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Ever since the first image of a coral reef was captured in 1885, people worldwide have been accumulating images of coral reefscapes that document the historic conditions of reefs. However, these innumerable reefscape images suffer from perspective distortion, which reduces the apparent size of distant taxa, rendering the images unusable for quantitative analysis of reef conditions. Here we solve this century-long distortion problem by developing a novel computer-vision algorithm, ReScape, which removes the perspective distortion from reefscape images by transforming them into top-down views, making them usable for quantitative analysis of reef conditions. In doing so, we demonstrate the first-ever ecological application and extension of inverse-perspective mapping—a foundational technique used in the autonomous-driving industry. The ReScape algorithm is composed of seven functions that (1) calibrate the camera lens, (2) remove the inherent lens-induced image distortions, (3) detect the scene's horizon line, (4) remove the camera-roll angle, (5) detect the transformable reef area, (6) detect the scene's perspective geometry, and (7) apply brute-force inverse-perspective mapping. The performance of the ReScape algorithm was evaluated by transforming the perspective of 125 reefscape images. Eighty-five percent of the images had no processing errors and of those, 95% were successfully transformed into top-down views. ReScape was validated by demonstrating that same-length transects, placed increasingly further from the camera, became the same length after transformation. The mission of the ReScape algorithm is to (i) unlock historical information about coral-reef conditions from previously unquantified periods and localities, (ii) enable citizen scientists and recreational photographers to contribute reefscape images to the scientific process, and (iii) provide a new survey technique that can rigorously assess relatively large areas of coral reefs, and other marine and even terrestrial ecosystems, worldwide. To facilitate this mission, we compiled the ReScape algorithm into a free, user-friendly App that does not require any coding experience. Equipped with the ReScape App, scientists can improve the management and prediction of the future of coral reefs by uncovering historical information from reefscape-image archives and by using reefscape images as a new, rapid survey method, opening a new era of coral-reef monitoring. [ABSTRACT FROM AUTHOR]

Along with other types of calculus, multiplicative calculus brings an entirely new perspective. Geometry now has a new field as a result of this new understanding. In this study, multiplicative differential geometry was used to explore peculiar surfaces. Multiplicative quaternions are also used to depict surfaces. Additionally, multiplicative differential geometry was used to generate the accretive surface subject, which is a developing subject. The derived surfaces' perspective silhouette curve equation is provided. The Bishop multiplicative frame was also established and applied when expressing surfaces along with these. Finally, the surfaces and perspective silhouette curves were visualized using Maple, and the equations were obtained. [ABSTRACT FROM AUTHOR]

Achieving precise 6 degrees of freedom (6D) pose estimation of rigid objects from color images is a critical challenge with wide-ranging applications in robotics and close-contact aircraft operations. This study investigates key techniques in the application of YOLOv5 object detection convolutional neural network (CNN) for 6D pose localization of aircraft using only color imagery. Traditional object detection labeling methods suffer from inaccuracies due to perspective geometry and being limited to visible key points. This research demonstrates that with precise labeling, a CNN can predict object features with near-pixel accuracy, effectively learning the distinct appearance of the object due to perspective distortion with a pinhole camera. Additionally, we highlight the crucial role of knowledge about occluded features. Training the CNN with such knowledge slightly reduces pixel precision, but enables the prediction of 3 times more features, including those that are not initially visible, resulting in an overall better performing 6D system. Notably, we reveal that the data augmentation technique of scale can interfere with pixel precision when used during training. These findings are crucial for the entire system, which leverages the Solve Perspective-N-Point (Solve-PnP) algorithm, achieving 6D pose accuracy within 1 ∘ and 7 cm at distances ranging from 7.5 to 35 m from the camera. Moreover, this solution operates in real-time, achieving sub-10ms processing times on a desktop PC. [ABSTRACT FROM AUTHOR]

Leibniz's manuscripts on perspective geometry remained unpublished and unknown until very recently. Among them, Scientia perspectiva stands out as the most complex and the most original. In this paper, we offer a thorough analysis of this manuscript, showing how Leibniz moves from perspective concepts fairly common at that time to a completely new idea of the practice that could have affected its entire history. This new science represents not only Leibniz's unique contribution to the development of perspective but also casts a new light on his own notion of space and geometry and their philosophical grounding. [ABSTRACT FROM AUTHOR]

The current highway abnormal event detection efficiency is low, the leakage rate is high, real-time poor, and so on, this paper proposed highway abnormal parking detection method based on space-time relationship. Firstly, it used the traffic flow frequency to quantify the split image and removed the smaller connectivity domain to extract the road surface information, then used the perspective geometry of the pinhole camera to normalize the same scale. It used YOLOv4 network to obtain the exact position of the vehicle target, and established the space-time information matrix. To detect abnormal region and the detection results can output by the update of the space-time matrix. The experimental results show that the accuracy of this method is 95% in long-distance scenes and 93% in crowded scenes. [ABSTRACT FROM AUTHOR]

Image stitching for two images without a global transformation between them is notoriously difficult. In this paper, noticing the importance of semantic planar structures under perspective geometry, we propose a new image stitching method which stitches images by allowing for the alignment of a set of matched dominant semantic planar regions. Clearly different from previous methods resorting to plane segmentation, the key to our approach is to utilize rich semantic information directly from RGB images to extract semantic planar image regions with a deep Convolutional Neural Network (CNN). We specifically design a module implementing our newly proposed clustering loss to make full use of existing semantic segmentation networks to accommodate region segmentation. To train the network, a dataset for semantic planar region segmentation is constructed. With the prior of semantic planar region, a set of local transformation models can be obtained by constraining matched regions, enabling more precise alignment in the overlapping area. We also use this prior to estimate a transformation field over the whole image. The final mosaic is obtained by mesh-based optimization which maintains high alignment accuracy and relaxes similarity transformation at the same time. Extensive experiments with both qualitative and quantitative comparisons show that our method can deal with different situations and outperforms the state-of-the-arts on challenging scenes. [ABSTRACT FROM AUTHOR]

Quantitative description of perspective geometries is a challenging task due to the complexities of geometric shapes. In this paper, we address this gap by proposing a new methodology based on variational autoencoders (VAE) to derive low‐dimensional and exploitable parameters of the perspective road geometry. First, road perspective images were generated based on different alignment scenarios. Then, a VAE was built to create a regularized and exploitable latent space from the data. The latent space is a compressed representation of perspective geometry, from which six latent parameters were derived. Without prior expert knowledge, four of the latent parameters were found to represent distinctive attributes of the geometry, such as visual curvature, slope, sight distance, and curve direction. The latent parameters provided quantitative measurements of how the design scheme looks like in perspective view. It was found that a road with low accident rate has low values for codes 4 and 5, high values for code 3, and low variance for codes 3 and 6. The trained VAE model also ensured accurate generation of the perspective images by decoding the latent parameters. Overall, this research advances the understanding of road design by considering the driver's perception. [ABSTRACT FROM AUTHOR]

The hand–eye measurements have recently been proven to be very efficient for spacecraft attitude determination relative to an ellipsoidal asteroid. However, the recent method does not guarantee full attitude observability for all conditions. This article refines this problem by taking the vector observations into account so that the accuracy and robustness of the spacecraft attitude estimation can be improved. The vector observations come from many sources including visual perspective geometry, optical navigation, and point clouds that frequently occur in aerospace electronic systems. Completely closed-form solutions along with their uncertainty descriptions are presented for the proposed problem. Experiments using our simulated dataset and real-world spacecraft measurements from National Aeronautics and Space Administration's Dawn spacecraft verify the effectiveness and superiority of the derived solution. [ABSTRACT FROM AUTHOR]

Noncontact optical imaging is frequently used in the inspection and metrology of stationary objects, including in particular the reconstruction of the 3-D surface profile. A technique, known as phase-measuring profilometry, involves projecting a sinusoidal pattern and then inferring the height of various points on the object by measuring the resulting phase changes at the respective locations. However, this method cannot be directly applied to systems involving moving objects, as the translation and the perspective geometry effect manifest as errors in the height calculations. In this paper, we report on an imaging and numerical surface profilometry with error compensation technology (INSPECT) measurement system that is tailored for moving objects. We model the imaging system that considers the nonlinear perspective geometry effect, and simplify to a first-order equation using Taylor series expansion. With this, we generalize the conventional phase shift algorithm, and develop the optimization procedures that can compute the height information effectively. We apply this technology to the INSPECT measurement system in semiconductor manufacturing and show significant improvement in accuracy and robustness. [ABSTRACT FROM PUBLISHER]

We outline the history of photogrammetry from the aspects of, perspective geometry, camera, platform, measure methods and measure instruments, and summarize previous contributions to photogrammetry. A brief review of computer vision history is given. The tight connections between computer vision and photogrammetry are discussed in terms of geometric principles, and some differences in applications are also considered. From the aspect of semantics, we analyze the development of remote sensing and its relations to machine learning and computer vision, including their common approaches and different applications. The prevailing deep learning raised from connectionism is also reviewed and its successful applications in photogrammetry are analyzed. At last, we expect that the future development of photogrammetry will be more tightly cross-integrated with computer vision, machine learning and artificial intelligence. [ABSTRACT FROM AUTHOR]

Luneburg's model has been the reference for experimental studies of visual space for almost seventy years. His claim for a curved visual space has been a source of inspiration for visual scientists as well as philosophers. The conclusion of many experimental studies has been that Luneburg's model does not describe visual space in various tasks and conditions. Remarkably, no alternative model has been suggested. The current study explores perspective transformations of Euclidean space as a model for visual space. Computations show that the geometry of perspective spaces is considerably different from that of Euclidean space. Collinearity but not parallelism is preserved in perspective space and angles are not invariant under translation and rotation. Similar relationships have shown to be properties of visual space. Alley experiments performed early in the nineteenth century have been instrumental in hypothesizing curved visual spaces. Alleys were computed in perspective space and compared with reconstructed alleys of Blumenfeld. Parallel alleys were accurately described by perspective geometry. Accurate distance alleys were derived from parallel alleys by adjusting the interstimulus distances according to the size-distance invariance hypothesis. Agreement between computed and experimental alleys and accommodation of experimental results that rejected Luneburg's model show that perspective space is an appropriate model for how we perceive orientations and angles. The model is also appropriate for perceived distance ratios between stimuli but fails to predict perceived distances. [ABSTRACT FROM AUTHOR]

Abstract: During his whole life, Leibniz attempted to elaborate a new kind of geometry devoted to relations and not to magnitudes, based on space and situation, independent of shapes and quantities, and endowed with a symbolic calculus. Such a “geometric characteristic” shares some elements with the perspective geometry: they both are geometries of situational relations, founded in a transformation preserving some invariants, using infinity, and constituting a general method of knowledge. Hence, the aim of this paper is to determine the nature of the relation between Leibnizʼs new geometry and the works on perspective, namely Desarguesʼ ones. [Copyright &y& Elsevier]

Abstract: We present a robust and automatic method for evaluating the accuracy of Crop/Weed discrimination algorithms. The proposed method is based on simulated agronomic images and a Crop/inter-row Weed discrimination algorithm can be divided into the two following steps. Firstly a crop row detection (Hough transform) is performed from the identification of the crop line vanishing point taking the opportunity of the perspective geometry of the scene. Afterwards, the discrimination between crop and weeds is done by a region-based segmentation method using a blob-colouring analysis and an inter-row Weed Infestation Rate (WIR) can be estimated. We propose to test and validate the robustness of this method on simulated images with perspective. To simulate photos taken from a virtual camera, a pinhole camera model is used and the field is modelled according to the spatial periodicity distribution of crop seedlings and the spatial distribution of weed species based on stochastic processes (Poisson process, Neyman–Scott aggregative process or a mixture of both). For each simulated image, the comparison between the initial inter-row WIR and the detected inter-row WIR informs us about the errors made by the algorithm. A pixel classification between the two classes – Crop and Weed – is performed in order to identify misclassification errors. This comparison demonstrates an accuracy of better than 85% is possible for inter-row weed detection. [Copyright &y& Elsevier]

Abstract: This paper presents a general method for weed infestation rate estimation for perspective wide-view images dedicated to real-time precision spraying. A colour camera was positioned above crop fields in order to get a wide angle view of crop rows in perspective. Before to test it on in-field images, the algorithm has been optimized on simulated images and its robustness face to different weed infestation rates is analysed. The proposed method can be divided into the two following steps. Firstly a crop row detection is performed from the identification of the vanishing point taking the opportunity of the perspective geometry of the scene. Hence, an algorithm based on a double Hough transform (DHT) is applied. Afterwards, the discrimination between crop and weeds is done by a region-based segmentation method using a blob colouring analysis. The DHT was proved to be applicable to different perspective angles and different spatial frequencies of crop seedlings. Based on the geometrical properties of the scene, the results showed that the DHT has been proved to be a reliable crop row detection method but the crop/weed discrimination algorithm needs to be optimized. The discussion focuses on the efficiency and the limits of this spatial method. [Copyright &y& Elsevier]

Two sources of document degradation are modeled: 1) perspective distortion that occurs while photocopying or scanning thick, bound documents; and 2) degradation due to perturbation in the optical scanning and digitization process: speckle blurr, jitter, and threshold. Perspective distortion is modeled by studying the underlying perspective geometry of the optical system of photocopiers and scanners. An Illumination model is described to account for the nonlinear intensity change occurring across a page In a perspective-distorted document. The optical distortion process is modeled morphologically. First, a distance transform on the foreground is performed; this is followed by a random inversion of binary pixels in which the probability of flip is a function of the distance of the pixel to the boundary of the foreground. Correlating the flipped pixels is modeled by a morphological closing operation. [ABSTRACT FROM AUTHOR]

In collective sports, reactive agility training methodologies allow to evaluate and improve the player performance, being able to consider a mixture of technical, tactical, physical, and psychological abilities, similarly to real game-play situations. In this article, we present a new methodology for reactive agility training (neural training), the technological setup for the methodology, and a new footstep tracking algorithm, as the key element for automating the speed data gathering process, necessary for obtaining the relevant variables of the neural training approach. This new methodology is oriented to accurately measure two of the most relevant variables for reactive agility training: total response time (sprint time) and response correctness, related to a stimuli sequence presented to a player. The stimuli were designed to properly represent realistic competitive conditions for player training, contextualized to soccer. In order to automate the gathering process, a new computer vision based automatic footstep detection algorithm has been integrated to the system. The algorithm combines Kalman Filters, segmentation techniques, and perspective geometry, for obtaining highly precise detections of the moment a relevant footstep occurs in real-time, reaching a precision higher than 97%. Plus, the algorithm does not require any special marker, invasive sensor, or clothing constraint on the player. [ABSTRACT FROM AUTHOR]

Geometric parameters that define the geometry of imaging systems are crucial for image reconstruction and image quality in x-ray computed tomography (CT). The problem of determining geometric parameters for an offset flat-panel cone beam CT (CBCT) system, a recently introduced modality with a large field of view, with the assumption of an unstable mechanism and geometric parameters that vary in each view, is considered. To accurately and rapidly find the geometric parameters for each projection view, we use the projection matrix method and design a dedicated phantom that is partially visible in all projection views. The phantom consists of balls distributed symmetrically in a cylinder to ensure the inclusion of the phantom in all views, and a large portion of the phantom is covered in the projection image. To efficiently use calibrated geometric information in the reconstruction process and get rid of approximation errors, instead of decomposing the projection matrix into actual geometric parameters that are manually corrected before being used in reconstruction, as in conventional methods, we directly use the projection matrix and its pseudo-inverse in projection and backprojection operations of reconstruction algorithms. The experiments illustrate the efficacy of the proposed method with a real offset flat-panel CBCT system in dental imaging. [ABSTRACT FROM AUTHOR]

It is well known that seven parameters completely describe a circular cone-beam geometry in either flat-panel X-ray computed tomography (CT) or single pinhole SPECT imaging. This paper considers the problem of determining one of the seven parameters only, the detector in-plane rotation or twist angle \eta. We describe a graphical procedure that can determine \eta independently of all other six parameters from a geometric calibration scan of point objects. Our method is exact in the ideal noise-free case and is general in that the other two out-of-plane detector rotation angles \theta and \phi can be nonzero. The calibration scan typically needs at least two point objects and an even number of projection views over a full 360^\circ data acquisition. Under certain conditions, projection data truncation or a short scan acquisition of 180^\circ+ fan angle can be accommodated without affecting the accuracy of the calibration result. The graphical method is equally applicable to rotational multipinhole SPECT geometry. In this case, the final result is averaged from the individual estimates considering each pinhole separately. We use computer simulations and a multipinhole SPECT experiment to demonstrate the accuracy and precision of the proposed method. [ABSTRACT FROM AUTHOR]