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This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution license (http://creativecommons.org/licenses/by/3.0/).

Contemporary 3D digitization systems employed by reverse engineering (RE) feature ever-growing scanning speeds with the ability to generate large quantity of points in a unit of time. Although advantageous for the quality and efficiency of RE modelling, the huge number of point datas can turn into a serious practical problem, later on, when the CAD model is generated. In addition, 3D digitization processes are very often plagued by measuring errors, which can be attributed to the very nature of measuring systems, various characteristics of the digitized objects and subjective errors by the operator, which also contribute to problems in the CAD model generation process. This paper presents an integral system for the pre-processing of point data,

Current demands of a globalized market for constant shortening of development time for novel and increasingly complex products—in order to maintain a competitive edge—have made Reverse Engineering (RE) an extremely popular technique, to the point of being practically indispensable in some design problems. The market today dictates sudden and frequent re-design of products with emphasis on aesthetic and ergonomic features, which, in turn, require the ever more complex organic forms and shapes. These are most often very difficult—sometimes even impossible—to model using conventional CAD tools, which is why they first have to be modelled by sculpting (using clay, plaster, wood,

Modern 3D digitization systems, which are employed by RE, feature ever-growing scanning speeds with the ability to generate large quantities of points in a unit of time [

Fundamental problems—caused by erroneous point data and a huge number of point data as the result of 3D digitization—are: deviations in shape of the resulting CAD model as compared to the original physical object, and impeded work with software applications for CAD model generation [

In order to improve the quality and efficiency, artificial intelligence methods—fuzzy logic (FL), artificial neural networks (ANN) and genetic algorithms (GA)—have so far been implemented at various stages of RE, whereby they have been most frequently used for data pre-processing, or precisely, point data reduction. Philippe

Amidst a number of developed approaches to point data reduction, three of them stand out as dominant: reduction by sampling, polygonal reduction, and mesh reduction [

The basic research objective of the study is the development of a system for quality pre-processing of 3D digitization data, which would satisfy current standards for accuracy in mechanical engineering. Special emphasis is placed on the development of a sub-system for the reduction of point data. The research is primarily focused on cross-sectional RE methodology and the results of digitization generated by the two, presently most widely used, systems for 3D digitization in mechanical engineering—contact scanning and optical triangulation. Bearing in mind that, from user’s perspective, the abstract nature of parameters is a significant problem in reduction of point data using sampling methods, the second objective of this study is to develop an approach which would allow more user-friendly and intuitive interaction. The result is the developed integral system for pre-processing of point data based on cross-sectional RE approach presented in this paper. The system, provisionally named

The system developed for point data pre-processing, which is primarily intended for the needs of reverse engineering modelling on the basis of the “cross-sectional” methodology, is designed on the modular principle and consists of (

Module for 3D filtering of points (errors);

Module for extraction of point data in cross-sections;

Module for filtering and smoothing of point data in cross-sections;

Module for reduction of point-data based on fuzzy logic;

Module for formatting of output data.

3D digitization most often results in numerous unwanted points. These points frequently belong to objects which surround the object being digitized, such as fixtures, measurement table, or some other part of the assembly to which the digitized part belongs. However, in the case of non-contact methods, such as the laser triangulation, those points can originate from objects located further away. To some extent, the unwanted points can also be the result of measurement errors (due to operator errors, system-specific errors and/or errors due to specific nature of the digitized object, some external disturbance

Volumetric filtering;

Filtering by segmented line;

Elimination of particular points (by selection).

The volumetric filtering method is based on forming a rectangular volume (

The segmented line filter is based on staggered lines which are composed of line segments, defined by the knot points (_{i}

The third tool allows individual selection of a larger number of points which could not be eliminated using the first two tools. Selection is performed in a graphical mode, from the point cloud. The three tools can be used each by itself, or in any other combination, iteratively, as shown by the algorithm in

Bearing in mind that SyPreF is dedicated to RE modelling based on cross-sectional methodology, prior to pre-processing (filtering, smoothing, and reduction) it is necessary to select and sort the points from the 3D point cloud—by cross-sections. Accordingly, within this module (points belonging to particular 2D cross-sectional curves are selected into a separate set

However, if the input point cloud is unsorted—_{max}

This module also provides an option to change the resolution of the cross-section,

The function of this module is two-fold: filtering and smoothing of point data in cross-sections (scanned lines). It is dedicated to elimination of errors left after 3D filtering, as well as elimination of noise which affects the quality of the resulting surface model. The module is based on four tools:

Elimination of points at the ends of scanned curves;

Filtering by the angle method;

Filtering/smoothing by the method of median;

Smoothing by the method of mean.

The first tool (a) is dedicated to elimination of points at the ends of scanned curves. These points are often problematic because they are the result of unwanted contacts between the sensor and the fixture, measurement table and similar objects, but were not eliminated in the process of 3D filtering. User is called to define the number of points that should be eliminated at the ends.

The angle method (b) is dedicated to elimination of outliers,

The principle of the method of median is mathematically defined as:

The principle of the method of mean is based on statistical mean of the specified data array

The method of median can also be used for elimination of outliers as well as for point data smoothing, while the method of mean is exclusively used for smoothing [

Moreover, the median filter tends to preserve the shape even in cases of stepped increments (

This module (

To eliminate the problems which stem from the specific values of decision-critical input parameters entered by the user, and create a more user-friendly system, a new, synthetic parameter was introduced under the name

Detailed descriptions of software procedures for the method of straightness is given below, while for other two integrated methods—spatial and chordal—they can be found in [

The straightness method for reduction of point data (the mathematical background of the method is explained by relations (3) and (4) and illustrated in

The procedure for fuzzy logic-based reduction is illustrated in

The input consists of two state variables—

Input space for the state variable

If (Ω is

If (Ω is

If (Ω is

If (Ω is

If (Ω is

If (Ω is

If (Ω is

If (Ω is

If (Ω is

The role of this module is to adjust and prepare the results of pre-processing by formatting them into form acceptable to some of the software systems for surface reconstruction. The proposed model supports two point data formats: PTS and IBL.

In realization of the SyPreF point data pre-processor, conventional programming tools as well as artificial intelligence (fuzzy logic) tools were used. SyPreF was developed in

The system for pre-processing of point data, described in previous chapter, was verified on three characteristic case studies:

timing belt tooth,

human face model and

sports glasses lens.

In the first case study 3D digitization was performed by laser scanning, while in other two case studies it was accomplished by contact scanning.

The first case study which was used to test the SyPreF included a timing belt tooth (

Point-data pre-processing was started by the application of the tools for cross-sectional filtering/smoothing of point data. Primarily filtering by the angle method (

The next phase of pre-processing was the extraction of point data in cross sections. In order to efficiently reconstruct the surface model, the cross-sectional resolution was changed from 5 to 10 μm. In this way the number of cross-sections was lowered from 3,000 to 1,500, which in turn decreased the number of points to 494,332.

A special focus here was on the tooth part with a factory error, so the frontal segment of the point data was extracted from the whole by application of a volume filter. According to this, the point data reduction was performed on the point cloud consisting of 263,791 points in 801 cross-sections. The reduction was performed by the fuzzy-chordal method with

The second verification case study was performed on a human face cast model (

Point-data pre-processing was started by the application of the tools for 3D filtering of point data. Considering that the model is symmetric about the

The next phase of point data pre-processing was the reduction. The point cloud prepared for reduction contained 564,612 points in 979 cross-sections. The reduction was performed by the fuzzy-straightness method with

The surface model was generated based on the reduced point data in IBL format. Generated cross-sectional curves and resulting surface models are shown in

The third case study involved a sports glasses lens (

The very first pre-processing phase was the 3D filtering of resulting point data, which included volumetric filtering, filtering by segmented line, and elimination of individual points. Parameters used for volumetric filtering are listed in

Cross-sectional filtering/smoothing of point data was performed in the next phase of pre-processing and comprised elimination of end points in two iterations—1st along the

Bearing in mind a relatively simple object geometry, in the next phase of pre-processing cross-sectional resolution was changed from 0.1 to 0.2 mm along

In the final phase of pre-processing, reduction of point data was performed. Fuzzy-chordal reduction method was chosen, with

As in previous two case studies, a surface model was generated by automated generation of cross-sectional curves from the prepared point clouds in IBL format. The generated cross-sectional curves and the resulting surface model are shown in

This part deals with the analysis of the obtained results in terms of point data filtering and point data reduction. Processing time is discussed in particular with reduction, since it is negligible in point data filtering.

In terms of filtering, the first and third case studies were more demanding, which imposed the application of a combination of tools for point data filtering. In the first case study, which is characterized by a large number of impulse errors typical for a laser triangulation digitization, filtering process was carried out without the need for manual user’s work, primarily due to efficient outliers’ filtering by the method of angle. The third case study is characterized by the need for using multiple filtering tools. Although the efficiency of the volumetric filter, segmented line filter and the end point filter showed satisfactory, object’s geometry in this case imposed a need for manual filtering of individual points by the user. Unlike in previous cases, in the second case study is—due to object’s geometry and point cloud’s features—filtering was effectively carried out using only the segmented line filter.

Related to point data reduction, it has to be emphasized that the presented approach allows the user to conduct the reduction process qualitatively by defining the desired value of the maximum tolerance,

The processing time can be taken as a conditional drawback of the presented reduction approach. Because of the high dependence of the reduction process on: object’s geometry, level of

The attribute “conditional”, at a stated time demanding as a drawback in previous paragraph, is specified taking into account the benefits in the process of creating surface models based on reduced point clouds. Direct benefits include a significant speed increase of the surface model’s generation process as well as enormously increased stability of the process (referring to software crash-down). The former imply time savings which are usually higher than needed to compensate time spent on the reduction of point clouds. Moreover, much greater working flexibility (e.g., in solidification,

Presented in this paper is an integral system for pre-processing of point data based on a cross-sectional RE approach. The system, provisionally entitled SyPreF, is of modular structure with a total of five modules containing the developed software tools for: 3D filtering, extraction of point data in cross-sections, filtering and smoothing of point data within cross-sections, reduction of point data and generation of output formats for application in dedicated software for surface reconstruction.

Major emphasis was placed on the module for point data reduction, which was designed according to a novel approach with integrated deviation analysis and fuzzy logic reasoning. Building on the weak spots and deficiencies of current approaches to reduction of point data by sampling methods—

The approach was tested with three different methods of sampling—chord, straightness and spatial—showing a significant improvement of the maximum deviation/level of reduction ratio,

Verification of the proposed pre-processing system was conducted through its application in three case-studies selected on the basis of geometry complexity, dimensions and applied system for 3D digitization. Achieved results—high reduction levels and low deviations of reconstructed models—confirm the system’s effectiveness on point data from parts of versatile geometries, obtained by contact and laser triangulation digitization systems. Additionally, productivity and speed of surface reconstruction based on pre-processed point clouds are significantly increased, maintaining stability of process on an average hardware configuration.

Future research will be oriented towards further development through implementation of additional modules/tools (e.g., for point data segmentation and registration) as well as on further advancement of point data reduction through improvement of the calculation speed and development of an expert system for proposing an optimal method for the given point data.

The research was supported by the Ministry of Education and Science of the Republic of Serbia and the Ministry of Higher Education, Science and Technology of Republic of Slovenia.

General model of the SyPreF system.

(

(

Principles and effects of methods for cross-sectional filtering/smoothing. (

Algorithm of module for cross-sectional filtering/smoothing.

(

Principle of point data reduction based on straightness [

(

SyPreF module’s interfaces.

(

Non-contact 3D digitization system (1-laser profilometer module, 2-laser plane, 3-belt, 4-pulleys, 5-movable cart). (

(

(

(

(

Results of filtering by segmented line. (

The result of point data reduction.

(

(

The result of volumetric filtering.

The result of filtering by segmented line.

The result of manual elimination of points.

Elimination of end-points in cross-sections. (

The result of point data reduction.

(

The results of point data reduction.

MAD | 0.01 mm |

Maximum error | 0.00968 mm |

Average error | 0.00159 mm |

Reduction level | 65.69 % |

Number of retained points | 90,494 |

Reduction time | 73.38 min |

Obtained on PC configuration:

Parameters of the applied segmented line filter.

_{1} |
130 | 260 |

_{2} |
145 | 235 |

_{3} |
165 | 215 |

_{4} |
290 | 215 |

_{5} |
333 | 238 |

The point data reduction results.

MAD | 0.04 mm |

Maximum error | 0.03993 mm |

Average error | 0.00491 mm |

Reduction level | 53.29 % |

Number of retained points | 275,811 |

Reduction time | 95.45 min |

Obtained on PC configuration:

Parameters used for volumetric filtering.

_{min} |
−8.5 |

_{max} |
36 |

_{min} |
43 |

_{max} |
116 |

_{min} |
17 |

_{max} |
35 |

Parameters of the applied segmented line filter.

_{1} |
41.6 | 20.0 |

_{2} |
51.2 | 23.1 |

_{3} |
50.8 | 20.8 |

_{4} |
61.1 | 23.9 |

_{5} |
73.8 | 27.0 |

_{6} |
80.2 | 27.2 |

_{7} |
88.7 | 26.7 |

_{8} |
94.0 | 25.3 |

_{9} |
106.7 | 21.4 |

_{10} |
116.8 | 16.2 |

The results of point data reduction.

MAD | 0.03 mm |

Maximum error | 0.02835 mm |

Average error | 0.00265 mm |

Reduction level | 97.82 % |

Number of retained points | 2,062 |

Reduction time | 23.05 min |

Obtained on PC configuration: