A Constraint-Based Generalization Model Incorporating a Quality Control Mechanism
1.1. Background and Recent Achievements on the Evaluation of Generalization
- evaluation for tuning before the commencement of generalization;
- evaluation for controlling during generalization;
- evaluation for assessing at the end of the generalization where the three processes are integrated, as proposed by .
- definition and formation of map requirements as constraints;
- identification of measures for automated evaluation;
- execution of data matching between initial and resulting data.
1.2. Research Goals and Innovation
2. A Constraint-Based Generalization Model Encompassing an Evaluation and Assessment Methodology for Cartographic Data
- Structural element 1: It includes a) the map specifications expressed as constraints along with their violation thresholds for guiding the generalization process, and b) the map quality specifications expressed as quality requirements along with their conformance levels for the evaluation and the quality assessment of the resulting cartographic data;
- Structural element 2: It includes the measures and techniques for the evaluation of the features’ state, the assessment of their compliance with the constraints before and during generalization, and their compliance with the quality requirements after the generalization transformations;
- Structural element 3: It includes the constraint-based generalization process (semantic and cartographic) and the quality control stage configured as follows:
- The process for the selection of the appropriate generalization transformation with its corresponding algorithm through the evaluation and the assessment of the state of the features before generalization with respect to the set constraints;
- The execution of the transformation algorithms and the evaluation of the features’ condition through the assessment of their compliance with the constraints during the generalization process. In case of non-compliance issues, a different calibration of the parameters of the algorithm used is performed, or a different algorithm suitable for the selected transformation is utilized;
- The quality checks evaluate the condition of the features at the end of each phase of the generalization process through the assessment of their compliance with the quality requirements. In the case of error detection, an extra generalization transformation is carried out, such as elimination or displacement.
2.1. Quality Management in Transitioning Geographic Databases to Spatial Databases at Different Scales
2.1.1. Spatial Database Development—Data Model
2.1.2. Compilation and Implementation of the Quality Model
2.1.3. Quality Results
2.2. Semantic Generalization Process
- Junction of two lines (Figure 2a). A junction of two lines is detected when the endpoints of two lines coincide, and the lines are not closed (they do not have the same coordinates at the start and the endpoints). Two lists with the coordinates of the endpoints of the reference line are created, as well as the other two lists with the coordinates of the endpoints of the intersected lines. When the coordinates of the intersected lines lists belong to the lists of the reference line, then there is a junction of two lines. A line is eliminated when 20% of its length is included in the buffer zone (buffer zone width is set according to the separation distance limit of 0.25 mm at the generalization scale) of the reference line. Regarding railway and road networks, the line with the shortest length is the reference line because it is retained considering that the longest line is a siding line. The reverse case is applied on the hydrographic network considering that the longest line is the main river due to its shape sinuosity.
- Junction of three lines (Figure 2b). A junction of three lines is detected when two lines having a node coinciding with each endpoint of the reference line have also another coinciding node that does not belong to the reference line. The longest line is eliminated, considering it as a bend when 20% of its length is included in the buffer zone (buffer zone width is set according to the separation distance limit of 0.25 mm at the generalization scale) of the reference line.
- Junction of lines constitutes a polygon with an area less than the threshold. A polygon-to-area transformation is applied, and the longest line is eliminated in the case of the railway and road networks and the smallest in the case of the hydrographic network.
- Two non-connected lines distinction (Figure 2c). A buffer zone is created around a reference line (buffer zone width is set according to the separation distance threshold of 0.25 mm at the generalization scale) of the reference line. The examined line included in the buffer zone of the reference line is eliminated if it does not intersect the reference line. To retain road continuity and considering that a road consists of several segments, a list is created containing the intersecting lines with the eliminated line each time an action is implemented. Each time an elimination need occurs for two lines, the elimination of the line included in the list is preferred.
- Elimination of lines with a dangling node that is not included in the buffer zone (buffer zone width is set according to the separation distance limit of 0.25 mm at the generalization scale) of a point or polygon is conceptually inconsistent considering that lines in a network should be connected to a location or to each other.
- “Orphan” lines. An “orphan” line is considered a line with dangling nodes at the endpoints. “Orphan” lines are eliminated as conceptually inconsistent.
- Before generalization:
- Compatibility evaluation between the initial and the cartographic database schemata regarding features classes and features’ attributes correspondence leading to the application of semantic transformations on features classes and features’ attributes (transformations on the schema level);
- Compatibility of projections, feature classes’ geometric types, features’ attributes field types, and domains compatibility evaluation (transformations on the schema level).
- During generalization: Transferring data between databases (from the spatial database to the cartographic one), implementing transformations on the instance level, and assessing transformation results per feature class to resolve possible conflicts.
- Features’ compatibility evaluation against each feature’s class rules (geometric and thematic) leading to features reclassification/merging, elimination/aggregation, and their attributes’ value modification (transformations on the instance level);
- Features’ compatibility evaluation to legibility rules (features distinction, density) leading to the features’ reclassification/merging, elimination/aggregation, and their attributes’ value modification (transformations on the instance level;
- The three kinds of relationships between feature classes of the initial database and the new one (one-to-one, many-to-one, none-to-one) correspond to transformations on the schema level along with feature class attributes’ transformation (attribute elimination, attribute aggregation). They signify the transformations to be applied on the instance level for the successful completion of the transferring process. Specifically, the class abstraction transformation applies feature reclassification or feature merging followed by attribute values modification. Class elimination/class composition transformations apply feature elimination and feature aggregation;
- Quality controls per feature class regarding features compliance with quality requirements: features number completeness (compatibility to the feature class rules), features correct categorization when subcategories’ attribute values are not null, attribute values completeness and correctness (no null values), attributes values compatibility to the attributes’ domains (domain consistency), conceptual consistency regarding “holes” creation when features are eliminated or merged.
- At the end of the generalization process: Quality controls between feature classes.
- Conceptual consistency evaluation and assessment in feature relationships regarding invalid overlaps usually occur because of the polygons merging when the space between them is filled. Conflicts are resolved by altering the features participating in the merging process or by canceling the action;
- Legibility preservation evaluation regarding features distinction
2.3. Cartographic Generalization Process
- Parametric description of the feature’s shape based on its geometric characteristics or its representation;
- Evaluation of the feature’s shape condition through the application of a similarity measure for measuring the distance (dissimilarity) between the initial and the generalized feature, considering that a short distance corresponds to similarity and a long distance corresponds to dissimilarity ;
- Evaluation of the feature’s shape condition through the implementation of a legibility measure in the feature’s geometric elements (vertices, part-lines) for the evaluation of its shape sharpness;
- Evaluation of the feature’s shape state through the application of a horizontal accuracy measure;
- Evaluation of the feature’s shape state through the application of a topological consistency measure regarding the feature’s geometry for the evaluation of its shape integrity;
- Assessment of the feature’s shape preservation degree based on the feature’s compliance with legibility, horizontal accuracy, and topological consistency constraints;
- Assessment of the feature’s shape through a technique for the determination of the suitable shape for portrayal.
- No, Νg = the number of vertices of the initial, generalized lines;
- Ltf = the turning function length considering the turning function as a step-function where on the x-axis, the normalized feature length [0,1] is set, and on the y-axis, the counterclockwise cumulative angle of the tangent at each feature vertex is set.
- Na,Νβ = the number of points in each set of points on lines A and B;
- the minimum Euclidean distance between point a on line A and the set of points on line B;
- the minimum Euclidean distance between point b on line B and the set of points on line A.
2.4. Road Network Generalization Example
2.4.1. Semantic Generalization of the Road Network (scale 1:500,000)
- Geodatabases compatibility controls (initial vs. final). Geometric types, attributes’ field types, and their domains and projections are compatible. All features are transferred from the geodatabase at scale 1:250,000 to the geodatabase at scale 1:500,000.
- Three out of the four categories of the road network are retained. The “national”, “primary” and “secondary” roads are retained. The “local” roads are eliminated.
- Junction cases (i), (ii), and (iii) described in Section 2.2 are simplified to achieve the network’s density reduction. The minimum separation distance is set to 125 m and the threshold of the polygon area considered as a junction (case iii) is set to 1 km2.
- The road hierarchy (national, primary, and secondary roads is retained in case there is a need for feature elimination.
- Elimination of lines with a dangling node that does not fall in the buffer zone of 500 m (map specification) of a built-up area.
- “Orphan” lines elimination.
- Quality controls are carried out on the feature class level regarding attribute fields with “null”/ “none” values and attributes fields values compatibility to their domains. No extra quality control regarding the network’s density is required.
- Quality controls are carried out between feature classes with respect to conceptual consistency (overlays) and legibility (features belonging to different classes) when the semantic generalization process is completed for each feature class. The road network’s conceptual consistency is checked against features of aggregated lakes (roads are not allowed to pass through lakes unless their initial condition implies that). The road network’s feature separation is checked against the railway and hydrographic network. In the case of conflicts, only the conflicts where elimination is applied are resolved. Displacement as a solution to resolve visual conflicts is implemented in cartographic generalization.
- Results are shown in Section 3.
2.4.2. Cartographic Generalization of the Road Network (scale 1:500,000)
- Point remove simplification algorithm  is applied. Tolerance is set in the range 20 m to 1000 m with 20 m intervals resulting in 50 generalized lines corresponding to each line of the initial road network;
- Legibility between features geometric elements (‘bottleneck phenomenon’ and very sharp corners), horizontal accuracy, and features topological consistency (self-intersections, self-overlaps) is checked for each generalized line. A group of generalized features complying with conformance levels is created, which corresponds to each initial line of the road network. Each feature of the group is bound to a tolerance value;
- Modified Hausdorff distance between the initial and the generalized line and the difference between the turning function weighted lengths of the initial and the generalized line are computed for each line in each group formed in the previous step (ii). These two parameters describe the shape of each line in each group;
- Hierarchical clustering is carried out on each group. Shape parameters computed in the previous step (iii) are used in clustering. The process is applied for the different number of clusters and different linkage criteria (Ward’s, average, complete, single). The best number of clusters of each group is chosen, the one which: a) retains the highest mean silhouette correlation coefficient, and b) clusters with members that present a positive value for the silhouette correlation coefficient. For each cluster of each group, the member with the highest silhouette correlation coefficient is selected as the “representative” one. Among the representative members, the one corresponding to the maximum tolerance value is selected as suitable for display on the map;
- Quality control at the feature class level is not necessary. Topological inconsistencies (overshoots, undershoots) are not expected as the applied point remove algorithm retains the endpoints of the lines. Quality control is carried out between feature classes. Legibility errors, such as features separation, are expected in cases where features displacement is required. Results are shown in Section 3.
3. Results and Conclusions
- Twelve (12) legibility conflicts were identified concerning roads and rivers (4364 lines were examined), fourteen (14) legibility conflicts were identified concerning roads and railways (3792 lines were examined) at scale 1:500,000;
- Twenty-seven (27) legibility conflicts were identified concerning roads and rivers (3974 lines were examined), twenty (20) legibility conflicts were identified concerning roads and railways (3699 lines were examined) at scale 1:1000,000.
- Four (4) legibility conflicts were identified concerning roads and rivers (4364 lines were examined), 2 legibility conflicts were identified concerning road and railway networks (3792 lines were examined) at scale 1:500,000;
- Twenty-eight (28) legibility conflicts were identified concerning roads and rivers (3974 lines were examined), twenty (20) legibility conflicts were identified concerning road and railway networks (3699 lines were examined), one (1) legibility conflict was identified involving rail and rivers (479 lines were examined) at scale 1:1,000,000.Semantic and cartographic generalization quality control on the geodatabase at scale 1:50,000 with cadastral data resulted in no errors (as expected).
4. Discussion and Future Work
Data Availability Statement
Conflicts of Interest
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|Phase of production||Quality Documentation||Goal for Quality||Quality Methods||Level|
|Before production||Specifications |
|Define quality requirements||Analysis of customer|
|Entity/Feature type level|
|Meet the specifications|
Record expected quality to database
|Measure conformance to quality requirements||Evaluation|
|Geospatial Database—Quality Model—ISO|
|Entity Type &|
|Completeness||Logical Consistency||Positional Accuracy|
|AdministrativeUnit||Error count |
|Error count id 6||Correctness indicator|
|Error count |
|Error count id 6|
|inspireId||Error indicator |
|country||Error indicator |
|geometry||Error count |
|Error count |
id 23, id 24
id 25, id 26
|nationalCode||Error indicator |
|HCCode||Error indicator |
|nationalLevel||Error indicator |
|nationalLevelName||Error indicator |
|Entity Type &|
|Geospatial Database—Quality Model ISO|
|Temporal Accuracy||Thematic Accuracy|
of a Time Measurement
|beginLifespanVersion||Error indicator |
|DQ ELEMENT||DQ Sub_ELEMENT||Name of|
|AU01||Administrative Unit||Completeness||Commission||error count||2||0||Integer|
|AU02||Administrative Unit||Completeness||Omission||error count||6||0||Integer|
|AU03||Administrative Unit||Logical Consistency||Conceptual Consistency||correctness indicator||9||True||Boolean|
|AU04||Administrative Unit||Logical Consistency||Format Consistency||error indicator||119||True||Boolean|
|AU05||Administrative Unit||Thematic Accuracy||Classification Correctness||error count||60||0||Integer|
|AU06||inspireId||Logical Consistency||Domain Consistency||error indicator||14||True||Boolean|
|AU07||country||Logical Consistency||Domain Consistency||error indicator||14||True||Boolean|
|AU09||geometry||Logical Consistency||Conceptual Consistency||error count||11||0||Integer|
|AU10||geometry||Logical Consistency||Topological Consistency||error count||23||0||Integer|
|AU11||geometry||Logical Consistency||Topological Consistency||error count||24||0||Integer|
|AU12||geometry||Logical Consistency||Topological Consistency||error count||25||3||Integer|
|AU13||geometry||Logical Consistency||Topological Consistency||error count||26||0||Integer|
|AU14||geometry||Logical Consistency||Topological Consistency||error count||27||0||Integer|
|AU15||geometry||Positional Accuracy||Absolute Accuracy||Mean value of positional uncertainties||28||1.22||Meters|
|AU16||name||Thematic Accuracy||Non-quantitative Attribute Correctness||error count||60||0||Integer|
|AU17||name||Thematic Accuracy||Non-quantitative Attribute Correctness||error count||65||0||Integer|
|AU18||nationalCode||Thematic Accuracy||Non-quantitative Attribute Correctness||error count||65||0||Integer|
|AU19||nationalCode||Logical Consistency||Domain Consistency||error indicator||14||True||Boolean|
|AU20||HCCode||Thematic Accuracy||Non-quantitative Attribute Correctness||error count||65||0||Integer|
|AU21||HCCode||Logical Consistency||Domain Consistency||error indicator||14||True||Boolean|
|AU22||nationalLevel||Thematic Accuracy||Non-quantitative Attribute Correctness||error count||65||0||Integer|
|AU23||nationalLevel||Logical Consistency||Domain Consistency||error indicator||14||True||Boolean|
|AU24||nationalLevelName||Thematic Accuracy||Non-quantitative Attribute Correctness||error count||65||0||Integer|
|AU25||nationalLevelName||Logical Consistency||Domain Consistency||error indicator||14||True||Boolean|
|AU26||surfaceArea||Thematic Accuracy||Quantitative Attribute Correctness||LE99.8||73||True||Boolean|
|AU27||beginLifespanVersion||Temporal Accuracy||Temporal Validity||error indicator||14||True||Boolean|
|Built area (polygon)||210||113||63|
|Built area (point)||1829||552||317|
|Road network||14,522 km||9014 km||8831 km|
|Railway network||1680 km||987 km||957 km|
|Watercourse (line)||5968 km||4294 km||2551 km|
(None of its parts are deleted)
|1356 km||1356 km||1356 km|
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Blana, N.; Kavadas, I.; Tsoulos, L. A Constraint-Based Generalization Model Incorporating a Quality Control Mechanism. Geographies 2023, 3, 321-343. https://doi.org/10.3390/geographies3020017
Blana N, Kavadas I, Tsoulos L. A Constraint-Based Generalization Model Incorporating a Quality Control Mechanism. Geographies. 2023; 3(2):321-343. https://doi.org/10.3390/geographies3020017Chicago/Turabian Style
Blana, Natalia, Ioannis Kavadas, and Lysandros Tsoulos. 2023. "A Constraint-Based Generalization Model Incorporating a Quality Control Mechanism" Geographies 3, no. 2: 321-343. https://doi.org/10.3390/geographies3020017