CN102682115B - Dot density thematic map making method based on Voronoi picture - Google Patents
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Abstract
The invention discloses a dot density thematic map making method based on a Voronoi picture, which comprises the following steps: firstly, reading data of discrete points, and building a V map according to the discrete points; then, rasterizing the whole V map area; according to the membership function of an image element and V polygon and distance between the center point of the internal image elements of the V polygon and the discrete points, calculating the density value of the image element, wherein in order to bring a more reasonable result, the neighbourhood mean value smooth treatment is carried out on generated grids, classifying is carried out again, and different gray values are assigned; and finally, rendering all grids. The V map built on the basis of the discrete points is divided by the space restricted by the shortest distance into influence ranges generated by each discrete point, and local density calculation is carried out within the ranges to guarantee the reliability and the comparability of a calculation result among influence ranges. In addition, the difference of different image element point densities within the influence ranges is considered in the method, a density value distribution method based on the distance is adopted in the V polygon in which each point is positioned, and therefore the result is more reasonable and accurate.
Description
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 application technology in computational geometry, Cartography and Geography Information System (GIS).
Background technology
The calculating of dot density refers to according to the distribution of point in zone estimates counting of any point position unit area in it.On ground, learn in application, the calculating of dot density be to the 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 application 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 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 that territory is corresponding.
At present, calculate place, any point place 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 element factor calculation unit area in neighborhood around each grid cell, raster cell.In concept, it to around each grid cell, raster cell center, having defined a neighborhood, by the quantity addition of putting in neighborhood, then divided by the neighborhood area, finally obtains the density of a key element take grid cell, raster cell as starting point.Another kind is the method for Density Estimator, and it is take a key element as starting point, the density of calculation level key element in neighborhood around it.The method think each the point above all be covered with a smooth surface.Face value is the highest at place, some position, and along with the increase face value of the distance with point reduces gradually, the position face value that equals search radius in the distance with point is zero.The search neighborhood of kernel density estimation method only allows to use circular, and the density of each output pixel is the value sum on all core 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, the size of still searching for neighborhood has certain influence to result: when the search radius parameter value is larger, it is higher that the density grid of generation more smoothly and is generally changed degree; When parameter value is less, 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 Statistics discrete point of unified size, but have ignored the difference of dot density in the neighborhood scope; And the Density Estimator method is usingd unified big or small circle as the search neighborhood, has considered the difference of dot density in neighborhood, but has 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 Voronoi figure for spatial division, a kind of thematic mapping of dot density based on Voronoi figure method is provided, it is take the corresponding Voronoi polygon of each discrete point as neighborhood, the method of distributing by anti-distance weighting realizes the difference assignment of dot density in neighborhood, can be fast, rationally, calculation level density output point density map accurately.
In order to solve above technical matters, a kind of thematic mapping of dot density based on Voronoi figure method provided by the invention comprises the following 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---based on all discrete points in discrete point set, build Voronoi figure;
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 to rasterizing, generate the center point coordinate of some pixels definite each pixel;
The 4th walks, 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 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, by 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
gFor the area of single pixel, 1≤i≤n, n are the polygonal number of Voronoi in Voronoi figure;
The 6th step, grid is level and smooth---and adopt the method for spatial domain smothing filtering to recalculate each picture element density value;
The 7th step, picture element density value reclassification---the density value size of all pixels in the statistical study grid map, reclassify all picture element density values accordingly, gives different gray-scale values;
The 8th step, drafting density map---according to the gray-scale value of each pixel, grid is played up to the acquisition density map.
In dot density thematic mapping method of the present invention, the Voronoi that builds based on discrete point schemes, use the Voronoi polygon to cut apart zone, make in each Voronoi polygon have and only have a discrete point (unit occurs), each Voronoi polygon can be considered corresponding discrete point and generates " coverage "; In the Voronoi polygon, the calculating of each picture element density value does not occur associated with other Voronoi polygons, therefore in the Voronoi polygon calculating of picture element density value to be disturbed degree low, in the Voronoi polygon, comparability and the reliability that has guaranteed result of calculation between each Voronoi polygon calculated by local density; 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 the 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, in the 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 to; Voronoi polygon V
iThe density value of j interior pixel is
R wherein
Ij, R
IkRepresent respectively Voronoi polygon V
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
iFor Voronoi polygon V
iInterior pixel number, i, j, k are natural number.
Scheme two:
In the second step of preceding method, set up the corresponding relation between discrete point and the Voronoi polygon under it; In described the 5th step, adopts anti-distance weighting apportion design to share each picture element density value in the Voronoi polygon, the density value of the interior pixel of Voronoi polygon and this pixel central point square are inversely proportional to the distance of the corresponding discrete point of this Voronoi polygon; Voronoi polygon V
iThe density value of j interior pixel is
R wherein
IjR
IkRepresent respectively Voronoi polygon V
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
iFor 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 picture element density value in the Voronoi polygon, Voronoi polygon V
iThe density value B of interior j pixel
Ij=1/ (S
g* m
i), m
iFor Voronoi polygon V
iInterior pixel number, j≤m
i, and j is natural number.
In aforementioned three kinds of schemes, what the first two method 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 larger, and the dot density value is lower; 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 of distance-based to distribute way, makes result more rationally accurately.
Wherein, in 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, in Voronoi polygon inside, further considered distance factor, 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.
The accompanying drawing explanation
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 build schematic diagram.
Fig. 3 is that pixel membership and density value calculate schematic diagram.
Fig. 4 is the level and smooth schematic diagram of grid neighboring mean value.
Fig. 5 is picture element density value reclassification schematic diagram.
Embodiment
Below describe with reference to the accompanying drawings the present invention in detail, it is more obvious that purpose of the present invention and effect will become.
Be illustrated in figure 1 the process flow diagram of the dot density thematic mapping method that the present invention is based on Voronoi figure, comprise the following 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---based on all discrete points in discrete point set, build Voronoi figure, set up the corresponding relation between discrete point and the Voronoi polygon under it;
In this example, take all discrete points in discrete point set as unit occurs, by scan-line algorithm, build Voronoi figure, 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 the Voronoi polygon under it; Set up simultaneously the topological relation that occurs between unit (discrete point) and Voronoi limit, generation unit (discrete point) and Voronoi polygon, in the data structure on Voronoi limit, record forms the straight-line equation coefficient on this limit, form two end points on this limit and with Lian De both sides, this frontier juncture, unit's (discrete point) occur, 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 to rasterizing, generate the center point coordinate of some pixels 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
2.Pixel can the two-dimensional array form be stored, and arrangement mode, for from left to right, is arranged from the top down.For arbitrary pixel a
IjIts pixel center point coordinate is
Wherein, 0≤i≤p-1,0≤j≤q-1.
The 4th walks, 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 this pixel belongs to this Voronoi polygon.
In this example, the polygonal membership of pixel and Voronoi provides as follows: if which Voronoi polygon the pixel central point drops in, this pixel just is under the jurisdiction of this Voronoi polygon; If the pixel central point drops on certain Voronoi limit, 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, 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 in Fig. 4 in 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 in the present invention.
The 5th walks, calculates density value---i Voronoi polygon V of each pixel
iTotal density value be 1/S
g, by 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
gFor the area of single pixel, 1≤i≤n, n are the polygonal number of Voronoi in Voronoi figure;
In this example, adopt anti-distance weighting apportion design to share each picture element density value in the Voronoi polygon, in the 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 to.
Be illustrated in figure 3 pixel membership and density value and calculate schematic 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 respectively Voronoi polygon V
iIn the central point of j and k pixel to Voronoi polygon V
iCorresponding discrete point P
iDistance, S
gThe area that represents single pixel, j≤m
i, k≤m
i, m
iFor 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, according to the geometric center of its each pixel that is subordinate to, to the inverse of the distance that unit occurs, account for all pixel geometric centers and distribute the share of " point " to the ratio of the first inverse distance sum of generation, then obtain dot density divided by the pixel area.As shown in Figure 5, the data in the grid of left side are the picture element density value for obtaining after calculating, next carries out the 6th step grid level and smooth.
The 6th step, grid is level and smooth---and adopt the method for spatial domain smothing filtering to recalculate each picture element density value.
The method of spatial domain smothing filtering can be neighboring mean value smoothing method, neighborhood median smoothing method, neighborhood extreme value smoothing method etc.In this example, adopt the field method of average, be about to the density value of a pixel in graticule mesh and the density value addition of contiguous pixel on every side, the mean value that then will try to achieve is as the density value of this pixel in 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 traveling through line by line each pixel, carry out the matrix multiple in required pixel neighborhood, as shown in Figure 4, what this example was selected is the template of 3*3 size, and in the grid after level and smooth, the picture element density value is shown in Fig. 5 right side.After grid is level and smooth, substantially can eliminate near " abrupt slope " phenomenon in Voronoi limit.In the present embodiment, adopt the mean value smoothing method, do not got rid of more rationally effective smoothing method of existence.
The 7th step, picture element density value reclassification---the density value size of all pixels in the statistical study grid map, reclassify all picture element density values accordingly, gives different gray-scale values.
The essence of reclassification is the method (as shown in Figure 5) that reclassifies picture element density value (property value) or input picture element density value is changed to substitution value.At first, travel through line by line each pixel, 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 accordingly rational interval threshold, by density value order from small to large, all pixels are divided into to some classes; Finally, to the rear pixel of classifying, give different gray-scale values.Density is larger, and the gray-scale value of giving is larger.
The 8th step, drafting density map---according to the gray-scale value of each pixel, grid is played up to the acquisition density map.
In the 5th step of the present embodiment, in the 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 to; 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 respectively Voronoi polygon V
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
iFor 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 picture element density value in the Voronoi polygon, Voronoi polygon V
iThe density value B of interior j pixel
Ij=1/ (S
g* m
i), m
iFor Voronoi polygon V
iInterior pixel number, j≤m
i, and j is natural number.
The 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 builds, and in this scope, carries out local density and calculates comparability and the reliability that has guaranteed result of calculation between each " coverage " (Voronoi polygon); In addition, in this method, considered the difference of different pixel dot densities in " coverage ", in the Voronoi at each point place polygon inside, adopted the density value of distance-based to distribute way, made 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 (2)
1. the thematic mapping of the dot density based on Voronoi figure method comprises the following 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---based on all discrete points in discrete point set, build Voronoi figure;
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 to rasterizing, generate the center point coordinate of some pixels definite each pixel;
The 4th walks, 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 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, by 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
gFor the area of single pixel, 1≤i≤n, n are the polygonal number of Voronoi in Voronoi figure;
In described the 5th step, adopt equal point-score to share each picture element density value in the Voronoi polygon, Voronoi polygon V
iThe density value B of interior j pixel
Ij=1/ (S
g* m
i), m
iFor Voronoi polygon V
iInterior pixel number, j≤m
i, and j is natural number
The 6th step, grid is level and smooth---and adopt the method for spatial domain smothing filtering to recalculate each picture element density value;
The 7th step, picture element density value reclassification---the density value size of all pixels in the statistical study grid map, reclassify all picture element density values accordingly, gives different gray-scale values;
The 8th step, drafting density map---according to the gray-scale value of each pixel, grid is played up to the acquisition density map.
2. the thematic mapping of the dot density based on Voronoi figure method according to claim 1 is characterized in that: in described the 6th step, the method for spatial domain smothing filtering is in neighboring mean value smoothing method, neighborhood median smoothing method, neighborhood extreme value smoothing method-kind.
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