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Scale Modeling
Published in Diane P. Michelfelder, Neelke Doorn, The Routledge Handbook of the Philosophy of Engineering, 2020
Note that the criterion of similarity in use here is objective. In spite of the fact that the situations compared have aesthetic aspects and that human cognition is involved in apprehending the two triangular figures associated with the two physical situations, the criterion of geometrical similarity between the two triangular figures indicated in Figure 29.4 is completely objective. The question of whether two plane triangles are geometrically similar is settled here by the fact that the two triangles are right triangles and the angle at the top of the tree and the angle at the top of the student’s head are formed by rays of the sun in the sky hitting them at the same angle. That angle need not even be known in order to conclude that the triangles indicated in Figure 29.4 are similar triangles. The reasoning from geometric similarity is objective, too, i.e., the consequence of the fact that these two triangles have the same shape, i.e., are geometrically similar, is that ratios between corresponding sides are the same. The reasoning from geometric similarity is straightforward reasoning according to the methods of Euclidean geometry. In Euclidean geometry, what’s similar are two dimensional closed curves (figures), or, if three dimensional, solid figures.
Physical Processes
Published in Ralph L. Stephenson, James B. Blackburn, The Industrial Wastewater Systems Handbook, 2018
Ralph L. Stephenson, James B. Blackburn
The scale up exponent eliminates some mistaken impressions often conveyed by other scale up terminology. Terms such as “tip speed,” “power per volume” and “torque per volume” imply more generality than is justified. These rules usually apply to geometric similarity or, at most, to a limited range of geometries. Changes in geometric configuration should be handled separately from scale changes. Since equivalent volume has been used throughout the design procedure as a measure of the magnitude of the problem, it is convenient to use volume ratio to determine the scale change. The cube root of the volume ratio is equivalent to the linear scale ratio for geometric similarity: R = (V2V1)1/3
Similarity, Modeling, and Various Examples of Application of Dimensional Theory
Published in L. I. Sedov, A. G. Volkovets, in Mechanics, 2018
In most cases, modeling is based on the analysis of physically similar phenomena. The study of the natural phenomenon in which we are interested is substituted by the study of a physically similar phenomenon, which can be realized more easily and to our advantage. Mechanical or, in general, physical similarity can be considered as a generalization of geometrical similarity. Two geometrical figures are similar if the ratios of all the corresponding lengths are identical. If the similarity ratio—the scale—is known, then by simple multiplication of the dimensions of one geometrical figure by the scale factor, one can easily obtain the dimensions of the other figure, similar to the first.
An efficient stacked ensemble model for the detection of COVID-19 and skin cancer using fused feature of transfer learning and handcrafted methods
Published in Computer Methods in Biomechanics and Biomedical Engineering: Imaging & Visualization, 2023
Geometric moments: In computer vision, object recognition, pattern recognition and related fields, the intensity values of the image pixels are represented by the specific weighted average (moment), which is usually chosen to have some appealing interpretation. Image moments are helpful in describing objects in image data (Chadha et al. 2012). Hu (1962) develops a geometric moment invariant feature extraction method that focuses on shape detection tasks from image data. The method extracts features via the Rotation Scale Translation (RST) invariant. This means that the features obtained through this method are not altered for the variation of translation, rotation and scaling. To represent the image by using geometric moments, Hu derives seven invariants. They are invariant for similarity, translation, rotation and reflection. The formulas from Equations (1) to (7) are the seven invariants:
3D coronary artery elastic registration based on differential invariant signatures
Published in Computer Methods in Biomechanics and Biomedical Engineering: Imaging & Visualization, 2022
In this paper, a new discrete point-set similarity measure model and calculation method have been established to study point set registration of coronary artery, which we call PSM. PSM is similar to curve similarity, and it can be adapted to various transformations such as translation, rotation and scaling. Our method is founded on the Euclidean invariant signature for curve matching and object recognition developed in Hoff and Olver (2013). We extend Hoff and Olver’s work to the similarity transformation in space and verify its effectiveness by matching 3D coronary artery point sets. The article is based on data preprocessing, feature calculation, curve classification and Dynamic Time Warping (DTW) algorithm. This paper is organised as follows: Section 2 gives detail of mathematical derivation of similarity invariant signature. In Section 3, the numerical approximations of the signature invariants are calculated to obtain the corresponding signature curve. In Section 4, the method of registration is proposed. Experimental results are shown in Section 5, and concluding remarks are given in Section 6.
Copy-move forgery detection of duplicated objects using accurate PCET moments and morphological operators
Published in The Imaging Science Journal, 2018
Khalid M. Hosny, Hanaa M. Hamza, Nabil A. Lashin
Invariance to the similarity transformations such as rotation and scaling is the very important property for pattern recognition applications. However, PCET moment invariants are negatively affected by the approximation and geometrical errors. To test the rotational invariance of PCETs moments, let be the rotated version of the image function ; Then , where denotes the rotation angle. The relation between the PCETs moments of the original and rotated images iswhere and are the PCET moments of andf, respectively. Since , then