Review of Current Vectorization Methods in .NET

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2. Review of Current Vectorization Methods
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Vectorization is a process that finds the vectors (such as straight lines, arcs and circles) from the raster images. Much research work on this area has been done, and many vectorization methods and their software have been developed. Although the vectorization for the lexical phase is more
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Review of Current Vectorization Methods
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mature than the technologies used for the other two higher level phases, it is yet quite far from being perfect. Current vectorization methods can be categorized into six types: Hough Transform (HT)-based methods [2], thinning-based methods, contour-based methods, sparse pixel-based methods, mesh pattern-based methods and black pixel region-based methods.
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2.1 The Hough Transform-based Method
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This visits each pixel of the image in the x y plane, detects peaks in its transform m c space, and uses each peak to form a straight line defined by the following equation: y = mx + c (19.1)
where m is its slope and c is its intercept. Since the slopes and intercepts are sampled sparsely, they may not be as precise as the original straight lines. Moreover, this method cannot generate polylines [3].
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2.2 Thinning-based Methods
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Thinning is a process that applies certain algorithms to the input raster image and outputs one-pixelwide skeletons of black pixel regions [4 7]. Three types of algorithm have been developed, i.e. iterative boundary erosion [5], distance transform [6] and adequate skeleton [7]. Although their speeds and accuracies are different, they all have disadvantages: high time complexities, loss of shape information (e.g. line width), distortions at junctions and false and spurious branches [3].
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2.3 The Contour-based Method
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This first finds the contour of the line object and then calculates the middle points of the pair of points on two opposite parallel contours or edges [8 10]. Although it is much faster than thinning-based methods and the line width is also much easier to obtain, joining up the lines for a merging junction or a cross intersection is problematic, and it is inappropriate for use in vectorization of curved and multicrossing lines [3].
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2.4 The Sparse Pixel-based Method
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Here, the basic idea is to track the course of a one-pixel-wide beam of light , which turns orthogonally each time when it hits the edge of the area covered by the black pixels, and to record the midpoint of each run [11]. With some improvement based on the orthogonal zig-zag, the sparse pixel vectorization algorithm can record the medial axis points and the width of run lengths [3].
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2.5 Mesh Pattern-based Methods
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These divide the entire image using a certain mesh and detect characteristic patterns by only checking the distribution of the black pixels on the border of each unit of the mesh [12]. A control map for the image is then prepared using these patterns. Finally, the extraction of long straight-line segments is performed by analyzing the control map. This method not only needs a characteristic pattern database, but also requires much more processing time. Moreover, it is not suitable for detection of more complex line patterns, such as arcs and discontinuous (e.g. dashed or dash-dotted) lines [3].
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Holo-Extraction and Recognition of Scanned Curves
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2.6 Black Pixel Region-based Methods
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These construct a semi-vector representation of a raster image first and then extract lines based on the semi-vector representation. The semi-vector representations can be a run graph (run graph-based methods)[13], a rectangular graph [14] or a trapezoidal graph [15]. A run is a sequence of black pixels in either the horizontal or vertical direction. A rectangle or trapezoid consists of a certain set of runs.
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2.7 The Requirements for Holo-extraction of Information
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It can be seen from the current vectorization methods that, except for black pixel region graph-based methods, other methods are mainly focused on the speed and accuracy of generating vectors themselves, not on holo-extraction of information. Although black pixel region graph-based methods build certain relationships between constructed runs, rectangles or trapezoids, the regions are so small that it is not appropriate for curve line vectorization and it is difficult to construct the relationships among vectors. In fact, the understanding process for its subsequent 3D reconstruction is an iterative process for searching different level relationships and performing corresponding connections. For instance, linking certain related pixels can form a vector. Connecting a certain set of vectors can form primitives or characters of the text. Combining two projection lines and a dimension line containing two arrowheads with the values for normal dimension and tolerance can produce a dimension set, which can then be used with a corresponding primitive for parametric modeling. Aggregating the equal-spaced parallel thin lines and the contour of their area can form a section, which can then be used with certain section symbols for solid modeling. Connecting certain primitives referring to corresponding symbols recognized can form certain features (e.g. bearing and threading), which can be used for feature modeling. Matching primitives in different views according to orthogonal projective relationships can produce a 3D model. If the primitives extracted are accurate, their projective relationships can be determined by analyzing the coordinates of end points of these vectors. But the primitives extracted and their projective relationships are inaccurate in paper drawings, so that this method cannot be applied. It needs an expert system that simulates the experienced human designer s thinking mode to transform the inaccurate outlines of parts orthographic projections into 3D object images, so that their relationships become more important and crucial. As mentioned in the first section of this chapter, the vectorization process in the first phase should not lose the information in a drawing or the information needed for 3D reconstruction, which are mainly different level relationships contained in the raster image. Accordingly, a holo-extraction of information from the raster image is needed. In order to facilitate the iterative process for searching different level relationships and performing corresponding connections, the method needs a compact representation of the raster image as a bridge from the raster image to understanding, which should satisfy the following requirements: it can distinguish different types of linking point for different relationships of the related elements (e.g. tangential point, intersecting point and merging junction) to provide necessary information for extracting lexical, syntactic and semantic information in the subsequent phases; it can provide a unified base for further recognizing both the outlines of orthogonal projections of parts and the annotations, and facilitate their separation; it can recognize line patterns and arrowheads, and facilitate the aggregation of related elements to form certain syntactic information, such as dimension sets; it can facilitate recognizing vectors quickly and precisely, including straight lines, arcs and circles; it can provide holo-graphs of all the elements as a base for the subsequent 3D reconstruction. The networks of SCRs reported in this chapter are developed for these purposes.
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