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Linear Measurement
Published in Joanne Kirkpatrick Price, Basic Math Concepts, 2018
The circumference of any circle is about three times the length of its diameter. More precisely, it is about 3.14 times its diameter. This constant ratio between the lengths of the circumference and diameter of any circle is called Pi, represented by the Greek letter π. The equation for calculating the circumference can be written as: C=πD,orC=(3.14)(D)
Geometry
Published in Dan Zwillinger, CRC Standard Mathematical Tables and Formulas, 2018
A chord of a circle is a line segment between two of its points (Figure 4.21). A diameter is a chord that goes through the center, or the length of such a chord (therefore the diameter is twice the radius). Given two points P1=(x1,y1) $ P_{1} = (x_{1} , y_{1} ) $ and P2=(x2,y2) $ P_{2} = (x_{2} , y_{2} ) $ , there is a unique circle whose diameter is P1P2; its equation is (x-x1)(x-x2)+(y-y1)(y-y2)=0. $$ (x - x_{1} )(x - x_{2} ) + (y - y_{1} )(y - y_{2} ) = 0. $$
The circle and its properties
Published in John Bird, Higher Engineering Mathematics, 2017
The ratio circumferencediameter = a constant for any circle.
Application of Image Processing Techniques and Artificial Neural Network for Detection of Diseases on Brinjal Leaf
Published in IETE Journal of Research, 2022
Area: Area of the region can be calculated by finding the ROI. In general, the area of the region is defined as where Perimeter: Perimeter is one of the structural properties of the region which is obtained by finding the sum of the distances from each coordinate and to the next. The perimeter measurement can be distorted due to the infected nature of certain boundaries. Let us suppose, a(t) and b(t) denote the parametric coordinates of a curve enclosing a region S, then the perimeter of the region is given by Centroid: The geometrical centre of a body is known as centroid, which gives the centre mass of an infected part of the leaf image. The centroid represents a point that can be obtained by finding the mean of the coordinates. The centroid of a non-self-intersecting closed region is defined by n vertices , … , the point is given by the following equations where A is the regions of the affected area Diameter: The distance around an infected region of the leaf image is called the circumference. The distance across a circle through the centre is called the diameter. The radius of the circumference of an affected area, , where C is the circumference and is the diameter. Even though it is possible to extract a large set of features, only a small subset of them is used for classification. As the dimensionality of the feature vector increases, the amount of training data required also increases exponentially. Furthermore, there may be a strong correlation between different types of features and thus by fusing these features can produce a feature vector. The features are grouped into three following categories based on the prescribed information. The important challenge in this step is to find the most appropriate representation and select a subset of the features extracted from the infected part of the leaf. The intensity-based features provide information on the intensity (grey-level or colour) and histogram of the pixels located in the infected part of the image. The textural features provide information about the variation in the intensity of a surface and structure of the leaf. The structural features provide information about the size and shape of the infected region found on the leaf image. The feature vector contains combined feature of fusing: intensity, textural and structural data of the images.