CN103336783A - Voronoi and inverse distance weighting combined density map drawing method - Google Patents
Voronoi and inverse distance weighting combined density map drawing method Download PDFInfo
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Abstract
The invention discloses a Voronoi (V) and inverse distance weighting combined density map drawing method which comprises the steps that discrete point data is read; a V map is constructed by discrete points; a whole V map area is rasterized; a density value of pixels is computed according to a subordination relationship between the pixels and a V polygon and distances between a pixel center point in the V polygon and the discrete points; and all generated grids are rendered finally after subjected to neighborhood mean value smoothing processing, re-classified, and endowed with different gray-scale values in order to make results more reasonable. The V map constructed based on the discrete points is divided into generation influence ranges of the discrete points by a space constrained based on the shortest distance, and local density computation is performed within the ranges, so that the comparability and the reliability of computation results among the various influence ranges are guaranteed; and the method takes account of differences of the point density of the different pixels within the influence ranges, and a density value distribution method based on the distances is adopted in the V polygon where each point is located, so that the results are more reasonable and accurate.
Description
This case is Chinese invention patent application 201210146965.2, applying date 2012-05-11, the dividing an application of title " a kind of dot density thematic map method for making based on Voronoi figure "
Technical field
What the present invention proposed is a kind of method for making of dot density thematic maps, belongs to the crossing domain of Voronoi figure (the Voronoi polygon is also referred to as " Thiessen polygon ") application technology in computational geometry, the Cartography and Geography Information System (GIS).
Background technology
The calculating of dot density refers to estimate counting of any point position unit area in it according to the distribution of point in the zone.Learn in the application on ground, the calculating of dot density be to problems such as residential area density calculation, building density calculating conclude with sum up after theoretical abstraction, in fields such as density of population distribution, image processing, cluster analysis, discriminatory analysis, independent component analysis (ICA), computer visions important use is arranged.The most direct method that embodies the dot density distribution is exactly by the graphical pointv density map.Dot-density plot is a kind of of thematic map in the cartography, and it shows the border corresponding with data value or field object with point (number), and total number of a field object mid point has represented the data value of territory correspondence.
At present, calculate place, arbitrarily some places dot density and mainly contain two kinds of common methods.A kind of is simple dot density computing method, namely according to the magnitude that falls into the some key element unit of account area in the neighborhood around each grid cell, raster cell.In concept, it is starting point with the grid cell, raster cell, to having defined a neighborhood around each grid cell, raster cell center, with the quantity addition of putting in the neighborhood, then divided by the neighborhood area, finally obtains the density of a key element.Another kind is the method for Density Estimator, and it is starting point with a key element, the density of calculation level key element in neighborhood around it.This method think each the point above all be covered with a smooth surface.The highest at place, a position face value, along with the increase face value with the distance of putting reduces gradually, the position face value that equals search radius in the distance with point is zero.The search neighborhood of kernel function density estimation method only allows to use circular, and the density of each output pixel is the value sum on all nuclear surfaces that are superimposed upon the grid cell, raster cell center.
These two kinds of methods all have a wide range of applications in dot density is calculated, but the size of searching for neighborhood has certain influence to the result: when the search radius parameter value is more big, the density grid of generation is more level and smooth and generally to change degree more high; When parameter value is more little, the shown information of the grid of generation is more detailed.In addition, simple dot density computing method are with the number of the neighborhood statistical straggling point of unified size, but have ignored the difference of the interior dot density of neighborhood scope; And the Density Estimator method with the circle of unified size as the search neighborhood, considered the difference of the interior dot density of neighborhood, but ignored the difference of different discrete points " coverage ".
Summary of the invention
The present invention wants the technical solution problem to be: the above-mentioned deficiency that overcomes prior art, by the technical advantage of Thiessen polygon for spatial division, a kind of Thiessen polygon and anti-distance weighted density map drafting method of uniting is provided, it is neighborhood with the corresponding Voronoi polygon of each discrete point (Thiessen polygon), the method of distributing by anti-distance weighting realizes the difference assignment of dot density in the neighborhood, can be fast, rationally, calculation level density and output point density map accurately.
In order to solve above technical matters, a kind of Thiessen polygon and anti-distance weighted density map drafting method of uniting provided by the invention may further comprise the steps:
The first step, discrete point read---and read the discrete point set as raw data, described discrete point has sequence number and coordinate data separately;
Second step, structure Voronoi figure---make up Voronoi figure based on all discrete points in the discrete point set;
The 3rd step, Voronoi figure rasterizing---according to the coordinate in the Voronoi figure upper left corner and the lower right corner, and the row, column number of given division grid cell, raster cell, whole Voronoi graph region is drawn rasterizing, generate the center point coordinate of some pixels and definite each pixel;
The 4th goes on foot, sets up pixel and the polygonal membership of Voronoi---according to center point coordinate and the polygonal topological relation of Voronoi of pixel, judge pixel and the polygonal membership of Voronoi, when the central point of pixel drops in certain Voronoi polygon, judge that then this pixel belongs to this Voronoi polygon;
Density value---i Voronoi polygon V of the 5th step, calculating pixel
iTotal density value be 1/S
g, with this total density value 1/S
gShare to Voronoi polygon V
iEach pixel, make Voronoi polygon V
iThe density value summation of interior all pixels equals 1/S
g, wherein, S
gBe the area of single pixel, 1≤i≤n, n are the polygonal number of Voronoi among the Voronoi figure;
The 6th step, grid is level and smooth---and adopt the method for spatial domain smothing filtering to recomputate each picture element density value;
The 7th step, picture element density value are heavily classified---the density value size of all pixels in the statistical study grid map, accordingly all picture element density values are reclassified, and give different gray-scale values;
The 8th step, draw that density map---the gray-scale value according to each pixel is played up the acquisition density map to grid.
In the dot density thematic map method for making of the present invention, the Voronoi that makes up based on discrete point schemes, use the Voronoi polygon that the zone is cut apart, making has and has only a discrete point (unit takes place) in each Voronoi polygon, each Voronoi polygon can be considered corresponding discrete point and generates " coverage "; The calculating of each picture element density value does not take place related with other Voronoi polygons in the Voronoi polygon, therefore the calculating of picture element density value is subjected to annoyance level low in the Voronoi polygon, and comparability and the reliability that has guaranteed result of calculation between each Voronoi polygon calculated by local density in the Voronoi polygon; And the polygonal total density value allocation way of Voronoi can be selected according to actual conditions, can select to divide equally method, also can select anti-distance weighting apportion design, uses more flexible; The Voronoi figure constructed based on discrete point has uniqueness, thus in the present invention program's implementation procedure subjective factor still less, easy operating.
The invention provides following three kinds of Voronoi polygon total density value pool schemes:
Scheme one:
In second step of preceding method, set up the corresponding relation between discrete point and the Voronoi polygon under it; In described the 5th step, adopt anti-distance weighting apportion design to share each interior picture element density value of Voronoi polygon, the density value of pixel and this pixel central point to the distance of the corresponding discrete point of this Voronoi polygon is inversely proportional in the Voronoi polygon; Voronoi polygon V
iThe density value of j interior pixel is
R wherein
Ij, R
IkRepresent Voronoi polygon V respectively
iIn the central point of j and k pixel to Voronoi polygon V
iCorresponding discrete point P
iDistance, j≤m
i, k≤m
i, m
iBe Voronoi polygon V
iInterior pixel number, i, j, k are natural number.
Scheme two:
In second step of preceding method, set up the corresponding relation between discrete point and the Voronoi polygon under it; In described the 5th step, adopt anti-distance weighting apportion design to share each picture element density value in the Voronoi polygon, the density value of pixel and this pixel central point square being inversely proportional to the distance of the corresponding discrete point of this Voronoi polygon in the Voronoi polygon; Voronoi polygon V
iThe density value of j interior pixel is
R wherein
IjR
IkRepresent Voronoi polygon V respectively
iIn the central point of j and k pixel to Voronoi polygon V
iCorresponding discrete point P
iDistance, j≤m
i, k≤m
i, m
iBe Voronoi polygon V
iInterior pixel number, i, j, k are natural number.
Scheme three:
In the 5th step of preceding method, adopt equal point-score to share each interior picture element density value of Voronoi polygon, Voronoi polygon V
iThe density value B of interior j pixel
Ii=1/ (S
g* m
i), m
iBe Voronoi polygon V
iInterior pixel number, j≤m
i, and j is natural number.
In aforementioned three kinds of schemes, what preceding two kinds of methods adopted is anti-distance weighting apportion design, the third employing be equal point-score.All point-score calculating is simpler, and the space distribution of dot density can reflect from the polygonal size of Voronoi (the Voronoi polygon comprises the quantity of pixel), and the Voronoi area of a polygon is more big, and then the dot density value is more low; Anti-distance weighting distributes rule to consider the difference of different pixel dot densities in " coverage " (Voronoi polygon), and the Voronoi polygon inside at each pixel place has adopted the density value based on distance to distribute way, makes the result more rationally accurately.
Wherein, in the anti-distance weighting apportion design, the space distribution of dot density can reflect from the size of the Voronoi area of a polygon that calculates, further considered distance factor in Voronoi polygon inside, the density value of pixel is assigned in each pixel by the shared proportion of the inverse of distance (or reciprocal square), makes result of calculation more reasonable.
Description of drawings
The present invention is further illustrated below in conjunction with accompanying drawing.
Fig. 1 is the inventive method process flow diagram.
Fig. 2 is that discrete point and Voronoi figure thereof make up synoptic diagram.
Fig. 3 is that pixel membership and density value calculate synoptic diagram.
Fig. 4 is grid neighborhood mean value smoothing synoptic diagram.
Fig. 5 is the picture element density value synoptic diagram of heavily classifying.
Embodiment
Describe the present invention below with reference to the accompanying drawings in detail, it is more obvious that purpose of the present invention and effect will become.
Be illustrated in figure 1 as the process flow diagram that the present invention unites Thiessen polygon and anti-distance weighted density map drafting method, may further comprise the steps:
The first step, discrete point read---and read the discrete point set as raw data, described discrete point has sequence number and coordinate data separately.
Read the coordinate of discrete point, and show each some position (Fig. 2 left side) according to the proportionate relationship of screen coordinate scope and discrete point coordinate range.In this example the discrete point numbering is stored as the attribute data of discrete point.
Second step, structure Voronoi figure---make up Voronoi figure based on all discrete points in the discrete point set, set up the corresponding relation between discrete point and the Voronoi polygon under it;
In this example, serve as that unit takes place with all discrete points in the discrete point set, make up Voronoi figure by scan-line algorithm, the number value of discrete point is passed to the polygonal number value of Voronoi, so just set up the corresponding relation between discrete point and its affiliated Voronoi polygon; Set up the topological relation that takes place between unit (discrete point) and Voronoi limit, generation unit (discrete point) and Voronoi polygon simultaneously, record constitutes the straight-line equation coefficient on this limit in the data structure on Voronoi limit, constitute two end points on this limit and the both sides generation units (discrete point) that join with this frontier juncture, this polygonal limit set of record in the polygonal data structure of Voronoi; Adopt such data to be conducive to the calculating of picture element density value in following the 5th step.
The 3rd step, Voronoi figure rasterizing---according to the coordinate in the Voronoi figure upper left corner and the lower right corner, and the row, column number of given division grid cell, raster cell, whole Voronoi graph region is drawn rasterizing, generate the center point coordinate of some pixels and definite each pixel.
For the graticule mesh of the arbitrary p*q that divides, the coordinate of establishing its whole regional lower left corner and the upper right corner is respectively (A
1, B
1) and (A
2, B
2), A wherein
1＜A
2, B
1＜B
2Pixel can the two-dimensional array form be stored, and arrangement mode is arranged from the top down for from left to right.For arbitrary pixel a
IjIts pixel center point coordinate is
Wherein, 0≤i≤p-1,0≤j≤q-1.
The 4th goes on foot, sets up pixel and the polygonal membership of Voronoi---according to center point coordinate and the polygonal topological relation of Voronoi of pixel, judge pixel and the polygonal membership of Voronoi, when the central point of pixel drops in certain Voronoi polygon, judge that then this pixel belongs to this Voronoi polygon.
In this example, the polygonal membership regulation of pixel and Voronoi is as follows: if which Voronoi polygon the pixel central point drops in, then this pixel just is under the jurisdiction of this Voronoi polygon; If the pixel central point drops on certain bar Voronoi limit, then search two Voronoi polygons that join with this frontier juncture, stipulate that this pixel is under the jurisdiction of the less Voronoi polygon of generation unit numbering; If the pixel center overlaps with certain Voronoi summit just, then search three Voronoi limits that are associated with this summit, and then find three Voronoi polygons that are associated with this summit, stipulate that this pixel is under the jurisdiction of generation unit numbering reckling in three Voronoi polygons.Pixel among Fig. 4 in the solid border is for being under the jurisdiction of this polygonal pixel.Situation about dropping on Voronoi polygonal Voronoi limit and the polygonal summit of Voronoi for the pixel center belongs to special case, the membership rule of these pixels can artificially define, be not strict with, so this partial content do not limited and describes in detail among the present invention.
The 5th goes on foot, calculates density value---i Voronoi polygon V of each pixel
iTotal density value be 1/S
g, with this total density value 1/S
gShare to Voronoi polygon V
iEach pixel, make Voronoi polygon V
iThe density value summation of interior all pixels equals 1/S
g, wherein, S
gBe the area of single pixel, 1≤i≤n, n are the polygonal number of Voronoi among the Voronoi figure;
In this example, adopt anti-distance weighting apportion design to share each interior picture element density value of Voronoi polygon, the density value of pixel and this pixel central point to the distance of the corresponding discrete point of this Voronoi polygon is inversely proportional in the Voronoi polygon.
Be illustrated in figure 3 as pixel membership and density value and calculate synoptic diagram.The computing method of the concrete density value of pixel are as follows:
Voronoi polygon V
iThe density value of j interior pixel is
R wherein
Ij, R
IkRepresent Voronoi polygon V respectively
iIn the central point of j and k pixel to Voronoi polygon V
iCorresponding discrete point P
iDistance, S
gThe area of representing single pixel, j≤m
i, k≤m
i, m
iBe Voronoi polygon V
iInterior pixel number, i, j, k are natural number.The essence that the picture element density value is calculated is exactly in a Voronoi polygon, geometric center according to its each pixel that is subordinate to accounts for the share that all pixel geometric centers are distributed " point " to the ratio that first inverse distance sum takes place to the inverse that first distance takes place, and obtains dot density divided by the pixel area again.As shown in Figure 5, the data in the grid of left side are the picture element density value for obtaining after calculating then, and it is level and smooth next to carry out the 6th step grid.
The 6th step, grid is level and smooth---and adopt the method for spatial domain smothing filtering to recomputate each picture element density value.
The method of spatial domain smothing filtering can be neighborhood mean value smoothing method, neighborhood median smoothing method, neighborhood extreme value smoothing method etc.Adopt the field method of average in this example, be about to the density value of a pixel in the graticule mesh and the density value addition of contiguous pixel on every side, then with the mean value of the trying to achieve density value as this pixel in the new graticule mesh; In addition according to generating what of grid cell, raster cell number, adopt the template of suitable size (as 5*5,9*9,25*25 etc.) by travel through line by line each pixel carry out ask matrix multiple in the pixel neighborhood, as shown in Figure 4, what this example was selected for use is the template of 3*3 size, and smoothly the picture element density value is seen Fig. 5 right side in the grid after.After level and smooth through grid, can eliminate near " abrupt slope " phenomenon in Voronoi limit substantially.In the present embodiment, adopted the mean value smoothing method, do not got rid of and have more rational and effective smoothing method.
The 7th step, picture element density value are heavily classified---the density value size of all pixels in the statistical study grid map, accordingly all picture element density values are reclassified, and give different gray-scale values.
Heavily Fen Lei essence is the method (as shown in Figure 5) that picture element density value (property value) is reclassified or input picture element density value is changed to substitution value.At first, travel through each pixel line by line, middle maximal value, minimum value and the frequency distribution thereof of all picture element density values of statistical study; Secondly, make histogram frequency distribution diagram and frequency variation curve, and select rational interval threshold by density value order from small to large all pixels to be divided into some classes accordingly; At last, give different gray-scale values to the back pixel of classifying.Density is more big, and the gray-scale value of giving is more big.
The 8th step, draw that density map---the gray-scale value according to each pixel is played up the acquisition density map to grid.
In the 5th step of present embodiment, the density value of pixel and this pixel central point to the distance of the corresponding discrete point of this Voronoi polygon is inversely proportional in the Voronoi polygon; In addition, the density value of pixel and this pixel central point square being inversely proportional to the distance of the corresponding discrete point of this Voronoi polygon in the Voronoi polygon; Voronoi polygon V
iThe density value of j interior pixel is
R wherein
IjR
IkRepresent Voronoi polygon V respectively
iIn the central point of j and k pixel to Voronoi polygon V
iCorresponding discrete point P
iDistance, j≤m
i, k≤m
i, m
iBe Voronoi polygon V
iInterior pixel number, i, j, k are natural number.
When calculating the picture element density value, also can adopt equal point-score to share each interior picture element density value of Voronoi polygon, Voronoi polygon V
iThe density value B of interior j pixel
Ij=1/ (S
g* m
i), m
iBe Voronoi polygon V
iInterior pixel number, j≤m
i, and j is natural number.
Present embodiment generates " coverage " by the spatial division based on the bee-line constraint for each discrete point based on the Voronoi figure that discrete point makes up, and carries out local density and calculate comparability and the reliability that has guaranteed result of calculation between each " coverage " (Voronoi polygon) in this scope; In addition, considered the difference of different pixel dot densities in " coverage " in this method, adopted the density value based on distance to distribute way in the Voronoi at each point place polygon inside, made the result more rationally accurately.
In addition to the implementation, the present invention can also have other embodiments.All employings are equal to the technical scheme of replacement or equivalent transformation formation, all drop on the protection domain of requirement of the present invention.
Claims (6)
1. unite Thiessen polygon and anti-distance weighted density map drafting method for one kind, may further comprise the steps:
The first step, discrete point read---and read the discrete point set as raw data, described discrete point has sequence number and coordinate data separately;
Second step, structure Voronoi figure---make up Voronoi figure based on all discrete points in the discrete point set;
In described second step, set up the corresponding relation between discrete point and the Voronoi polygon under it;
The 3rd step, Voronoi figure rasterizing---according to the coordinate in the Voronoi figure upper left corner and the lower right corner, and the row, column number of given division grid cell, raster cell, whole Voronoi graph region is drawn rasterizing, generate the center point coordinate of some pixels and definite each pixel;
The 4th goes on foot, sets up pixel and the polygonal membership of Voronoi---according to center point coordinate and the polygonal topological relation of Voronoi of pixel, judge pixel and the polygonal membership of Voronoi, when the central point of pixel drops in certain Voronoi polygon, judge that then this pixel belongs to this Voronoi polygon;
Density value---i Voronoi polygon V of the 5th step, calculating pixel
iTotal density value be 1/S
g, with this total density value 1/S
gShare to Voronoi polygon V
iEach pixel, make Voronoi polygon V
iThe density value summation of interior all pixels equals 1/S
g, wherein, S
gBe the area of single pixel, 1≤i≤n, n are the polygonal number of Voronoi among the Voronoi figure;
In described the 5th step, adopt anti-distance weighting apportion design to share each interior picture element density value of Voronoi polygon, the density value of pixel and this pixel central point to the distance of the corresponding discrete point of this Voronoi polygon is inversely proportional in the Voronoi polygon;
The 6th step, grid is level and smooth---and adopt the method for spatial domain smothing filtering to recomputate each picture element density value;
The 7th step, picture element density value are heavily classified---the density value size of all pixels in the statistical study grid map, accordingly all picture element density values are reclassified, and give different gray-scale values;
The 8th step, draw that density map---the gray-scale value according to each pixel is played up the acquisition density map to grid.
2. associating Thiessen polygon according to claim 1 and anti-distance weighted density map drafting method is characterized in that: Voronoi polygon V
iThe density value of j interior pixel is
R wherein
Ij, R
IkRepresent Voronoi polygon V respectively
iIn the central point of j and k pixel to Voronoi polygon V
iCorresponding discrete point P
iDistance, j≤m
i, k≤m
i, m
iBe Voronoi polygon V
iInterior pixel number, i, j, k are natural number.
3. according to each described associating Thiessen polygon of claim 1-2 and anti-distance weighted density map drafting method, it is characterized in that: in described the 6th step, the method for spatial domain smothing filtering is a kind of in neighborhood mean value smoothing method, neighborhood median smoothing method, the neighborhood extreme value smoothing method.
4. unite Thiessen polygon and anti-distance weighted density map drafting method for one kind, may further comprise the steps:
The first step, discrete point read---and read the discrete point set as raw data, described discrete point has sequence number and coordinate data separately;
Second step, structure Voronoi figure---make up Voronoi figure based on all discrete points in the discrete point set;
In described second step, set up the corresponding relation between discrete point and the Voronoi polygon under it;
The 3rd step, Voronoi figure rasterizing---according to the coordinate in the Voronoi figure upper left corner and the lower right corner, and the row, column number of given division grid cell, raster cell, whole Voronoi graph region is drawn rasterizing, generate the center point coordinate of some pixels and definite each pixel;
The 4th goes on foot, sets up pixel and the polygonal membership of Voronoi---according to center point coordinate and the polygonal topological relation of Voronoi of pixel, judge pixel and the polygonal membership of Voronoi, when the central point of pixel drops in certain Voronoi polygon, judge that then this pixel belongs to this Voronoi polygon;
Density value---i Voronoi polygon V of the 5th step, calculating pixel
iTotal density value be 1/S
g, with this total density value 1/S
gShare to Voronoi polygon V
iEach pixel, make Voronoi polygon V
iThe density value summation of interior all pixels equals 1/S
g, wherein, S
gBe the area of single pixel, 1≤i≤n, n are the polygonal number of Voronoi among the Voronoi figure;
In described the 5th step, adopt anti-distance weighting apportion design to share each picture element density value in the Voronoi polygon, the density value of pixel and this pixel central point square being inversely proportional to the distance of the corresponding discrete point of this Voronoi polygon in the Voronoi polygon;
The 6th step, grid is level and smooth---and adopt the method for spatial domain smothing filtering to recomputate each picture element density value;
The 7th step, picture element density value are heavily classified---the density value size of all pixels in the statistical study grid map, accordingly all picture element density values are reclassified, and give different gray-scale values;
The 8th step, draw that density map---the gray-scale value according to each pixel is played up the acquisition density map to grid.
5. associating Thiessen polygon according to claim 4 and anti-distance weighted density map drafting method is characterized in that: Voronoi polygon V
iThe density value of j interior pixel is
R wherein
IjR
IkRepresent Voronoi polygon V respectively
iIn the central point of j and k pixel to Voronoi polygon V
iCorresponding discrete point P
iDistance, j≤m
i, k≤m
i, m
iBe Voronoi polygon V
iInterior pixel number, i, j, k are natural number.
6. according to each described associating Thiessen polygon of claim 4-5 and anti-distance weighted density map drafting method, it is characterized in that: in described the 6th step, the method for spatial domain smothing filtering is a kind of in neighborhood mean value smoothing method, neighborhood median smoothing method, the neighborhood extreme value smoothing method.
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