CN113204607B - Vector polygon rasterization method for balancing area, topology and shape characteristics - Google Patents

Abstract

The invention relates to a vector diagram rasterization method for balancing area, topology and shape characteristics, which repairs topology changes of a grid area according to the true topology of a vector polygon; the grid pixels of the polygonal narrow channels, the protruding and recessed parts are reserved, so that the loss of shape characteristics can be reduced; the area difference of the adjacent grid areas and the original polygon is compared, and the rasterization area is re-coordinated. Experimental results show that compared with the conventional algorithm, the algorithm can effectively reserve the area, shape and topological characteristics of the polygon, and the overall rasterization error is obviously reduced.

Description

Vector polygon rasterization method for balancing area, topology and shape characteristics

Technical Field

The invention relates to a vector polygon rasterization method for balancing area, topology and shape characteristics, and belongs to the technical field of vector data to raster data conversion methods.

Technical Field

Vector and grid are the basic formats of spatial data in Geographic Information Systems (GIS) (Maguire et al, 1991). These two data structures have fundamental differences (Mattikali, 1995) that render many data processing and analysis tools not versatile and therefore often face the problem of vector and grid interconversion. The raster data is generally more suitable for scientific research than vector data due to the advantages of simple structure, simple data acquisition and analysis method, etc. (Peuque, 1984; goodchild, 2011). In recent years, the application scene of raster data is greatly expanded by the remote sensing technology. Applications such as GIS-based spatial analysis and spatial modeling in particular (polymers, 2001;Kuhnert et al, 2005), such as resource and environmental supervision (Hong et al, 2016), land utilization/land cover change simulation (Mustafa et al, 2017), have led to more intensive research into vector-grid conversion. The values of the internal pixels in the process of rasterizing the polygon are generally derived from the polygon, and the key problem is the determination and assignment of boundary pixels. Algorithms such as boundary algebra (Feito, 1995), boundary tracing (Wu, 1998) have been developed to find boundary pixels. Since each grid pel can only be assigned one attribute value, rules must be formulated to trade off multiple attribute values when a boundary pel overlaps multiple polygons (Wehde et al, 1980). The conventional rounding rules of such pixels include a center point method based on a polygon containing the center point of the pixel and a maximum area method based on a polygon having the largest area overlapping the pixel.

Discrete pixels of raster data cannot express smooth boundaries of polygons, resulting in vector-to-raster conversion being a lossy process (Van Der Knaap, 1992). The rasterization errors are mainly manifested by variations in the perimeter, area, shape, position, topology, etc. of the polygon (Carver & Brunsdon,1994; galton,2003; short, 2004). Although reducing the pixel size can effectively reduce various rasterization errors, it can result in a significant increase in data volume and processing time (Bettinger et al, 1996; bai et al, 2011), so that in practical applications the smaller the grid pixel is, the better. Analysis and evaluation of gridding errors is an important task in the GIS field, where area errors are the dominant (Wade et al, 2003). Bregt et al (1991) propose an area error analysis method based on double conversion, which finds that the error has a linear positive correlation with the boundary index (the boundary length of a polygon per unit area). Kam et al (2000) found that the area errors were different due to the different rules of choice of various GIS software for grid pixels, which can cause problems for spatial analysis that depends on the pixel area and number. Zhou et al (2006) use domain compensation principles to minimize the area error based on the spatial relationship of the polygon to its boundary pixels. Liao et al (2012) established a functional relationship between area error and arc length density, polygon density and grid pixel size by analyzing the impact factors of the rasterization error. Wei et al (2019) developed a multi-scale gridding test based on grid purity index, and the area error analysis results showed that the method was significantly better than the maximum area method.

Vector-to-grid conversion can also significantly affect the shape and topology characteristics of polygons. Congalton (1988) studied the spatial complexity and error pattern of 3 landscapes of cultivated, grass and woodland, and found that polygons with a relatively large perimeter-area were easily lost or severely deformed in the grid representation. Bettinger et al (1996) state that when the size of the grid pixel is too coarse with respect to the polygon, the shape and topology of the latter can change greatly, e.g. a certain polygon breaks up due to a loss of a narrow channel, and two adjacent polygons separate. Congalton (1997) explored the area and shape change of the polygon after multi-scale rasterization, indicating that smaller grid pixels are needed to preserve the shape of the polygon than to merely maintain the presence of the polygon. Galton (2003) has analyzed the effect of rasterization on polygonal area, shape, topology, position and orientation features in detail, where shape loss is discussed in terms of symmetry and convexity, and topology differences are judged in terms of region connectivity. Zhou et al (2017) compared different types of topology changes and their causes of formation, and then proposed a rasterization algorithm that preserves topology.

Conventional rasterization algorithms based on the simple center point method or the maximum area method are still widely used (Longley et al 2005), and a large number of rasterization error studies indicate that the spatial features of polygons are severely lost during the conversion process. A few students strive to preserve the area or topology of the polygon, ignoring that this approach would cause greater disruption to other features. The area, shape and topology are important spatial features of polygons, and the invention aims to develop an algorithm for balancing and preserving the three features in vector-grid conversion so as to achieve the aim of comprehensively reducing the rasterization error. The accuracy and performance of the algorithm under various grid pixel sizes are evaluated and compared with the scene of repairing a single error. And analyzing the area change of various types of lands in the conventional rasterization result and the repair result thereof. Finally, the influence of different pixel sizes and vector data on the algorithm is discussed, and some application scenes of the algorithm and future works are discussed.

Disclosure of Invention

The invention aims to solve the technical problems that: the vector polygon rasterization method overcomes the defects of the prior art and provides a vector polygon rasterization method for balancing area, topology and shape characteristics.

In order to solve the technical problems, the technical scheme provided by the invention is as follows: vector polygon rasterization method for balancing area, topology and shape characteristics, and respectively rasterizing polygons P1 and P2 into an area set R= { R ₁ ,R ₂ ,...,R _n And region R2, performing the following steps to repair the rasterization error:

step 1, obtaining boundary pixels of a polygon as candidate pixels to be classified;

step 2, ifOr n>1, performing shape restoration, and preferentially guaranteeing that grid areas of the polygon P1 exist and are communicated to obtain an area R1, wherein the specific implementation steps are as follows:

obtaining boundary pixels lost by the polygon P1 as a candidate set P _o ；

If it isI.e. there is no grid area, then from candidate set P _o Taking out one pixel and distributing the pixel to P1;

if n>1, i.e. the grid areas are not connected, search for picture elements of the disconnected part of polygon P1, take them from P _o After being taken out, the mixture is distributed to P1;

identifying raised parts lost by polygon P1 from P _o The picture element of the part is taken out and allocated to P1;

so far, obtaining a region R1 corresponding to the polygon P1;

step 3, if the region R1 is separated from the region R2 and the polygon P1 is adjacent to the polygon P2, or if the region R1 is adjacent to the region R2 and the polygon P1 is separated from the polygon P2, repairing the topological relationship of the region specifically comprises the following steps:

if the region R1 is separated from the region R2 and the polygon P1 is adjacent to the polygon P2, obtaining the lost pixel at the common boundary of the polygons as a candidate set P _o The method comprises the steps of carrying out a first treatment on the surface of the The pixels occupied by the polygon P1 and the polygon P2 are respectively used as starting points and stopping points, and the pixel is positioned at P based on the shortest path idea _o Search pixels in (C) and assigned theretoOverlapping polygons P1 or P2;

if the region R1 is adjacent to the region R2 and the polygon P1 is separated from the polygon P2, searching for the pixel pair causing the region to be adjacent to as the candidate set P _c ＝{(p ₁₁ ,p ₁₂ ),(p ₂₁ ,p ₂₂ ),...,(p _n1 ,p _n2 ) P is }, P _c One of each pair of pixels is allocated to the other polygons except the polygon P1 and the polygon P2;

step 4, if the long and narrow convex part of the polygon is lost, reassigning the boundary pixels of the part to the polygon;

and 5, combining the polygonal area with the size of the grid pixels, and utilizing the areas of the R1 and R2 of the rest boundary pixels to coordinate the areas of the polygonal area and the grid area so that the difference between the polygonal area and the area of the grid area is not more than half of the pixel area.

The invention repairs the topology change of the grid area according to the true topology of the vector polygon. The grid pixels of the polygonal narrow channels, the protruding and recessed parts are reserved, so that the loss of shape characteristics can be reduced. The area difference of the adjacent grid areas and the original polygon is compared, and the rasterization area is re-coordinated. Experimental results show that compared with the conventional method, the method provided by the invention can effectively reserve the area, shape and topological characteristics of the polygon, and the overall rasterization error is obviously reduced.

Drawings

The invention is further described below with reference to the accompanying drawings.

Fig. 1 is a plot of experimental region data (s=10m), where (a) is a vector data plot and (b) is a raster data plot obtained using a balancing strategy.

Fig. 2 is a comparative graph of rasterization results (s=10m), where (a) is a vector polygon; (b) is an initial rasterization result; (c) - (e) are three conventional strategy processing result graphs; (f) a process result graph of the balancing strategy.

Detailed Description

The technical route and operation steps of the present invention will be more apparent from the following detailed description of the present invention with reference to the accompanying drawings.

The vector of the present invention balancing area, topology and shape featuresMethod for rasterizing a vector polygon, which converts polygons P1 and P2 into a region set r= { R ₁ ,R ₂ ,...,R _n And region R2, performing the following steps to repair the rasterization error:

step 1, obtaining boundary pixels of a polygon as candidate pixels to be classified;

step 2, ifOr n>1, performing shape restoration, and preferentially guaranteeing that grid areas of the polygon P1 exist and are communicated to obtain an area R1, wherein the specific implementation steps are as follows:

obtaining boundary pixels lost by the polygon P1 as a candidate set P _o ；

If it isI.e. there is no grid area, then from candidate set P _o Taking out one pixel and distributing the pixel to P1;

if n>1, i.e. the grid areas are not connected, search for picture elements of the disconnected part of polygon P1, take them from P _o After being taken out, the mixture is distributed to P1;

identifying raised parts lost by polygon P1 from P _o The picture element of the part is taken out and allocated to P1;

so far, obtaining a region R1 corresponding to the polygon P1;

step 3, if the region R1 is separated from the region R2 and the polygon P1 is adjacent to the polygon P2, or if the region R1 is adjacent to the region R2 and the polygon P1 is separated from the polygon P2, repairing the topological relationship of the region specifically comprises the following steps:

if the region R1 is separated from the region R2 and the polygon P1 is adjacent to the polygon P2, obtaining the lost pixel at the common boundary of the polygons as a candidate set P _o The method comprises the steps of carrying out a first treatment on the surface of the The pixels occupied by the polygon P1 and the polygon P2 are respectively used as starting points and stopping points, and the pixel is positioned at P based on the shortest path idea _o The search pixels are allocated to the polygon P1 or the polygon P2 overlapped with the search pixels;

if the region R1 is adjacent to the region R2 and the polygon P1 is adjacent to the polygon P2 separating, searching pixel pairs causing region adjacency as candidate set P _c ＝{(p ₁₁ ,p ₁₂ ),(p ₂₁ ,p ₂₂ ),...,(p _n1 ,p _n2 ) P is }, P _c One of each pair of pixels is allocated to the other polygons except the polygon P1 and the polygon P2;

step 4, if the long and narrow convex part of the polygon is lost, reassigning the boundary pixels of the part to the polygon;

and 5, combining the polygonal area with the size of the grid pixels, and utilizing the areas of the R1 and R2 of the rest boundary pixels to coordinate the areas of the polygonal area and the grid area so that the difference between the polygonal area and the area of the grid area is not more than half of the pixel area.

The specific implementation process of the step 5 is as follows:

a1, calculating the area difference between the polygon P and the region R obtained after rasterization, and determining the quantity k of pixels needing reclassifying according to the area difference, wherein adjacent pixels with the same attribute value form the region R;

wherein S is _p Is the area of polygon P, S _R The area of the region R, s is the area of the grid pixel;

a2, obtaining boundary pixels of the polygon P, and taking pixels belonging to the region R as a candidate set P _a Other picture elements as candidate set P _o ；

a3, if k > 0, from candidate set P _a Taking out one pixel and distributing the pixel to other polygons; if k<0, from candidate set P _o Taking out one pixel and distributing the pixel to a polygon P;

a4, repeating the step a3 until the average area error of the region R and the adjacent regions thereof is not reduced or the candidate set P _o Is empty.

After the rasterization is completed, the rasterization error evaluation is performed, and the area error AE, the shape error SE and the topology error TE are calculated by using the following methods,

wherein A is _v 、A _r Areas before and after rasterization of the polygon, max (a _v ,A _r ) Representation taking A _v And A is a _r The larger of the two; c (C) _v 、C _r Compactness before and after polygon rasterization, respectively, if the polygon disappears or breaks into multiple small areas after conversion, then |C _r -C _v |＝1.0；

N _r Polygon pairs or polygon numbers, N, for true topology changes _v Polygon pairs or polygon numbers that are topology changes that may occur;

the compactness calculation formula of the polygon is as follows:

wherein A and P are the area and perimeter of the polygon, and C is (0, 1).

The total number of polygon pairs or polygon numbers, where topology changes may occur, is determined according to the following equation:

where i and j represent two polygons, d (i, j) represents the shortest distance between polygon i and polygon j boundary, and s is the area of the grid pixel.

If the error of the initial rasterization result is AE ₀ 、SE ₀ And TE (TE) ₀ Error of repair result is AE ₁ 、SE ₁ And TE (TE) ₁ The overall repair capability OFC of the algorithm was evaluated using the following formula:

the test data is land utilization data of Wei Cun streets in Changzhou city in China and is derived from land utilization change investigation results in Changzhou city in 2018. The vector data is formatted as ESRI shape, the geographic location is as shown in FIG. 1. There were 14,000 polygons in the layer with a total area of 7,462 hectares. Including 6 land use types: cultivated land, garden land, water area, construction land, traffic land, and other land uses. Table 1 lists the number of polygons, the average area, and the average compactness for different types of land.

TABLE 1 number of polygons, average area and average compactibility for different types of land

The algorithm is implemented using the Python programming language. A geospatial data abstraction library (Geospatial Data Abstraction Library, GDAL) provides a series of spatial classes and spatial operating functions for reading, writing, converting and processing of vector and raster data. And calling an existing vector-grid conversion algorithm to acquire an initial grid initialization result. Each polygon in the vector data has a unique id value, which is assigned to the grid pixel during rasterization. Based on the area of the polygon and its initial grid area, the optimal number of reclassifying pixels needed to minimize its area error is calculated. To efficiently query neighboring polygons, a quadtree spatial index (manolomoulos et al, 2018) is designed and applied for trial data. All pixels that the polygon boundary passes through are calculated based on the basic idea of Bresemhan algorithm (Gaol, 2013). The adjacency state of the grid area is obtained by searching the boundary pixels and the 4-neighbors thereof for identifying the topology change. In addition, new topology changes are avoided being introduced when reclassifying grid pixels.

The algorithm runs on a Windows 10 platform with an Intel (R) Core (TM) i7-6700 processor (clock frequency 3.4 GHz), 8GB memory and a 1TB hard disk.

Control experiments were performed at a variety of rasterization scales. And acquiring an initial rasterization result based on the center point rule. The corresponding type of rasterization error is repaired using three conventional policies (hereinafter abbreviated as area policy, shape policy, and topology policy) and balancing policies, respectively. These repair results were compared and analyzed in detail. Meanwhile, the precision and the performance of the algorithm are evaluated, and the area change of different types of lands after errors are repaired.

Taking a 10m grid pixel as an example, the vector polygon of fig. 1 (a) is rasterized. Three conventional strategies and a balance strategy obtain four repaired rasterization results. Fig. 1 (b) is the result of the balancing strategy.

As shown in fig. 2, the same position is selected in each rasterization result to compare the effects of different strategies on the spatial features of the polygon and its neighbors. Fig. 2 (a) is a vector layer, and the shape of the polygon P2 approximates a triangle. FIG. 2 (b) shows the initial rasterization result, where the polygon P1 is transformed into two non-connected regions with an area error of 2.72%; the shape of the region R2 approximates a rectangle. The area variation is reduced in fig. 2 (c), the area error of the polygon P1 is reduced to 0.02%, but the areas R1 and R4 are brought into abutment and R5 and R6 are separated. In fig. 2 (d), region R2 retains one lobe of polygon P2, but it adjoins R3; the area error of P1, P2 increases. The topology change is repaired in fig. 2 (e), but the area error of the polygon P1 is still 2.61%, and the inclined narrow channel becomes vertical. FIG. 2 (f) shows the result of the balancing strategy, the area error of polygon P1 is reduced to 0.02%; narrow channels and lobe losses for P1, P2 are reduced; the topology of the region is consistent with that of a polygon. The comparison shows that the balance strategy has better comprehensive effect on the reserved area, shape and topology.

The rasterization test was performed using six pixel sizes of 5, 10, 15, 20, 25, 30 m. Table 2 records the area error AE, shape error SE and topology error TE of the rasterization results obtained by the conventional strategy and the balancing strategy. An index OFC reflecting the ability of each policy to repair the rasterization error is calculated.

The results indicate that the rasterization error is sensitive to the pixel size. As the picture element increases, AE, SE and TE all increase significantly. The conventional strategy has a good effect of repairing single-type rasterization errors. But the area strategy leads to increased shape errors and topology errors, especially when the picture element size is small. Shape or topology strategies help reduce shape and topology errors, but introduce new area errors. The balancing strategy can reduce these three rasterization errors simultaneously. The OFC index indicates that as the pel increases, the repair capabilities of the area policy and shape policy increase, and the repair capabilities of the topology policy and balance policy gradually decrease. The main reason is that too coarse grid pixels make the loss of spatial features of the polygon severe. Many topology changes are difficult to repair and interactions between different errors are reinforced. Overall, although rasterization errors are always present, the result of the balancing strategy is significantly better than other strategies. When the pixel size is less than 10m, more than half of the errors can be repaired.

TABLE 2 rasterization errors for conventional strategy and balance strategy for different grid element sizes

Vector-to-raster conversion can destroy the spatial features of the polygon, such as area, shape, topology, etc., thereby introducing various types of rasterization errors. The invention designs three conventional strategies for independently repairing area errors, shape errors and topology errors, and develops a balance strategy capable of repairing the three errors simultaneously on the basis. Under different grid pixel sizes, the balancing strategy can more effectively repair multiple types of rasterization errors. Conventional strategies may increase other types of errors while repairing one type of error. When the pixel size is less than 10m, more than 50% of rasterization errors in the results of the balancing strategy are repaired, significantly better than the results of the conventional strategy, but the former requires a longer execution time.

In addition to the embodiments described above, other embodiments of the invention are possible. All technical schemes formed by equivalent substitution or equivalent transformation fall within the protection scope of the invention.

Claims (5)

1. A vector polygon rasterization method for balancing area, topology and shape features respectively rasterizes polygons P1 and P2 into a region set R= { R ₁ ,R ₂ ,...,R _n And region R2, performing the following steps to repair the rasterization error:

step 1, obtaining boundary pixels of a polygon as candidate pixels to be classified;

step 2, ifOr n>1, performing shape restoration, and preferentially guaranteeing that grid areas of the polygon P1 exist and are communicated to obtain an area R1, wherein the specific implementation steps are as follows:

obtaining boundary pixels lost by the polygon P1 as a candidate set P _o ；

If it isI.e. there is no grid area, then from candidate set P _o Taking out one pixel and distributing the pixel to P1;

if n>1, i.e. the grid areas are not connected, search for picture elements of the disconnected part of polygon P1, take them from P _o After being taken out, the mixture is distributed to P1;

identifying raised parts lost by polygon P1 from P _o The picture element of the part is taken out and allocated to P1;

so far, obtaining a region R1 corresponding to the polygon P1;

step 3, if the region R1 is separated from the region R2 and the polygon P1 is adjacent to the polygon P2, or if the region R1 is adjacent to the region R2 and the polygon P1 is separated from the polygon P2, repairing the topological relationship of the region specifically comprises the following steps:

if the region R1 is separated from the region R2 and the polygon P1 is adjacent to the polygon P2, obtaining the lost pixel at the common boundary of the polygons as a candidate set P _o The method comprises the steps of carrying out a first treatment on the surface of the The pixels occupied by the polygon P1 and the polygon P2 are respectively used as starting points and stopping points, and the pixel is positioned at P based on the shortest path idea _o The search pixels are allocated to the polygon P1 or the polygon P2 overlapped with the search pixels;

if the region R1 is adjacent to the region R2 and the polygon P1 is separated from the polygon P2, searching for the pixel pair causing the region to be adjacent to as the candidate set P _c ＝{(p ₁₁ ,p ₁₂ ),(p ₂₁ ,p ₂₂ ),...,(p _n1 ,p _n2 ) P is }, P _c One of each pair of pixels is allocated to the other polygons except the polygon P1 and the polygon P2;

step 4, if the long and narrow convex part of the polygon is lost, reassigning the boundary pixels of the part to the polygon;

and 5, combining the polygonal area with the size of the grid pixels, and utilizing the areas of the R1 and R2 of the rest boundary pixels to coordinate the areas of the polygonal area and the grid area so that the difference between the polygonal area and the area of the grid area is not more than half of the pixel area.

2. The method of vector polygonal rasterization of balancing area, topology and shape features of claim 1, wherein: the specific implementation process of the step 5 is as follows:

a1, calculating the area difference between the polygon P and the region R obtained after rasterization, and determining the quantity k of pixels needing reclassifying according to the area difference, wherein adjacent pixels with the same attribute value form the region R;

wherein S is _p Is the area of polygon P, S _R The area of the region R, s is the area of the grid pixel;

a2, obtaining boundary pixels of the polygon P, wherein the boundary pixels belong to the regionThe picture elements of R are taken as candidate sets P _a Other picture elements as candidate set P _o ；

a3, if k > 0, from candidate set P _a Taking out one pixel and distributing the pixel to other polygons; if k<0, from candidate set P _o Taking out one pixel and distributing the pixel to a polygon P;

a4, repeating the step a3 until the average area error of the region R and the adjacent regions thereof is not reduced or the candidate set P _o Is empty.

3. A method of vector polygonal rasterization for balancing area, topology and shape features as recited in claim 1, wherein: after the rasterization is completed, the rasterization error evaluation is performed, and the area error AE, the shape error SE and the topology error TE are calculated by using the following methods,

wherein A is _v 、A _r Areas before and after rasterization of the polygon, max (a _v ,A _r ) Representation taking A _v And A is a _r The larger of the two; c (C) _v 、C _r Compactness before and after polygon rasterization, respectively, if the polygon disappears or breaks into multiple small areas after conversion, then |C _r -C _v |＝1.0；N _r Polygon pairs or polygon numbers, N, for true topology changes _v Polygon pairs or polygon numbers that are topology changes that may occur;

if the error of the initial rasterization result is AE ₀ 、SE ₀ And TE (TE) ₀ Error of repair result is AE ₁ 、SE ₁ And TE (TE) ₁ The overall repair capability OFC of the algorithm was evaluated using the following formula:

4. a method of vector polygonal rasterization for balancing area, topology and shape features as recited in claim 3, wherein: the compactness calculation formula of the polygon is as follows:

wherein A and P are the area and perimeter of the polygon, and C is (0, 1).

5. A method of vector polygonal rasterization for balancing area, topology and shape features as recited in claim 3, wherein: the total number of polygon pairs or polygon numbers, where topology changes may occur, is determined according to the following equation:

where i and j represent two polygons, d (i, j) represents the shortest distance between polygon i and polygon j boundary, and s is the area of the grid pixel.