Benchmark for Automatic Clear-Cut Morphology Detection Methods Derived from Airborne Lidar Data
Abstract
:1. Introduction
2. Materials and Methods
2.1. Study Site
2.2. Data Processing
Rasterization
- The retain critical points algorithm (Douglas–Peucker) functions based on the concept of reducing the number of points while preserving those that are crucial for defining the polygon’s shape. It iteratively eliminates points by dividing the line segment and repeating the process until no more points can be removed. Initially, it creates a line segment by connecting the first and last points. Next, it identifies the point on the line segment that is farthest from the straight line connecting the endpoints. If the distance between this point and the straight line is smaller than the specified epsilon value (tolerance), the point is discarded. The algorithm then restarts the process with the remaining points between the endpoints, as proposed by Visvalingam and Whyatt in 1990 [18]. This simplified version of the Douglas–Peucker algorithm is demonstrated graphically in Figure 4.
- 2.
- The Visvalingam–Whyatt algorithm, also known as the retain effective areas algorithm, identifies triangles with effective area and uses that information to remove vertices to simplify the polygon’s outline while preserving its overall shape characteristics. This method shares similarities with the Douglas–Peucker algorithm, but instead of a distance-based tolerance, it utilizes a triangle’s area as the tolerance criterion. The algorithm starts by identifying the smallest triangle and compares its area to a predefined value also called epsilon [29]. The areas of triangles are continuously compared to the tolerance value. The algorithm removes triangles whose areas are smaller than epsilon. This process is repeated until all triangles with areas smaller than the tolerance value are eliminated [18]. The simplification process using this algorithm is illustrated in Figure 5.
- 3.
- The Zhou–Jones algorithm (Figure 6), known as the weighted effective area preservation algorithm, assesses the effective areas of triangles associated with each vertex. These effective areas are determined by considering the shape of the triangle and various metrics, such as flatness, skewness, and convexity [30]. The computation of effective areas for triangles involves applying a weight factor to the initial effective area. This weight factor serves to capture certain aspects of the triangle’s shape. Consequently, the introduction of weighted effective area values allows for the distinction between triangles that share the same area but exhibit different shape characteristics. Utilizing various weight definitions enables highlighting of different aspects of triangle shapes. In this context, the functions serve as filters. These filters designate certain triangles as “standard forms” by assigning them a weight of 1, making their effective areas equal under the filter. When examining a triangle’s shape characteristics, parameters such the base line length (W), height (H), and length of the middle line (ML) are considered. These parameters allow the measurement of a triangle’s flatness, skewness (deviation from an isosceles triangle with the same W and H values), and convexity (orientation relative to a predefined vertex order). There are two models that measure flatness. The first model, which constitutes a high-pass filter, gives priority to taller triangles and reduces the significance of flatter triangles. The second model, a low-pass filter, is identified as a symmetric version of the previously described high-pass filter; its purpose is to eliminate extreme points. The skewness filter is designed to retain points using effective triangles close to being isosceles. The convexity filter is characterized by a constant. If this constant is less than 1, the convexity filter tends to retain points with convex effective triangles. Otherwise, points with concave effective triangles are retained [30]. After weighted areas are calculated, the algorithm strategically eliminates vertices to achieve the maximum possible simplification of the line while still preserving its essential characteristics to the greatest extent possible [31].
- 4.
- The retain critical bends algorithm (Wang–Müller) aims to eliminate insignificant bends in polygons. Figure 7, Figure 8 and Figure 9 depict the process for outline simplification. The minimum diameter for a semicircular bend is set as the tolerance and reference for bend removal. One of the operations in this algorithm is bend elimination (Figure 7); a curved segment is replaced with a straight line. As consecutive straight lines representing bends are not connected, the elimination process must be iteratively performed by removing local minimal bends in each loop. A local minimal bend refers to a bend smaller than both of its neighboring bend points, whereas at the endpoints it is assumed that bends are larger than their neighbors.
2.3. Statistical Analysis and Accuracy Assessment
3. Results
4. Discussion
5. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
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Melichová, Z.; Pekár, S.; Surový, P. Benchmark for Automatic Clear-Cut Morphology Detection Methods Derived from Airborne Lidar Data. Forests 2023, 14, 2408. https://doi.org/10.3390/f14122408
Melichová Z, Pekár S, Surový P. Benchmark for Automatic Clear-Cut Morphology Detection Methods Derived from Airborne Lidar Data. Forests. 2023; 14(12):2408. https://doi.org/10.3390/f14122408
Chicago/Turabian StyleMelichová, Zlatica, Stano Pekár, and Peter Surový. 2023. "Benchmark for Automatic Clear-Cut Morphology Detection Methods Derived from Airborne Lidar Data" Forests 14, no. 12: 2408. https://doi.org/10.3390/f14122408
APA StyleMelichová, Z., Pekár, S., & Surový, P. (2023). Benchmark for Automatic Clear-Cut Morphology Detection Methods Derived from Airborne Lidar Data. Forests, 14(12), 2408. https://doi.org/10.3390/f14122408