Perimeter Estimation Research Articles

Иглоподобные листовые органы хвойных. Часть I. Моделирование периметра поперечного сечения иглы

Despite the availability of measuring systems for estimating the surface area of leaf organs of higher plants, the need for simple standard methods for determining this indicator area remains relevant for plant physiologists. The methods for estimating the surface area of needle-like leaf organs of conifers, based on the geometry of an individual needle rest on the general principle of calculating the needle surface area as the product of its length by the perimeter of its cross-section. This makes the cross-section perimeter one of the most important parameters needed to characterize the needle surface area. The strong variability of this parameter depending on the species necessitates the development of individual models of the cross-section of individual needles. The aim of this study has been to create a universal model for estimating the needle cross-section perimeter, irrespective of the tree species. For the practical implementation of the aim, a method was proposed for estimating the perimeter of the needle cross-section, based on the well-known fact that any closed line is transformable into an equivalent circle, while the length of the closed line does not change. The perimeter of the equivalent circle can be related to the parameters of the geometric figure before the transformation. This approach allows us to relate the width and thickness of the needle cross-section to its perimeter. The developed universal model of the needle cross-section has been verified on cross-sections of Siberian fir (Abies sibirica L.) and common juniper (Juniperus communis L.) needles. The samples of needles of these woody plants have been collected from a bilberry-sphagnum spruce forest in the boreal zone of the north-east of the European part of Russia (Knyazhpogostkiy district, the Komi Republic). Statistical analysis has shown the significance and adequacy of the model. It can be used to assess the perimeter of coniferous needles, irrespective of their species. In this case, the accuracy of perimeter estimation is comparable to the accuracy of direct perimeter measurement by the piecewise linear approximation method.

On the perimeter estimation of pixelated excursion sets of two‐dimensional anisotropic random fields

AbstractWe are interested in creating statistical methods to provide informative summaries of random fields through the geometry of their excursion sets. To this end, we introduce an estimator for the length of the perimeter of excursion sets of random fields on observed over regular square tilings. The proposed estimator acts on the empirically accessible binary digital images of the excursion regions and computes the length of a piecewise linear approximation of the excursion boundary. The estimator is shown to be consistent as the pixel size decreases, without the need of any normalization constant, and with neither assumption of Gaussianity nor isotropy imposed on the underlying random field. In this general framework, even when the domain grows to cover , the estimation error is shown to be of smaller order than the side length of the domain. For affine, strongly mixing random fields, this translates to a multivariate Central Limit Theorem for our estimator when multiple levels are considered simultaneously. Finally, we conduct several numerical studies to investigate statistical properties of the proposed estimator in the finite‐sample data setting.

High Precision Individual Tree Diameter and Perimeter Estimation from Close-Range Photogrammetry

Close-range photogrammetry (CRP) can be used to provide precise and detailed three-dimensional data of objects. For several years, CRP has been a subject of research in forestry. Several studies have focused on tree reconstruction at the forest stand, plot, and tree levels. In our study, we focused on the reconstruction of trees separately within the forest stand. We investigated the influence of camera lens, tree species, and height of diameter on the accuracy of the tree perimeter and diameter estimation. Furthermore, we investigated the variance of the perimeter and diameter reference measurements. We chose four tree species (Fagus sylvatica L., Quercus petraea (Matt.) Liebl., Picea abies (L.) H. Karst. and Abies alba Mill.). The perimeters and diameters were measured at three height levels (0.8 m, 1.3 m, and 1.8 m) and two types of lenses were used. The data acquisition followed a circle around the tree at a 3 m radius. The highest accuracy of the perimeter estimation was achieved when a fisheye lens was used at a height of 1.3 m for Fagus sylvatica (root mean square error of 0.25 cm). Alternatively, the worst accuracy was achieved when a non-fisheye lens was used at 1.3 m for Quercus petraea (root mean square error of 1.27 cm). The tree species affected the estimation accuracy for both diameters and perimeters.

Evaluating the walking perimeter in patients with spinal stenosis. A comparison between clinical interview and standardized walk test at comfortable speed

Gait dysfunctions are common in patients with spinal stenosis. In fact, these patients may present intermittent radicular claudication, which result in a decreased walking perimeter. Thus in these patients, the walking perimeter reveals the impact of the disease on quality of life and accounts for the therapeutic decision, notably surgical. Usually, in clinical practice, walking perimeter is assessed by a medical interview. Some authors highlight the error of subjective verbal quantification. Therefore, the main objective was to quantify the difference between the walking perimeter determined using either a medical interview or a walk test at comfortable speed. The secondary objective was to correlate functional tests with walking perimeter. In this monocentric study, each patient was asked to verbally estimate his walking perimeter during a preoperative consultation. Walking perimeter was then evaluated using a walking test at comfortable speed in which the patient walked a maximal distance. Functional muscular tests (Sorensen and Shirado) were also performed. Twenty patients have been included (age: 68.9 ± 8.6 years, BMI: 28.7 ± 3.5 kg.m −2 ). During medical interview, patients reported a significantly lower average walking perimeter than during walk test (317 ± 178 m and 442 ± 99 m respectively; P < 0.05). Among functional tests (Shirado: 84.2 ± 51.0 s; Sorensen: 75.4 ± 39.1 s), only Shirado test was correlated with walking perimeter assessed by walk test (Shirado: r = 0.48; P = 0.03) whereas no correlation was found for walking perimeter assessed by medical interview. Our study confirms previous results showing that subjective walking perimeter estimation is not a valid outcome. Patients with spinal stenosis underestimated their actual walking perimeter during the preoperative consultation. Thus comfortable walk test should be used in clinical practice to quantify the walking perimeter in patients with spinal stenosis, and more broadly, because it seems correlated to functional capacities of patients. The underlying reasons explaining the difference observed need to be explored.

An efficient algorithm to decompose a compound rectilinear shape into simple rectilinear shapes

Detection of a compound object is a critical problem in target recognition. For example, buildings form an important class of shapes whose recognition is important in many remote sensing based applications. Due to the coarse resolution of imaging sensors, adjacent buildings in the scenes appear as a single compound shape object. These compound objects can be represented as the union of a set of disjoint rectilinear shaped objects. Separating the individual buildings from the resulting compound objects in a segmented image is often difficult but important nevertheless. In this paper we propose a new and efficient technique to decompose a compound shape into a set of simple rectilinear shapes. First, the true interior and exterior corner points of the compound object are extracted. A modified corner detector based on polygonal approximation is proposed to accurately determine the boundaries of compound shapes. The compound shape is then split at the interior corner points to minimize the difference between the perimeter of the compound object and the sum of the perimeters of the decomposed objects. We have systematically compared the results our algorithm with those of existing approaches and the results show that the proposed algorithm is more accurate than the algorithms in the literature in terms of accuracy of perimeter estimation and computational cost.

Polygonal estimation of planar convex-set perimeter from its two projections

This paper deals with the problem of extracting qualitative and quantitative information from few tomographic projections of an object without reconstructing this object. It focuses on the extraction of quantitative information, precisely the border perimeter estimation for a convex set from horizontal and vertical projections. In the case of a multiple reconstruction, lower and upper bounds for the perimeter are established. In the case of a unique reconstruction, we give conditions and a method for constructing an inscribed polygon in a convex set only from the convex-set projections. An inequality on border perimeter is proved when a convex set is included in another one. The convergence of the polygon perimeter, when the number of vertices increases, is established for such polygons.

Superresolution border segmentation and measurement in remote sensing images

Segmentation and measurement of linear characteristics in remote sensing imagery are among the first stages in several geomorphologic studies, including the length estimation of geographic features such as perimeters, coastal lines, and borders. However, unlike area measurement algorithms, widely used methods for perimeter estimation in digital images have high systematic errors. No precision improvement can be achieved with finer spatial resolution images because of the inherent geometrical inaccuracies they commit. In this work, a superresolution border segmentation and measurement algorithm is presented. The method is based on minimum distance segmentation over the initial image, followed by contour tracking using a superresolution enhancement of the marching squares algorithm. Thorough testing with synthetic and validated field images shows that this algorithm outperforms traditional border measuring methods, regardless of the image resolution or the orientation, size, and shape of the object to be analyzed.

Uniqueness results for nonlocal Hamilton–Jacobi equations

We are interested in nonlocal eikonal equations describing the evolution of interfaces moving with a nonlocal, non-monotone velocity. For these equations, only the existence of global-in-time weak solutions is available in some particular cases. In this paper, we propose a new approach for proving uniqueness of the solution when the front is expanding. This approach simplifies and extends existing results for dislocation dynamics. It also provides the first uniqueness result for a Fitzhugh–Nagumo system. The key ingredients are some new perimeter estimates for the evolving fronts as well as some uniform interior cone property for these fronts.

Interior sphere property for level sets of the value function of an exit time problem

We consider an optimal control problem for a system of the form ˙ x = f(x,u), with a running cost L. We prove an interior sphere property for the level sets of the corresponding value function V. From such a property we obtain a semiconcavity result for V , as well as perimeter estimates for the attainable sets of a symmetric control system. Mathematics Subject Classification. 93B03, 49L20, 49L25

Camera calibration using a genetic algorithm

An autonomous robot will have to detect moving obstacles online before it can plan its collision-free path, while navigating in a dynamic environment. The robot collects information about the environment with the help of a camera and determines the inputs for its motion planner through image analysis. The present article deals with issues related to camera calibration and online image processing. The problem of camera calibration is treated as an optimization problem and solved using a genetic algorithm so as to achieve minimum distorted image plane error. The calibrated vision system is then utilized for the detection and identification of the objects by analysing the images collected at regular intervals. For image processing, five different operations, such as median filtering, thresholding, perimeter estimation, labelling and size filtering, have been carried out. To show the effectiveness of the developed camera-based vision system, inputs of the motion planner of a navigating robot are calculated for two different cases. It is observed that online detection of the shapes and configurations of the obstacles is possible by using the vision system developed.

Ahlfors type estimates for perimeter measures in Carnot-Carathéodory spaces

We study the relationship between the geometry of hypersurfaces in a Carnot-Carathéodory (CC) space and the Ahlfors regularity of the corresponding perimeter measure. To this end we establish comparison theorems for perimeter estimates between an hypersurface and its tangent space, and between a CC geometry and its “tangent” Carnot group structure.

Effects of polyline simplification of dynamic GPS data under forest canopy on area and perimeter estimations

The objectives of this study were to determine Global Positioning System (GPS) positional errors while moving under the forest canopy and to clarify the effects of polyline simplification on area and perimeter estimations. We used the Pathfinder Pro XR and GPSMAP 76S, which are categorized as “high-end mapping” and “general navigation” GPS receivers, respectively. The field tests were conducted in both natural and plantation forests. The results showed that the Pathfinder Pro XR, which has better multipath rejection technology, worked well, especially in the plantation forest under unfavorable conditions of higher stand density. We used analysis of variance to clarify the effects of the receiver type, positioning mode, stand type, and polyline simplification method on area and perimeter estimations. The receiver type and positioning mode were found to be significant factors that affected area estimation. The Pathfinder Pro XR estimated the area more accurately than the GPSMAP 76S, and differential GPS estimated the area more accurately than autonomous GPS. With respect to the perimeter, the receiver type, positioning mode, and polyline simplification method were found to be significant factors. The results showed that perimeter estimation was improved by using the velocity filter, and further improved by using the velocity filter and Douglas-Peucker algorithm, especially when the Pathfinder Pro XR was used. The GPSMAP 76S estimated the perimeter accurately without any filtering because its default speed filter worked well, even though the GPSMAP 76S is a general navigation GPS receiver.

Alternative Tilings for Improved Surface Area Estimates by Local Counting Algorithms

In this paper, we first review local counting methods for perimeter estimation of piecewise smooth binary figures on square, hexagonal, and triangular grids. We verify that better perimeter estimates, using local counting algorithms, can be obtained using hexagonal or triangular grids. We then compare surface area estimates using local counting techniques for binary three-dimensional volumes under the three semi-regular polyhedral tilings: the cubic, truncated octahedral, and rhombic dodecahedral tilings. It is shown that for surfaces of random orientation with a uniform distribution, the expected error of surface area estimates is smaller for the truncated octahedral and rhombic dodecahedral tilings than for the standard cubic or rectangular prism tilings of space. Additional properties of these tessellations are reviewed and potential applications of better surface area estimates are discussed.

Design of perimeter estimators for digitized planar shapes

Measurement of perimeters of planar shapes from their digitized images is an important task of computer vision systems. A general methodology for the design of simple and accurate parameter estimation algorithms is described. It is based on minimizing the maximum estimation error for digitized straight edges over all orientations. Two perimeter estimators are derived and their performance is tested and digitized circles using computer simulations. The experimental results may be used to predict the performance of the algorithm on shapes with arbitrary contours of continuous curvature. The simulations also show that fast and accurate perimeter estimation is possible, even for objects that are small relative to pixel size. >

Fractal Description of the Structure of Fresh and Eroded Aluminum shot fineparticles

AbstractFractal dimensions are numbers between the classical whole number dimensions which can be used to describe the ruggedness of a fineparticle boundary. This communication explores the utility of fractal dimensions between 1 and 2 for characterizing the ruggedness of fineparticle profiles. This type of fractal boundary is evaluated by estimating the perimeter of a profile of a fineparticle at various levels of scrutiny and then plotting a graph of the logarithm of the perimeter estimates against the logarithm of a unit representing the scale of scrutiny. Such a graph is known as a Richardson plot. Boundaries describable by fractal dimensions exhibit characteristic datalines on this type of graph.Aluminum shot fineparticles produced by the break up of turbulent jet of molten metal have irregular shapes because of the fluid turbulence in the regions where they solidify, but a smooth texture because of the effect of surface tension forces as the fineparticle solidifies. It is shown in this communication that the dataline on a Richardson plot of the estimated perimeter of an aluminum shot fineparticle consists of two regions. The first portion, at coarse levels of scrutiny, permits the calculation of a fractal dimension descriptor of the ruggedness of the profile. A second dataline at high resolution is parallel to the scrutiny axis indicating that at such levels of inspection the profile is effectively smooth and euclidean. Studies are reported of the changes in the ruggedness of an eroding aluminum shot fineparticle suspended in acid. It is shown that fractals can be used to describe the progress of corrosion and that, as corrosion proceeds, the euclidean portion of the Richardson plot of perimeter estimate recedes and disappears within the levels of scrutiny employed in these experiments.