China
Africa
Explore chapters and articles related to this topic
Fundamentals to Geometric Modeling and Meshing
Published in Yongjie Jessica Zhang, Geometric Modeling and Mesh Generation from Scanned Images, 2018
Given discretized sampling data or scanned images, we need a technique to extract the contour from them. The Marching Squares technique is such an isocontouring technique for 2D images, which is also a simplified version of the Marching Cubes technique [256] in 3D. The Marching Squares technique displaces isocurves or contours for function f (x, y) = c. For a continuous function f(x,y), we first sample it on a regular grid with {f(x,y)}, where i and j are indices of the grids along the x and y directions, respectively. {fi,j (x, y)} can also be obtained directly from scanned images. For each pixel cell as shown in Figure 4.28 (a), it has four corners and each corner has a function value. We have fi,j(x,y), fi+1,j(x,y), fi+1,j+1(x,y) and fi,j+1(x,y). These function values are compared with the isovalue c and we color the corner green if its function value is greater than or equal to c; otherwise we color it white. By using this way, we convert the scalar field into binaries.
Scalar Visualization
Published in Alexandru Telea, Data Visualization, 2014
The marching squares algorithm constructs independent line segments for each cell, which are stored in an unstructured dataset type, given that isolines have no regular structure with respect to the grid they are computed on. An useful postprocessing step is to merge the coincident end points of line segments originating from neighbor grid cells that share an edge. Besides decreasing the isoline dataset size, this also creates a dataset on which operations such as computing vertex data from cell data via averaging (see Section 3.9.1) is possible.
Contour detection with bicubic spline surfaces
Published in International Journal of Digital Earth, 2023
The predominant approach is a piecewise linear approximation: given observed or simulated values on a square or rectangular lattice, the entire surface comprises a set of triangles, in addition to continuity on all edges. Due to piecewise planarity, each contour entity is comprised of successive straight segments, i.e. a polygon. There are two major approaches to contour manipulation. The first type is based on tracking (Lihua, Ai-jun, and Lu-ming 2008; Rui, Song, and Ju 2010; Jang and Bang 2017): identifying an initial point that follows , and the following point is determined to link these two points. This is repeated until the control point returns to the initial location or encounters a boundary, and a contour entity is composed. The second is referred to as the marching squares algorithm (Maple 2003; Neto, Santos, and Vidal 2016). By identifying intercepts on the borders of all square or rectangular patches, each patch is associated with a delineation pattern with reference to a lookup table. This is significant in that the associations are independent of each other, and therefore, the framework allows for parallel processing (Martínez-Frutos and Herrero-Pérez 2017; Tan et al. 2017; Zhou and Li 2021).
Algorithm for detecting cyclone and anticyclone centres from mean sea level pressure layer
Published in Journal of Spatial Science, 2022
Martin Prantl, Michal Žák, David Prantl
Detecting isobars from raster data of size is a straightforward process. We use the simple Marching Squares (Lorensen and Cline 1987) algorithm. It is a 2D version of the well-known Marching Cubes algorithm for iso-surface extraction. The detected isobars form enclosed polygons and have a fine, pixel-based, resolution. For further computations, these polygons can be simplified (e.g. using polyline simplification from Douglas and Peucker 1973) to improve the performance of the following steps.
Alternatives for the generation of triangle meshes to represent bone fragments
Published in Computer Methods in Biomechanics and Biomedical Engineering: Imaging & Visualization, 2018
Félix Paulano-Godino, Juan J. Jiménez-Delgado, J. Roberto Jiménez-Pérez
The first stage of the conducted study is to segment all the bone fragments from CT scans. For that purpose, a segmentation method based on 2D region growing is used Paulano et al. (2014). The segmentation method generates a region for each bone fragment in each slice. These segmented regions are the input of the MC from regions approach. However, the rest of the mesh generation methods in this study are applied to the outer contours of the segmented regions. For that purpose, contours are generated after the segmentation process and then internal contours are removed in 2D. With the aim of extracting the external contour of each segmented region, an approach similar to the proposed in Pulido et al. (2014) is applied. First, the Marching Squares (MS) algorithm is utilised in order to generate contours from the segmented regions (Ho et al. 2005). This algorithm can be considered as a 2D adaptation of MC. Using a divide-and-conquer approach, the algorithm studies each cell composed of four points in a slice to detect boundaries. The algorithm does not ensure that the generated contours are closed, but this is not relevant in this case since the final goal is to generate point clouds. Due to the noise present in the regions because of trabecular tissue, inner contours may be obtained. These inner contours are removed using the point-in-polygon algorithm by Feito and Torres (1997); hence only the outer contour of each fragment is extracted in each slice. This algorithm allows determining if a contour is inside other contours without the need to perform complex calculations, such as solving systems of equations. After inner contours were removed, external contours were mapped to an empty CT stack. By doing this, a new stack containing only information of the outer part of each fragment was generated. This new stack is used as input for the MC from contours approach.