Eugene Bodansky

Smoothing and Compression of Lines Obtained by Raster-to-Vector Conversion

This paper presents analyses of different methods of post-processing lines that have resulted from the raster-to-vector conversion of black and white line drawing. Special attention was paid to the borders of connected components of maps. These methods are implemented with compression and smoothing algorithms. Smoothing algorithms can enhance accuracy, so using both smoothing and compression algorithms in succession gives a more accurate result than using only a compression algorithm. The paper also shows that a map in vector format may require more memory than a map in raster format. The Appendix contains a detailed description of the new smoothing method (continuous local weighted averaging) suggested by the authors.

A new method of polyline approximation

Many methods of a raw vectorization produce lines with redundant vertices. Therefore the results of vectorization usually need to be compressed. Approximating methods based on throwing out inessential vertices are widely disseminated. The result of using any of these methods is a polyline, the vertices of which are a subset of source polyline vertices. When the vertices of the source polyline contain noise, vertices of the result polyline will have the same noise. Reduction of vertices without noise filtering can disfigure the shape of the source polyline. We suggested a new optimal method of the piecewise linear approximation that produces noise filtering. Our method divides the source polyline into clusters and approximates each cluster with a straight line. Our optimal method of dividing polylines into clusters guarantees that the functional, which is the integral square error of approximation plus the penalty for each cluster, will be the minimum one.

Approximation of a polyline with a sequence of geometric primitives

The problem of recognition of a polyline as a sequence of geometric primitives is important for the resolution of applied tasks such as post-processing of lines obtained as a result of vectorization; polygonal line compression; recognition of characteristic features; noise filtering; and text, symbol, and shape recognition. Here, a method is proposed for the approximation of polylines with straight segments, circular arcs, and free curves.

Using local deviations of vectorization to enhance the performance of raster-to-vector conversion systems

Abstract. This paper presents a method of quantitatively measuring local vectorization errors that evaluates the deviation of the vectorization of arbitrary (regular and irregular) raster linear objects. This measurement of the deviation does not depend on the thickness of the linear object. One of the most time-consuming procedures of raster-to-vector conversion of large linear drawings is manually verifying the results. Performance of raster-to-vector conversion systems can be enhanced with auto- localization of places that have to be corrected. The local deviations can be used for testing results and automatically showing the parts of resulting curves where deviations are greater than a threshold value and have to be corrected.

Reconstruction of orthogonal polygonal lines

An orthogonal polygonal line is a line consisting of adjacent straight segments having only two directions orthogonal to each other. Because of noise and vectorization errors, the result of vectorization of such a line may differ from an orthogonal polygonal line. This paper contains the description of an optimal method for the restoration of orthogonal polygonal lines. It is based on the method of restoration of arbitrary ground truth lines from the paper [1]. Specificity of the algorithm suggested in the paper consists of filtering vectorization errors using a priori information about orthogonality of the ground truth contour. The suggested algorithm guarantees that obtained polygonal lines will be orthogonal and have minimal deviations from the ground truth line. The algorithm has a low computational complexity and can be used for restoration of orthogonal polygonal lines with many vertices. It was developed for a raster-to-vector conversion system ArcScan for ArcGIS and can be used for interactive vectorization of orthogonal polygonal lines.

Vectorization with the voronoi L-diagram

A new precision vectorization method has beendeveloped for building centerlines of plain shapes. Firsta dense skeleton is computed. Centerlines are obtained asa subset of branches of the dense skeleton. The denseskeleton can also be used for obtaining medial axes ofshapes. To obtain high precision, the distancetransformation 12-17-38 was developed, which gives agood approximation of the Euclidean metrics. Theexpression the Voronoi L-diagram was coined.

Vectorization and parity errors

In the paper, we analyze the vectorization methods and errors of vectorization of monochrome images obtained by scanning line drawings. We focused our attention on widespread errors inherent in many commercial and academic universal vectorization systems. This error, an error of parity, depends on scanning resolution, thickness of line, and the type of vectorization method. The method of removal of parity errors is suggested. The problems of accuracy, required storage capacity, and admissible slowing of vectorization are discussed in the conclusion.

Approximation of Polylines with Circular Arcs

Approximation of piecewise linear polylines with circle arcs is an important problem. The approximation is used for polyline compression, noise filtering, feature detection, and inspection of mechanical parts [1-5]. A new accurate and fast iterative method of polyline approximation with a circle arc is described in the paper.

Smoothing a Network of Planar Polygonal Lines Obtained with Vectorization

A new method of smoothing polygonal lines obtained as the result of vectorization and creating the network is suggested. This method performs not only smoothing but also filtering of vectorization errors taking into account that these errors appear not only as the errors of vertices but as errors of node coordinates as well. An important part of this algorithm is a technique of building piecewise polynomial base functions for local approximation of the polylines of the network. The suggested algorithm has a linear computational complexity for exponential weight functions. The necessity of using finite weight functions is shown. Algorithms of calculating tangents and curvatures are derived. Shrinking errors and errors of parameters are analyzed. A method of compensation of the shrinking errors is suggested and how to do smoothing with variable intensity is shown.

Automatic Measuring the Local Thickness of Raster Lines

This paper describes a procedure for measuring the local thickness of raster lines. The operator has only to place the cursor near the point where measuring needs to be done. The suggested algorithm is designed only for black and white raster images.