer, while the reconstruction accuracy was comparable to that of the "reference" tomography.

Sphere2Vec: A general-purpose location representation learning over a spherical surface for large-scale geospatial predictions

Generating learning-friendly representations for points in space is a fundamental and long-standing problem in machine learning. Recently, multi-scale encoding schemes (such as Space2Vec and NeRF) were proposed to directly encode any point in 2D or 3D Euclidean space as a high-dimensional vector, and has been successfully applied to various (geo)spatial prediction and generative tasks. However, all current 2D and 3D location encoders are designed to model point distances in Euclidean space. So when applied to large-scale real-world GPS coordinate datasets (e.g., species or satellite images taken all over the world), which require distance metric learning on the spherical surface, both types of models can fail due to the map projection distortion problem (2D) and the spherical-to-Euclidean distance approximation error (3D). To solve these problems, we propose a multi-scale location encoder called Sphere2Vec which can preserve spherical distances when encoding point coordinates on a spherical surface. We developed a unified view of distance-reserving encoding on spheres based on the Double Fourier Sphere (DFS). We also provide theoretical proof that the Sphere2Vec encoding preserves the spherical surface distance between any two points, while existing encoding schemes such as Space2Vec and NeRF do not. Experiments on 20 synthetic datasets show that Sphere2Vec can outperform all baseline models including the state-of-the-art (SOTA) 2D location encoder (i.e., Space2Vec) and 3D encoder NeRF on all these datasets with up to 30.8% error rate reduction. We then apply Sphere2Vec to three geo-aware image classification tasks - fine-grained species recognition, Flickr image recognition, and remote sensing image classification. Results on 7 real-world datasets show the superiority of Sphere2Vec over multiple 2D and 3D location encoders on all three tasks. Further analysis shows that Sphere2Vec outperforms other location encoder models, especially in the polar regions and data-sparse areas because of its nature for spherical surface distance preservation. Code and data of this work are available at https://gengchenmai.github.io/sphere2vec-website/.

A reconstruction method for volumetric tomography within two parallel transparent plates

Flame emission tomography is a powerful tool for spatially-resolved combustion diagnostics. Modalities for measuring both open and confined flames have been developed and found in extensive applications. However, the available methods for confined space are restricted to cylindrical enclosures. There is another common confinement, i.e., rectangular enclosure. The key characteristic of this confinement is two pairs of parallel transparent plates. The light will be refracted when passing through the plates, causing projection distortion. Another key point is the reflection of the plates, which will induce secondary projections. However, reflection is seldomly discussed in the literature. The existing methods for rectangular enclosure are all based on Zhang’s model [Seventh IEEE International Conference on Computer Vision (ICCV) (IEEE, 1999), Vol. 661, pp. 666–673], which ignores the refraction and reflection of the enclosure. As a result, this work proposes a modified calibration model, i.e., refraction-reflection model for volumetric tomography, which for the first time incorporates both the refraction and reflection processes. The synthetic calibration shows refraction of the plate can not only shift the projection but also rotate it. The simulation and experiment show that the imaging model based on Zhang’s model will not only wrongly estimate the position of the target, but also have a low accuracy. Nevertheless, the imaging model based on the refraction-reflection model can successfully resolve the above problems and show its superiority to the imaging model based on Zhang’s model.

Perception-Oriented U-Shaped Transformer Network for 360-Degree No-Reference Image Quality Assessment

Generally, 360-degree images have absolute senses of reality and three-dimensionality, providing a wide range of immersive interactions. Due to the novel rendering and display technology of 360-degree images, they have more complex perceptual characteristics than other images. It is challenging to perform comprehensive image quality assessment (IQA) learning by simply stacking multichannel neural network architectures for pre/postprocessing, compression, and rendering tasks. To thoroughly learn the global and local features in 360-degree images, reduce the complexity of multichannel neural network models and simplify the training process, this paper proposes a joint architecture with user perception and an efficient transformer dedicated to 360-degree no-reference (NR) IQA. The input of the proposed method is a 360-degree cube map projection (CMP) image. Furthermore, the proposed 360-degree NRIQA method includes a saliency map-based non-overlapping self-attention selection module and a U-shaped transformer (U-former)-based feature extraction module to account for perceptual region importance and projection distortion. The transformer-based architecture and the weighted average technique are jointly utilized for predicting local perceptual quality. Experimental results obtained on widely used databases show that the proposed model outperforms other state-of-the-art methods in NR 360-degree image quality evaluation cases. Furthermore, a cross-database evaluation and an ablation study also demonstrate the inherent robustness and generalization ability of the proposed model.

Toward Visual Behavior and Attention Understanding for Augmented 360 Degree Videos

Augmented reality (AR) overlays digital content onto reality. In an AR system, correct and precise estimations of user visual fixations and head movements can enhance the quality of experience by allocating more computational resources for analyzing, rendering, and 3D registration on the areas of interest. However, there is inadequate research to help in understanding the visual explorations of the users when using an AR system or modeling AR visual attention. To bridge the gap between the saliency prediction on real-world scenes and on scenes augmented by virtual information, we construct the ARVR saliency dataset. The virtual reality (VR) technique is employed to simulate the real-world. Annotations of object recognition and tracking as augmented contents are blended into omnidirectional videos. The saliency annotations of head and eye movements for both original and augmented videos are collected and together constitute the ARVR dataset. We also design a model that is capable of solving the saliency prediction problem in AR. Local block images are extracted to simulate the viewport and offset the projection distortion. Conspicuous visual cues in the local block images are extracted to constitute the spatial features. The optical flow information is estimated as an important temporal feature. We also consider the interplay between virtual information and reality. The composition of the augmentation information is distinguished, and the joint effects of adversarial augmentation and complementary augmentation are estimated. The Markov chain is constructed with block images as graph nodes. In the determination of the edge weights, both the characteristics of the viewing behaviors and the visual saliency mechanisms are considered. The order of importance for block images is estimated through the state of equilibrium of the Markov chain. Extensive experiments are conducted to demonstrate the effectiveness of the proposed method.

Vision measuring technology for the position degree of a hole group.

The hole is one of the most important geometric elements in mechanical parts. The center distance of a hole group measurement method based on machine vision is proposed for solving the influence of perspective distortion and improving the applicability of vision systems. In the method, the plane equation of the measured plane is obtained by the line structured light vision technology, and the process is free from the constraints of the calibration plate. In order to eliminate the effect of projection distortion on the measurement accuracy, a local coordinate system is established on the plane of the measured hole group, the hole diameter, and the center distance of the hole group, which could be calculated by the local coordinates of the hole edge points. In the experiment, the flange is taken as the measured object, the distances between the holes on the flange are obtained by the method proposed in this paper, and the measurement results compared with the data are obtained by a coordinate measuring machine (CMM). The experimental results show that the average measurement error of center distance is 0.0739mm, and the standard deviation is 0.0489mm.

Spherical Convolution Empowered Viewport Prediction in 360 Video Multicast with Limited FoV Feedback

Field of view (FoV) prediction is critical in 360-degree video multicast, which is a key component of the emerging virtual reality and augmented reality applications. Most of the current prediction methods combining saliency detection and FoV information neither take into account that the distortion of projected 360-degree videos can invalidate the weight sharing of traditional convolutional networks nor do they adequately consider the difficulty of obtaining complete multi-user FoV information, which degrades the prediction performance. This article proposes a spherical convolution-empowered FoV prediction method, which is a multi-source prediction framework combining salient features extracted from 360-degree video with limited FoV feedback information. A spherical convolutional neural network is used instead of a traditional two-dimensional convolutional neural network to eliminate the problem of weight sharing failure caused by video projection distortion. Specifically, salient spatial-temporal features are extracted through a spherical convolution-based saliency detection model, after which the limited feedback FoV information is represented as a time-series model based on a spherical convolution-empowered gated recurrent unit network. Finally, the extracted salient video features are combined to predict future user FoVs. The experimental results show that the performance of the proposed method is better than other prediction methods.

Feature Correspondences Increase and Hybrid Terms Optimization Warp for Image Stitching.

Feature detection and correct matching are the basis of the image stitching process. Whether the matching is correct and the number of matches directly affect the quality of the final stitching results. At present, almost all image stitching methods use SIFT+RANSAC pattern to extract and match feature points. However, it is difficult to obtain sufficient correct matching points in low-textured or repetitively-textured regions, resulting in insufficient matching points in the overlapping region, and this further leads to the warping model being estimated erroneously. In this paper, we propose a novel and flexible approach by increasing feature correspondences and optimizing hybrid terms. It can obtain sufficient correct feature correspondences in the overlapping region with low-textured or repetitively-textured areas to eliminate misalignment. When a weak texture and large parallax coexist in the overlapping region, the alignment and distortion often restrict each other and are difficult to balance. Accurate alignment is often accompanied by projection distortion and perspective distortion. Regarding this, we propose hybrid terms optimization warp, which combines global similarity transformations on the basis of initial global homography and estimates the optimal warping by adjusting various term parameters. By doing this, we can mitigate projection distortion and perspective distortion, while effectively balancing alignment and distortion. The experimental results demonstrate that the proposed method outperforms the state-of-the-art in accurate alignment on images with low-textured areas in the overlapping region, and the stitching results have less perspective and projection distortion.

Memory Efficient Local Features Descriptor for Identity Document Detection on Mobile and Embedded Devices

In this paper, we propose a data-driven approach to training a memory-efficient local feature descriptor for identity documents location and classification on mobile and embedded devices. The proposed algorithm for retrieving a dataset of patches is based on the specifics of document detection in smartphone camera-captured images with a template matching approach. The retrieved dataset of patches relevant to the domain, which includes splits for features training, features selection, and testing, is made public. We train a binary descriptor using the retrieved dataset of patches, each bit of the descriptor relies on a single computationally-efficient feature. To estimate the influence of different feature spaces on the descriptor performance, we perform descriptor training experiments using gradient-based and intensity-based features. Extensive experiments in identity document location and classification benchmarks showed that the resulting 128 and 192-bit descriptors which use gradient-based features outperformed a state-of-the-art 512-bit BEBLID descriptor for arbitrary keypoints matching in all cases except the cases of extreme projective distortions, being significantly more efficient in cases of low lighting. The 64-bit gradient-based descriptor obtained within the approach showed better quality than 128 and 256-bit BinBoost descriptors in scanned document images. To evaluate the influence of the descriptor size on the matching speed, we propose a model based on the required number of processor instructions for computing the Hamming distance between a pair of descriptors on various energy-efficient processor architectures.

Image correction for perspective projection distortion of cylindrical surface

Image correction for perspective projection distortion of cylindrical surface