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Cultural Differences between Materials Science and Image Processing
Published in Jeffrey P. Simmons, Lawrence F. Drummy, Charles A. Bouman, Marc De Graef, Statistical Methods for Materials Science, 2019
Mary Comer, Charles A. Bouman, Jeffrey P. Simmons
Before Kolmogorov, there were two commonly used methods: (1) the counting approach and (2) the relative frequency approach. The counting approach simply defines the probability of an event to be the number of outcomes in the event divided by the total number of possible outcomes. For example, the probability of rolling an even number on a six-sided die would be 1/2, since 2, 4, and 6 are even and there are 6 possibilities. Note that the counting approach assumes that all events that contain the same number of outcomes are equally likely. In the relative frequency approach, the probability of an event is defined as the relative frequency with which the event occurs in repeated independent trials of an experiment. For example, if we are interested in the accuracy of a test on a known standard, we can run n tests and count the number of times that the correct result was obtained (nc). The relative frequency of success is ncn. Practically, this number will be dependent upon the specific experiments run, but it can be extended using an asymptotic relative frequency, limn→∞ncn.
Modeling and Calibration
Published in Stephen Horan, Introduction to PCM Telemetering Systems, 2018
One of the most intuitive methods for representing the concept of the probability that an event will occur is using the relative frequency probability definition. If A is an event, for example, winning at 21, losing a baseball game, or having a meteor hit your car, the probability, p(A), out of a total sample of N events is related to the number of times the event A occurs, n(A), by the equation: () p(A)=limN→∞n(A)N
Introduction to Probability Theory
Published in Khalid Khan, Tony Lee Graham, Engineering Mathematics with Applications to Fire Engineering, 2018
It is not always possible to assign a probability using equally likely outcomes. If someone wanted to know the probability of going to the bus stop and having to wait for a bus for more than 5 minutes, then some trials would have to be done to find the waiting times. The relative frequency of an event is the proportion of times it has been observed to happen. If somebody went for a bus on 40 weekday mornings and on 16 of these they had to wait more than 5 minutes, one could assign a probability of 1640 = 0.4 to the event of having to wait more than 5 minutes.
Fast retrieval and efficient identification of monument images using features based adaptive clustering and optimized deep belief network
Published in The Imaging Science Journal, 2023
Jaimala Jha, Sarita Singh Bhaduaria
The statistical evaluations are deployed for extracting the texture features from the real Gabor-filtered HH component of the image and DWT high-level highpass (HH) subband [41]. For extracting the features from the monument images, uniformity and entropy were chosen. Because both the information are hypothesized to distinguish the image with the same contrast data, the frequent changes in texture. The mathematical formula for entropy and uniformity is given in equation (12). Where is denoted as the probability of occurrence as evaluated by its relative frequency. The random variable is indicated as , which is a coefficient in Gabor filtered image. Moreover, the feature vector for every DWT image is defined in the following equation:
Experimental study of the fiber orientations in single and multi-ply continuous filament yarns
Published in The Journal of The Textile Institute, 2020
Aurélien Sibellas, Jérôme Adrien, Damien Durville, Eric Maire
Radial distribution of orientations: As previously shown, the global orientation density function is a way of describing the yarn structure but it hides the potential relationship between the orientation angle θ of a fiber segment and its relative radial position r/Rin the yarn section. To highlight this aspect, bivariate histograms showing the relative frequency of the two previous parameters combined are plotted in Figure 8. This representation gives an overview of the orientation distribution for each radial position in the yarn cross-section. About a few million fiber segments were used from the numerical data extracted with X-ray tomography to create these histograms. Note that the fibers can exceed a relative radial position greater than 1 because the value Ryarn of the yarn radius is measured with a specific set up (a laser Z-Mike) which provides the mean radius of the yarn. Furthermore, these bivariate histograms also show that the amount of fiber segments decreases above a relative radial position of 0.8. This reflects the low radial packing density of fibers at the yarn surface.
Investigation of pedestrian crashes using multiple correspondence analysis in India
Published in International Journal of Injury Control and Safety Promotion, 2020
Sathish Kumar Sivasankaran, Venkatesh Balasubramanian
In MCA plot, the associated categories are placed close to each other, representing a cloud or combination of points having similar characteristics. MCA produces two cloud points separately each for individual variables and for variable categories represented on the two-dimensional graph. The cloud depends on the individual distance between the variables having different categories. The square of the distance between the individual categories variables is calculated using the Eq. (1) in Table 1. The relative frequency of each category is calculated by dividing the number of individuals in the given category to the total number of individual records in the dataset. The overall squared distance between the two individual records is determined by adding all individual square distances using the Eq. (2). Both clouds of individual variables and cloud of variable categories have the same dimension which is defined by a point and a weight. The squared distance between two different categories j and j' is calculated using the Eq. (3). When two categories belong to the same variable, njj, will be zero.