Homographic Model Research Articles

Green-Blue Spaces and Population Density versus COVID-19 Cases and Deaths in Poland.

In the last year, in connection with the COVID-19 pandemic caused by the SARS-CoV-2 coronavirus, scientific papers have appeared in which the authors are trying to identify factors (including environmental) favoring the spread of this disease. This paper presents the spatial differentiation in the total number of COVID-19 cases and deaths during the full year (March 2020–March 2021) of the SARS-CoV-2 pandemic in Poland versus green-blue spaces (green—i.a. forests, orchards, meadows and pastures, recreational and rest areas, biologically active arable land; blue—lakes and artificial water reservoirs, rivers, ecological areas and internal waters) and population density. The analysis covers 380 counties, including 66 cities. This study used daily reports on the progress of the pandemic in Poland published by the Ministry of Health of the Republic of Poland and unique, detailed data on 24 types of land use available in the Statistics Poland database. Statistical relationships were determined between the above-mentioned environmental variables and the variables characterizing COVID-19 (cases and deaths). Various basic types of regression models were analysed. The optimal model was selected, and the determination coefficient, significance level and the values of the parameters of these relationships, together with the estimation error, were calculated. The obtained results indicated that the higher the number of green-blue spaces in individual counties, the lower the total number of COVID-19 infections and deaths. These relationships were described by logarithmic and homographic models. In turn, an increase in the population density caused an increase in COVID-19 cases and deaths, according to the power model. These results can be used in the current analysis of the spread of the pandemic, including the location of potential outbreaks. In turn, the developed models can be used as a tool in forecasting the development of the pandemic and making decisions about the implementation of preventive measures.

Kinetic pattern and microbial population dynamic characterization ofEscherichia coliandSalmonella enteritidisin Frankfurter sausage: An experimental and modeling study

AbstractConcerns over the safety of nitrite and its role in the formation of nitrosamines have aroused considerable interest in developing alternative antimicrobial agents to replace nitrite. Plant‐derived antimicrobial agents could serve against food spoilage and pathogens. For the first time in this study, three semiempirical kinetic models, that is, exponential, homographic, andn‐order kinetic models were established to describe the microbiological population pattern and dynamic behavior. TheEscherichia coliandSalmonella enteritidispopulation dynamics were investigated in Frankfurter sausage as a complex food system, contained four different antimicrobial redcurrant extract (RE) concentrations (0, 0.1, 0.2, and 0.4% wt/wt) at two temperatures (4 and 25°C) during 17 days storage. Furthermore, the results were compared with a neuro‐fuzzy system. Although, all three kinetic models showed a reasonable prediction accuracy, homographic kinetic model was the best for predicting antibacterial effects of RE againstE. coli(R2= 0.94–1,= 0.93–0.99,Q‐squared = 0.80–0.89, and RMSE = 0.21–0.68) and then‐order kinetic model did the best in describing the kinetic pattern ofS. enteritidis(R2= 0.97–0.99,= 0.94–0.99,Q‐squared = 0.85–0.93, RMSE = 0.06–0.74). The increase in the RE concentration and temperature resulted in the increase of kinetic parameters of microbial population decline rate and extent for both bacteria, significantly. Furthermore, all the homographic model parameters (except of equilibrium population,p∞) and all the kinetic model parameters withnorder (except of reaction order) the synergistic effect of temperature and concentration was clear. RE at 0.4% concentration induced 0.12 log colony forming unit (CFU)/gE. coliand 0.45 log CFU/gS. enteritidisequilibrium population (p∞) at 17th day of storage at 25°C. Compared toS. enteritidis,E. coliwas more sensitive to RE concentration at both temperatures.Practical applicationsMost formulations of the meat products contain nitrite as a main ingredient to prohibit the pathogenic bacteria growth. The results of the present study showed that all the three studied kinetic models (exponential, homographic, andn‐order kinetic models) appropriately modeled theS. enteritidisandE. colipopulation dynamics. Regarding the statistical parameters,n‐order and homographic kinetic models were found to be the best models for predicting antibacterial effects of RE againstS. enteritidisandE. coli, respectively. Furthermore,E. coliwas more sensitive against RE thanS. enteritidisin Frankfurter sausage samples at 4 and 25°C during 17 days storage. With the increase in the RE concentration at the constant temperature and with the increase in temperature at the constant extract concentration, the decline rate ofE. colipopulation increased significantly (p < .05), while the needed time for 50% reduction decreased; besides,S. enteritidispopulation dynamics showed the increase in the rate and extent of decline, and a decrease in the equilibrium microbial population at these conditions (p < .05). No significant differences were observed between the neuro‐fuzzy system results and semiempirical kinetic models in the prediction of microbiological population dynamic. Nevertheless, the novel semiempirical models presented important biological parameters, which provided a better understanding of the systems biological state than the neuro‐fuzzy system. These results could offer new perspectives in the field of microbiology.

Parallax beam: a vision-based motion estimation method robust to nearly planar scenes

In computer vision, the epipolar geometry embeds the geometrical relationship between two views of a scene. This geometry is degenerated for planar scenes as they do not provide enough constraints to estimate it without ambiguity. Nearly planar scenes can provide the necessary constraints to resolve the ambiguity. But classic estimators such as the 5-point or 8-point algorithm combined with a random sampling strategy are likely to fail in this case because a large part of the scene is planar and it requires lots of trials to get a nondegenerated sample. However, the planar part can be associated with a homographic model and several links exist between the epipolar geometry and homographies. The epipolar geometry can indeed be recovered from at least two homographies or one homgraphy and two noncoplanar points. The latter fits a wider variety of scenes, as it is unsure to be able to find a second homography in the noncoplanar points. This method is called plane-and-parallax. The equivalence between the parallax and the epipolar lines allows to recover the epipole as their common intersection and the epipolar geometry. Robust implementations of the method are rarely given, and we encounter several limitations in our implementation. Noisy image features and outliers make the lines not to be concurrent in a common point. Also off-plane features are unequally influenced by the noise level. We noticed that the bigger the parallax is, the lesser the noise influence is. We, therefore, propose a model for the parallax that takes into account the noise on the features location to cope with the previous limitations. We call our method the “parallax beam.” The method is validated on the KITTI vision benchmark and on synthetic scenes with strong planar degeneracy. The results show that the parallax beam improves the estimation of the camera motion in the scene with planar degeneracy and remains usable when there is not any particular planar structure in the scene.

OPTIMAL IMAGE STITCHING FOR CONCRETE BRIDGE BOTTOM SURFACES AIDED BY 3D STRUCTURE LINES

Abstract. Crack detection for bridge bottom surfaces via remote sensing techniques is undergoing a revolution in the last few years. For such applications, a large amount of images, acquired with high-resolution industrial cameras close to the bottom surfaces with some mobile platform, are required to be stitched into a wide-view single composite image. The conventional idea of stitching a panorama with the affine model or the homographic model always suffers a series of serious problems due to poor texture and out-of-focus blurring introduced by depth of field. In this paper, we present a novel method to seamlessly stitch these images aided by 3D structure lines of bridge bottom surfaces, which are extracted from 3D camera data. First, we propose to initially align each image in geometry based on its rough position and orientation acquired with both a laser range finder (LRF) and a high-precision incremental encoder, and these images are divided into several groups with the rough position and orientation data. Secondly, the 3D structure lines of bridge bottom surfaces are extracted from the 3D cloud points acquired with 3D cameras, which impose additional strong constraints on geometrical alignment of structure lines in adjacent images to perform a position and orientation optimization in each group to increase the local consistency. Thirdly, a homographic refinement between groups is applied to increase the global consistency. Finally, we apply a multi-band blending algorithm to generate a large-view single composite image as seamlessly as possible, which greatly eliminates both the luminance differences and the color deviations between images and further conceals image parallax. Experimental results on a set of representative images acquired from real bridge bottom surfaces illustrate the superiority of our proposed approaches.

OPTIMAL IMAGE STITCHING FOR CONCRETE BRIDGE BOTTOM SURFACES AIDED BY 3D STRUCTURE LINES

Crack detection for bridge bottom surfaces via remote sensing techniques is undergoing a revolution in the last few years. For such applications, a large amount of images, acquired with high-resolution industrial cameras close to the bottom surfaces with some mobile platform, are required to be stitched into a wide-view single composite image. The conventional idea of stitching a panorama with the affine model or the homographic model always suffers a series of serious problems due to poor texture and out-of-focus blurring introduced by depth of field. In this paper, we present a novel method to seamlessly stitch these images aided by 3D structure lines of bridge bottom surfaces, which are extracted from 3D camera data. First, we propose to initially align each image in geometry based on its rough position and orientation acquired with both a laser range finder (LRF) and a high-precision incremental encoder, and these images are divided into several groups with the rough position and orientation data. Secondly, the 3D structure lines of bridge bottom surfaces are extracted from the 3D cloud points acquired with 3D cameras, which impose additional strong constraints on geometrical alignment of structure lines in adjacent images to perform a position and orientation optimization in each group to increase the local consistency. Thirdly, a homographic refinement between groups is applied to increase the global consistency. Finally, we apply a multi-band blending algorithm to generate a large-view single composite image as seamlessly as possible, which greatly eliminates both the luminance differences and the color deviations between images and further conceals image parallax. Experimental results on a set of representative images acquired from real bridge bottom surfaces illustrate the superiority of our proposed approaches.

Estimation of fundamental matrix by using layer-by-layer iterative approach

Concerning the estimation of fundamental matrix in motion sequences under the unknown environment, a layerby-layer iterative approach was proposed. This approach was based on optimal robust estimation method, and added the constrained condition of motion continuity and multi-scale correspondence to reduce false correspondence. Then data inliers of model from high level were added into the data set of low level in order to update the data set and estimate the homographic model simultaneously. Finally, global optimization was done on bottom level to rectify the model. The experiments show that geometric transform error is no more than 2. 891 821 pixel and variance of error fluctuated range is no more than 0. 295 172pixel, both the mean and the fluctuated variance of error are reduced in some degree when the scene surface has relatively plentiful depth levels and good continuity from motion sequences.

Assessing foliar chlorophyll contents with the SPAD-502 chlorophyll meter: a calibration test with thirteen tree species of tropical rainforest in French Guiana

• Chlorophyll meters such as the SPAD-502 offer a simple, inexpensive and rapid method to estimate foliar chlorophyll content. However, values provided by SPAD-502 are unitless and require empirical calibrations between SPAD units and extracted chlorophyll values. • Leaves of 13 tree species from the tropical rain forest in French Guiana were sampled to select the most appropriate calibration model among the often-used linear, polynomial and exponential models, in addition to a novel homographic model that has a natural asymptote.• The homographic model best accurately predicted total chlorophyll content (μg cm−2 ) from SPAD units (R 2 = 0.89). Interspecific differences in the homographic model parameters explain less than 7% of the variation in chlorophyll content in our data set. • The utility of the general homographic model for a variety of research and management applications clearly outweighs the slight loss of model accuracy due to the abandon of the species’ effect.

Simultaneous two-view epipolar geometry estimation and motion segmentation by 4D tensor voting

We address the problem of simultaneous two-view epipolar geometry estimation and motion segmentation from nonstatic scenes. Given a set of noisy image pairs containing matches of n objects, we propose an unconventional, efficient, and robust method, 4D tensor voting, for estimating the unknown n epipolar geometries, and segmenting the static and motion matching pairs into n independent motions. By considering the 4D isotropic and orthogonal joint image space, only two tensor voting passes are needed, and a very high noise to signal ratio (up to five) can be tolerated. Epipolar geometries corresponding to multiple, rigid motions are extracted in succession. Only two uncalibrated frames are needed, and no simplifying assumption (such as affine camera model or homographic model between images) other than the pin-hole camera model is made. Our novel approach consists of propagating a local geometric smoothness constraint in the 4D joint image space, followed by global consistency enforcement for extracting the fundamental matrices corresponding to independent motions. We have performed extensive experiments to compare our method with some representative algorithms to show that better performance on nonstatic scenes are achieved. Results on challenging data sets are presented.

One-dimensional dense disparity estimation for three-dimensional reconstruction

We present a method for fully automatic three-dimensional (3D) reconstruction from a pair of weakly calibrated images in order to deal with the modeling of complex rigid scenes. A two-dimensional (2D) triangular mesh model of the scene is calculated using a two-step algorithm mixing sparse matching and dense motion estimation approaches. The 2D mesh is iteratively refined to fit any arbitrary 3D surface. At convergence, each triangular patch corresponds to the projection of a 3D plane. The proposed algorithm relies first on a dense disparity field. The dense field estimation modelized within a robust framework is constrained by the epipolar geometry. The resulting field is then segmented according to homographic models using iterative Delaunay triangulation. In association with a weak calibration and camera motion estimation algorithm, this 2D planar model is used to obtain a VRML-compatible 3D model of the scene.