TWI398828B - A Method of Seeking Range Query in Hilbert Curve - Google Patents

Description

Method for finding range query in Hilbert curve

The present invention relates to a range query method, and more particularly to a method for finding a range query in a Hilbert curve.

The Space-filling Curve is a line segment that can travel through every point in the 2 ⁿ × 2 ⁿ plane, and each point can only be passed once, so that 2D coordinates can be converted to 1D. Coordinates, that is, can help a 2D data to determine a global index. The Hilbert curve is the most representative Space-filling curve. Because it can effectively preserve the locality of space, it has been widely used in many fields, such as image processing and compression. Spatial query and wireless broadcast system. In image applications, if you follow the path of the Hilbert curve, you can find that it walks to its neighboring points each time. This path, which is in the order of Hilbert index, is called Hilbert scan. Many image compression methods are developed based on Hilbert scan.

In the application of image database, window query is a very important query function. Suppose the compressed image size is T×T, the window size is n ₁ ×n ₂ , and the lower left corner of the window is (x,y). The window query is the sub-image that requires the range represented by the window. . The easiest way is to decompress the image and then do the window query. If the image is large (such as satellite maps), it will waste a lot of decompression time. In addition, the method of Liu et al. calculates all Hilbert indexes in the window, and the required time complexity is O(n ₁ n ₂ log T) (refer to the prior art document: LIU X., SCHRACK GF: 'Encoding and decoding the Hilbert Order', Softw. Pract. Exp., 1996, 26, (12), pp. 1335-1346).

Chung et al. proposed a fast window query method for compressed images with Hilbert scan (refer to the previous technical literature: CHUNG KL, TASI YH, HU FC: 'Space-filling approach for fast window query on compressed images', IEEE Trans. Image Process., 2000, 9, (12), pp. 2109-2116), which uses the maximum block segmentation method and the Hilbert index mutual conversion method of scholars such as Liu to find all the Hilbert indexes in the window. The required time complexity is O(nlogT), where n is the longest side of the window. However, the above conventional methods require additional steps of sorting and merging, adding a lot of computational execution time.

Therefore, it is necessary to provide an innovative and progressive method for finding a range query in the Hilbert curve to solve the above problem.

The present invention provides a method of finding a range query in a Hilbert curve. The Hilbert curve is a curve passing through each block of a query range by the Hilbert scan method, the query range includes N ₁ ×N ₁ blocks, and the block at the beginning of the Hilbert curve has a minimum order according to the Hilbert The path of the curve sequentially defines the ordering of the blocks, and the query method includes the following steps:

(a) Four types of positioning patterns are defined according to the starting point and the ending position of the four orientations and the path of the corresponding query area, and the starting point and the ending point of each of the positioning patterns are respectively located in the lower, left, upper and right directions;

(b) distinguishing the query range from a quarter-divided query area, each query area containing a sub-Hilbert curve;

(c) calculating a relative minimum order in the block of each query area based on the minimum order and the N ₁ value;

(d) calculating a window aspect according to the query area and a query window, and defining a part of the window located in the corresponding query area as a sub-window, the query window includes a query window information, and each sub-window includes a sub-window News;

(e) calculating corresponding positioning patterns and corresponding positioning patterns of each sub-Hilbert curve path according to the path of the Hilbert curve;

(f) calculating an upper-level query information according to the path of the Hilbert curve and its corresponding positioning state, the N ₁ value, the relative minimum order of the starting point of the Hilbert curve path, and the query window information;

(g) calculating corresponding lower-order query information according to the corresponding positioning information of the upper-level query information and the corresponding sub-Hilbert curve, the window mode, the sub-window information of each sub-window, and the relative minimum order of the corresponding query regions;

(h) Divide the query area near the start of the Hilbert curve path and include the sub-window into a new four-partition query area, each new query area containing a new sub-Hilbert curve and defined in the new query area The child window is a new query window, and the new relative minimum order in the block of each new query area is calculated according to the minimum order and the N ₁ value in the upper query information of each new query window;

(i) Repeat steps (d) to (h). When the height and width of the new query window are equal to the number of blocks in the height and width of the new query area, define it as the terminal query area and query the area according to the terminal. Calculating a terminal minimum order and a terminal maximum order by relative minimum ordering and its height and width; and

(j) According to the path direction of the Hilbert curve, repeat steps (d) to (i) to sequentially calculate the terminal minimum order and the terminal maximum order corresponding to the query area including the sub-window.

In the method for finding a range query in the Hilbert curve of the present invention, using the characteristics of the Hilbert curve, the positioning pattern of the query area is defined according to the path of the Hilbert curve, and the window mode is defined according to the query area and the window (window), and After the Quad-Splitting method distinguishes the query range and the query area, the order of all the blocks in the query window (the value of the Hilbert index) is calculated, and the required time complexity is low, and the calculated sorting segment is not Additional sorting and merging steps are required, which can effectively reduce the calculation execution time.

The Hilbert curve is a curve passing through each block of a query range by the Hilbert scan method, the query range includes N ₁ ×N ₁ blocks, and the block at the beginning of the Hilbert curve has a minimum order according to the Hilbert The path of the curve sequentially defines the ordering of the blocks (as shown in Figure 1). Regarding the Hilbert scanning and sorting method, it is well known to those of ordinary skill in the art to which the invention pertains, and will not be further described herein.

2 is a flow chart showing a method for finding a range query in a Hilbert curve according to the present invention; and FIG. 3 is a schematic diagram showing an orientation pattern of a Hilbert curve and a sub-path positioning pattern of the four orientation starting and ending positions of the present invention. Referring to FIG. 2 and FIG. 3, first referring to step S11, four kinds of positioning patterns are defined according to the starting point and the ending position of the four directions and the path of the corresponding query area. In this embodiment, the starting point and the ending point of each group corresponding to the positioning modes are respectively located in the lower, left, upper, and right directions.

In this embodiment, the positioning modes include a first positioning aspect (the starting point and the ending point are in the lower direction, as shown in FIG. 3( a )), and a second positioning mode (the starting point and the ending point are in the left direction, As shown in Fig. 3(b), a third positioning pattern (the starting point and the ending point are in the upper direction, as shown in Fig. 3(c)) and a fourth positioning pattern (the starting point and the ending point are in the right direction, as shown in the figure). 3(d))). The first positioning aspect, the second positioning aspect, the third positioning aspect, and the fourth positioning aspect are denoted by A, B, C, and D, respectively.

Referring to step S12, the query range is divided into four equal-divided query areas, and each query area includes a sub-Hilbert curve. In this embodiment, the four query areas of the lower left, lower right, upper left, and upper right are respectively defined as P ₀ , P ₁ , P ₂ , and P ₃ (as shown in FIG. 4 ).

Referring to step S13, a relative minimum order in the block of each query area is calculated according to the minimum order and the N ₁ value. In this embodiment, the N ₁ value is 2 ^r , and according to the path direction of the Hilbert curve, the relative minimum order in the blocks of the query regions is the minimum order, and the minimum order is added (2 ^{r- 1} × 2 ^r-1 ) × 1, the minimum order is added by (2 ^{r - 1} × 2 ^{r - 1} ) × 2 and the minimum order is added by (2 ^{r - 1} × 2 ^{r - 1} ) × 3.

Referring to FIG. 5( a ) to FIG. 5( d ), respectively, in the four query regions corresponding to the first positioning mode, the second positioning mode, the third positioning mode and the fourth positioning mode, the relative relative order The method of calculating the minimum order. Referring to FIG. 4 and FIG. 5, taking FIG. 5(a) as an example, FIG. 5(a) shows that the Hilbert curve path of the first positioning mode sequentially passes through the query regions P ₀ , P ₂ , P ₃ , P ₁ , This minimum order (represented here by min_order) is also the relative minimum ordering in the query area P ₀ (here denoted by min ₀ ); the relative minimum order in the query area P ₂ min ₂ =min_order+(2 ^{r-1 × 2 r-1) × 1} ; the query area P ₃ in the relative minimum sort ^{_{min 3 = min_order + (2 r}} -1 × 2 r-1) × 2; the query area P ₁ in the relative minimum sort min ₁ = Min_order+(2 ^r-1 ×2 ^r-1 )×3.

As illustrated by FIG. 1 , the query range is a query range of 2 ³ × 2 ³ (ie, N ₁ ×N ₁ ), and the Hilbert curve included therein is the first positioning state, where r=3. According to the path of the Hilbert curve, the relative minimum order in the blocks of the query regions is 0 (the minimum order), 16 (the minimum order 0 + (2 ^3-1 × 2 ^3-1 ) × 1) 32 (the minimum order 0 + (2 ^3-1 × 2 ^3-1 ) × 2) and 48 (the minimum order 0 + (2 ^3-1 × 2 ^3-1 ) × 3).

Referring to step S14, a window aspect is calculated according to the query areas and a query window, and a part of the window located in the corresponding query area is defined as a sub-window, and the query window includes a query window information, and each sub-window includes a sub-view. Window information. In step S14, the window modes can be divided into nine aspects as shown in FIG. 6(a) to FIG. 6(i), and the query windows in the window modes are respectively included in: four query areas, upper left and The upper right query area, the lower left and lower right query areas, the lower left and upper left query areas, the lower right and upper right query areas, the upper left query area, the upper right query area, the lower left query area, and the lower right query area. The query window information includes the coordinates, height and width of the lower left corner of the query window, and each sub-window information includes the coordinates, height and width of the lower left corner of the sub-window.

With reference to FIG. 6 and FIG. 7, for a query range including T×T (ie, N ₁ ×N ₁ , N ₁ =T) blocks, the four query areas P of the lower left, lower right, upper left, and upper right of the query range are P. ₀ , P ₁ , P ₂ , P ₃ (refer to Figure 4). A query window displays its window information in W(x, y, p, q), where (x, y) is the coordinates of the lower left corner of the query window, and p and q are the height and width of the query window. The lower left corner and the upper right corner of the query window are defined as llw and urw, respectively, and their positions are represented by llw=(x, y) and urw=(x+q, y+p), respectively. The window modes can be divided into the following nine types of Type 0 to Type 8, and the window states can be judged by the following conditions:

Type 0: When llw belongs to And (As shown in Fig. 7(a)), the window state judgment condition is (x<T/2, y<T/2, (x+q)≧T/2 and (y+p)≧T/2 ), the query window can be divided into four sub-windows.

Type 1: When And (As shown in Fig. 7(b)), the window state judgment condition is (x<T/2, y≧T/2, (x+q)≧T/2 and (y+p)≧T/2 ), the query window can be divided into two sub-windows.

Type 2: When And (As shown in Fig. 7(c)), the window state judgment condition is (x<T/2, y<T/2, (x+q)≧T/2 and (y+p)<T/2 ), the query window can be divided into two sub-windows.

Type 3: When And (As shown in Fig. 7(d)), the window state judgment condition is (x<T/2, y<T/2, (x+q)<T/2 and (y+p)≧T/2 ), the query window can be divided into two sub-windows.

Type 4: When And (As shown in Fig. 7(e)), the window state judgment condition is (x≧T/2, y<T/2, (x+q)≧T/2 and (y+p)≧T/2 ), the query window can be divided into two sub-windows.

Type 5: When llw and (As shown in Fig. 7(f)), the window state judgment condition is (x<T/2, y≧T/2, (x+q)<T/2 and (y+p)≧T/2 ), the query window is only in the query area in the upper left corner.

Type 6: When llw and (As shown in Fig. 7(g)), the window state judgment condition is (x≧T/2, y≧T/2, (x+q)≧T/2 and (y+p)≧T/2 ), the query window is only in the query area in the upper right corner.

Type 7: When llw and (As shown in Fig. 7(h)), the window state judgment condition is (x<T/2, y<T/2, (x+q)<T/2 and (y+p)<T/2 ), the query window is only in the query area in the lower left corner.

Type 8: When llw and (As shown in Fig. 7(i)), the window state judgment condition is (x≧T/2, y<T/2, (x+q)≧T/2 and (y+p)<T/2 ), the query window is only located in the query area in the lower right corner.

Referring to FIG. 6 and FIG. 7 again, taking the query window (Type 0) in FIG. 7(a) as an example, each sub-window information can be expressed as follows: SW ₀ = W (x, y, T/2-y , T/2-x); SW ₁ = W(0, y, T/2-y, x+qT/2); SW ₂ = W(x, 0, y+pT/2, T/2-x ); SW ₃ = W (0, 0, y + pT/2, x + qT/2). The lower left corner of each query area is its starting coordinate (0, 0). For example, in the sub-window information SW ₁ =W(0, y, T/2-y, x+qT/2), the sub-window SW ₁ takes the lower left corner of the query area P ₁ as a starting coordinate (0, 0). Therefore, the coordinates of the lower left corner of the sub-window SW ₁ are (0, y), and the height and width of the sub-window SW ₁ are (T/2-y, x + qT/2).

The sub-window information representation of the query window (Type 1-8) in Figures 7(b) to 7(i) is the same as the sub-window information representation of the query window (Type 0) in Figure 7(a) above. Let me repeat them.

Please refer to FIG. 3 and FIG. 7 , the first positioning aspect (orientation A), the second positioning aspect (orientation B), the third positioning aspect (orientation C), and the fourth positioning aspect (orientation D), and The window mode Type 0-8 can be composed of 36 cases as shown in FIG.

Referring to step S15, the corresponding positioning manner and the corresponding positioning manner of each sub-Hilbert curve path are calculated according to the path of the Hilbert curve. In step S15, the respective positioning modes of the Hilbert curve path and the sub-Hilbert curve path may have the following conditions: according to the path direction of the Hilbert curve, the sub-Hilbert curves sequentially correspond to the second positioning mode, The first positioning aspect, the first positioning aspect, and the fourth positioning aspect (refer to FIG. 3( a )); or the sub-Hilbert curves sequentially corresponding to the first positioning aspect, the second a positioning aspect, the second positioning aspect, and the third positioning aspect (refer to FIG. 3(b)); or the sub-Hilbert curve sequentially corresponding to the fourth positioning aspect, the third positioning aspect And the third positioning aspect and the second positioning aspect (refer to FIG. 3(c)); or the sub-Hilbert curve sequentially corresponding to the third positioning aspect, the fourth positioning aspect, the first Four positioning patterns and the first positioning pattern (refer to FIG. 3(d)).

Referring to step S16, an upper query information is calculated according to the path of the Hilbert curve and its corresponding positioning mode, the N ₁ value, the relative minimum order of the starting point of the Hilbert curve path, and the query window information. In this embodiment, the query window information includes a coordinate, a height, and a width of a lower left corner of the query window.

Referring to step S17, the corresponding lower-order query information is calculated according to the corresponding positioning manner of the upper-level query information and the corresponding sub-Hilbert curve, the window mode, the sub-window information of each sub-window, and the relative minimum order of the corresponding query regions. In this embodiment, the sub-window information includes the coordinates, height, and width of the lower left corner of the corresponding sub-window.

Referring to step S18, the query area near the starting point of the Hilbert curve path and including the sub-window (such as the query area P _{0 in} FIG. 4) is divided into new four-partition query areas, each new query area including a new sub- Hilbert curve, and define the sub-window located in the new query area as a new query window, and calculate the block of each new query area according to the minimum order and N ₁ value in the upper query information of each new query window. The new relative minimum order.

Referring to step S19, steps S14 to S18 are repeated. When the height and width of the new query window are equal to the number of blocks in the height and width of the new query area, the last query area is defined as the terminal query area and the relative minimum order is defined as the terminal minimum. Sorting, and calculating a terminal maximum order according to the minimum order of the terminal and the height and width of the terminal query area.

Referring to step S20, according to the path direction of the Hilbert curve, steps S14 to S19 are repeated to sequentially calculate the terminal minimum order and terminal corresponding to the query area including the sub-window (such as the query areas P ₂ , P ₃ , P _{1 of} FIG. 4 ). Maximum sorting.

The present invention is described in detail with reference to the examples shown in Figures 9-21, and is not intended to limit the scope of the present invention.

In this example, the query range is a query range of 2 ⁴ × 2 ⁴ , and the method of finding a range query in the Hilbert curve includes the following steps:

1. Define four kinds of positioning modes A, B, C, and D according to the starting point and ending position of the four directions and the path of the corresponding query area. (Refer to Figure 3)

2. The query range is divided into four query areas P ₀ , P ₁ , P ₂ , and P ₃ of the lower left, lower right, upper left, and upper right. (Refer to Figure 4)

3. According to the path of the Hilbert curve, the relative minimum order in the blocks of the query regions is 0 (the minimum order), 64 (the minimum order 0 + (2 ^4-1 × 2 ^4-1 ) × 1), 128 (the minimum order 0 + (2 ^4-1 × 2 ^4-1 ) × 2) and 192 (the minimum order 0 + (2 ^4-1 × 2 ^4-1 ) × 3). (Refer to Figure 5)

4. The query window is included in the four query areas, and the window mode is defined as Type 0. The query window includes a query window information W(x, y, p, q)=W(1,6,9,8), and the query window information W(x, y, p, q) is the lower left of the query window. Corner coordinates, height and width. Each sub-window contains a sub-window information SW (x, y, p, q), which is the coordinates, height and width of the lower left corner of the corresponding sub-window, wherein the lower left corner of each query area is its starting coordinate (0 , 0). Here, the sub-window information is SW ₀ (1, 6, ₂ , 7), SW ₂ ( ₁ , 0, ₇ , 7), SW ₃ (0, 0, 7, ₁ ), SW ₁ (0 , 6, 2, 1). (Refer to Figure 6(a))

5. The start and end points of the Hilbert curve are below, so it is the first positioning pattern A, and r=4. According to the first positioning mode A, the corresponding positioning modes of each sub-Hilbert curve path are the second positioning mode B, the first positioning mode A, the first positioning mode A and the fourth positioning mode D ( Refer to Figure 3). The Hilbert curve is the first positioning mode A and the window mode is Type 0, which can correspond to the situation shown in orientation A and Type 0 in FIG. 8 .

6. According to the path of the Hilbert curve and its corresponding positioning pattern A, N ₁ value (2 ^r = 16), the relative minimum order 0 in the query area P ₀ close to the starting point of the Hilbert curve path and the query window information W (1) , 6, 9, 8) Calculate an upper-level query information QSplit=(A,16,0,1,6,9,8). (Refer to Figure 9)

7. According to the upper query information QSplit=(A,16,0,1,6,9,8) and the corresponding sub-Hilbert curve corresponding positioning pattern A, the window aspect (Type 0), the sub-windows Information (SW(1,6,2,7), SW(1,0,7,7), SW(0,0,7,1), SW(0,6,2,1)) and their corresponding queries The relative minimum order of the regions (0, 64, 64*2, 64*3) calculates the corresponding lower order query information: QSplit(B,8,0,1,6,2,7), QSplit(A,8,64 , 1, 0, 7, 7), QSplit (A, 8, 64*2, 0, 0, 7, 1), QSplit (D, 8, 64*3, 0, 6, 2, 1). (Refer to Figure 10)

Wherein, the first parameter of the lower-order QSplit represents the path state of the sub-Hilbert curve in the query region; the second parameter represents the height of each query region after each fourth-order partition, and the third parameter represents the query region. The relative minimum ordering (refer to Figure 5(a)); the fourth to seventh digit parameters indicate the coordinates, height and width of the lower left corner of the sub-window.

8. Divide the query area P ₀ near the start of the Hilbert curve path and include the sub-window into a new quarter-divided query area, each new query area containing a new sub-Hilbert curve and defining the new query area The child window in P ₀ is a new query window, and according to the query information of each new query window (refer to the calculation method of the upper query information in step 6 above), the minimum order and N ₁ /2 value (A value after the discrimination) Calculates the new relative minimum order in the block of each new query area (please refer to the calculation of the relative minimum order in step 3 above).

9. Repeat steps 4 through 8 above, first based on QSplit(B,8,0,1,6,2,7) and the new window aspect Type 1 (depending on the corresponding new query area and the new query window). Calculate the corresponding query information of QSplit(B,8,0,1,6,2,7): QSplit(B,4,32,0,2,2,4), QSplit(C,4,48,1 , 2, 2, 3). (Refer to Figure 11)

Where the relative minimum order of QSplit(B, 4, 32, 0, 2, 2, 4) is 32 (the relative minimum order of the new query area is 0 + (2 ^4-2 × 2 ^4-2 ) × 2), The relative minimum order of QSplit(C, 4, 48, 1, 2, 2, 3) is 48 (the relative minimum order of the new query area is 0 + (2 ^4-2 × 2 ^4-2 ) × 3), (4 -2) indicates that the query range of 2 ⁴ × 2 ⁴ is sub-stepped by the second fourth-order partition.

Referring to Figure 12, QSplit (B, 4, 32, 0, 2, 2, 4) can be differentiated to form QSplit (B, 2, 40, 0, 0, 2, 2) and QSplit. (C, 2, 44, 0, 0, 2, 2).

Referring to Figure 13, where QSplit(B, 2, 40, 0, 0, 2, 2) and QSplit (C, 2, 44, 0, 0, 2, 2) are the last two parameters (representing the new query window) The height and width are equal to the number of blocks in the height and width of the new query area (the second two parameters), the last query area is defined as the terminal query area and the relative minimum order is defined as the terminal minimum order (40, 44), and The maximum ordering of a terminal (43, 47) is calculated according to the minimum ordering of the terminal (40, 44) and the height and width of the terminal query area (second bit two parameter 2). The maximum ordering of the terminal (43, 47) is (terminal minimum ordering 40+(2 ^4-3 × 2 ^4-3 )-1) and (terminal minimum ordering 44+(2 ^4-3 × 2 ^4-3 )- 1). (4-3) indicates that the query range of 2 ⁴ × 2 ⁴ is sub-stepped by the third fourth-order partition. Wherein, a terminal maximum ordering 43 is consecutive with another terminal minimum ordering 44, and the terminal minimum ordering (40, 44) and the terminal maximum ordering (43, 47) can be combined into one sorting section (40, 47).

Referring to FIG. 14, referring to the above method for calculating terminal minimum ordering and terminal maximum ordering according to QSplit (B, 4, 32, 0, 2, 2, 4), according to the path direction of the Hilbert curve, first distinguishing QSplit (C, 4, 48, 1, 2, 2, 3) form QSplit (D, 2, 48, 0, 0, 2, 2) and QSplit (B, 2, 60, 1, 0, 2, 1).

Referring to FIG. 15, the last two parameters of QSplit(D, 2, 48, 0, 0, 2, 2) are equal to the number of blocks of the height and width of the new query area, and the last query area is defined as the terminal query area. The relative minimum order is defined as the terminal minimum order (48), and a terminal maximum order (51) is calculated according to the terminal minimum order (48) and the height and width of the terminal query area. The terminal minimum ordering (48) and the terminal maximum ordering (51) form a sorting section (48, 51).

Referring to Figures 16 and 17, with respect to QSplit (B, 2, 60, 1, 0, 2, 1), the last two parameters are not equal to the number of blocks in the height and width of the new query area, and then divided into four equal parts. Step, QSplit(B, 2, 60, 1, 0, 2, 1) can distinguish between QSplit(B,1,61,0,0,1,1) and QSplit(B,1,62,0,0, 1,1). Among them, QSplit (B, 1, 61, 0, 0, 1, 1) terminal minimum order and terminal maximum order are also 61, QSplit (B, 1, 62, 0, 0, 1, 1) terminal minimum order And the maximum order of the terminal is also 62. The terminal maximum order 61 is discontinuous with the above-mentioned sorting section (48, 51), and therefore cannot be combined to form a new sorting section, and the terminal maximum sorting 61 and the terminal minimum sorting 62 are continuous, so that a sorting section can be formed ( 61, 62).

10. According to the path direction of the Hilbert curve, repeat steps 4 to 9 to sequentially calculate all the sorted sections of the upper left, upper right, and lower right query areas (including the query area of the sub-window) of the query range. Among them, the query information QSplit (A, 8, 64, 1, 0, 7, 7) in the upper left query area can be distinguished into QSplit (B, 4, 64, 1, 0, 4, 3), QSplit (A, 4) , 80, 1, 0, 3, 3), QSplit (A, 4, 96, 0, 0, 3, 4), QSplit (D, 4, 112, 0, 0, 4, 4). (Refer to Figure 18)

Referring to Figure 19, QSplit(B, 4, 64, 1, 0, 4, 3) can be further distinguished into QSplit (A, 2, 64, 1, 0, 2, 1), QSplit (B, 2, 68, 0) , 0, 2, 2), QSplit (B, 2, 72, 0, 0, 2, 2), QSplit (C, 2, 76, 1, 0, 2, 1). Referring to Figure 20, QSplit(A, 2, 64, 1, 0, 2, 1) can be further distinguished into QSplit (A, 1, 66, 1, 0, 1, 1) and QSplit (D, 1, 67, 1). , 0, 1, 1).

Among them, QSplit (A,1,66,1,0,1,1) terminal minimum ordering and terminal maximum ordering are also 66, QSplit (D,1,67,1,0,1,1) terminal minimum ordering And the maximum order of the terminal is also 67. The terminal maximum order 66 is discontinuous with the above-mentioned sorting section (61, 62), and therefore cannot be combined to form a new sorting section, and the terminal maximum sorting 66 and the terminal minimum sorting 67 are continuous, so that a sorting section can be formed ( 66, 67).

Regarding the corresponding QSplit(A,8,64,1,0,7,7), QSplit(A,8,64*2,0,0,7,1) and QSplit(D,8,64*3,0, Sorting sections of 6, 2, 1), calculated as (66, 77), (81, 82), (87, 88), (91, 100), (103, 104), (107, 129), (142, 144), (147, 148) ), (213, 214). The sorting sections are the same as the sorting section calculation method of the corresponding query information QSplit (B, 8, 0, 1, 6, 2, 7), and will not be further described herein.

Referring to FIG. 21, in summary, the query result of the query window (query information QSplit=(A, 16, 0, 1, 6, 9, 8)) in the query range of 2 ⁴ × 2 ⁴ can be calculated as described above. All of the sorting sections are combined into a corresponding matching code representation: (40, 45), (61, 62), (66, 77), (81, 82), (87, 88), (91, 100), (103, 104), (107, 129), (142, 144), (147, 148), (213, 214). The corresponding encoding is the ordering of all the blocks in the query window (the value of the Hilbert index).

In the method for finding a range query in the Hilbert curve of the present invention, using the characteristics of the Hilbert curve, the positioning pattern of the query area is defined according to the path of the Hilbert curve, and the window state is defined according to the query area and the query window, and is cut in four equal parts. After the Quad-Splitting distinguishes between the query scope and the query area, the order of all the blocks in the query window (the value of the Hilbert index) is calculated, the required time complexity is low, and the calculated sorting segment is not required. After additional sorting and merging steps, the calculation execution time can be effectively reduced. The actual calculation results show that the method of the invention for finding the range query in the Hilbert curve can reduce the calculation execution time by 92-98% compared with the method of the scholars of Chung et al.

In application, the method for finding a range query in the Hilbert curve can be applied to various fields, such as image processing and compression, spatial query, and wireless broadcast system. Wait. For example, a large image compressed on the basis of a Hilbert curve (such as an aerial picture, etc.) can quickly capture images within a range by using the method of the present invention to obtain a range query in a Hilbert curve.

The above embodiments are merely illustrative of the principles and effects of the invention and are not intended to limit the invention. Therefore, those skilled in the art can make modifications and changes to the above embodiments without departing from the spirit of the invention. The scope of the invention should be as set forth in the appended claims.

(no component symbol description)

Figure 1 shows a schematic diagram of the Hilbert curve sequentially defining the ordering of the blocks through each block of a query range;

2 is a flow chart showing a method for finding a range query in a Hilbert curve according to the present invention;

3 is a schematic diagram showing an orientation state of a Hilbert curve of four orientation starting points and an end position of the present invention and a sub-path positioning aspect thereof;

4 is a schematic diagram showing that the query range of the present invention is divided into four equal-divided query regions;

Figure 5 is a diagram showing the calculation of the relative minimum ordering in the four query areas of the present invention;

6 and 7 are schematic views showing nine window modes of the present invention;

Figure 8 shows the combination of the four positioning modes of the present invention and nine window modes;

9 to 21 are schematic diagrams showing an example of a method for finding a range query in a Hilbert curve.

(no component symbol description)

Claims (8)

A method for finding a range query in a Hilbert curve, the Hilbert curve is a curve passing through each block of a query range by a Hilbert scan method, the query range includes N ₁ ×N ₁ blocks, the starting point of the Hilbert curve The block has a minimum order, and the order of the blocks is sequentially defined according to the path of the Hilbert curve. The query method includes the following steps: (a) according to the start and end positions of the four directions and the path of the corresponding query area Four kinds of positioning patterns are defined, and each set of starting point and ending point of each of the positioning patterns is located at the lower, left, upper and right directions; (b) the query range is divided into four equal-divided query areas, and each query area includes a sub-Hilbert curve; (c) calculating a relative minimum order in each block of the query region based on the minimum order and the N ₁ value; (d) calculating a window pattern based on the query regions and a query window, and A portion of the window located in the corresponding query area is defined as a sub-window, the query window includes a query window information, and each sub-window includes a sub-window information; (e) a path according to the Hilbert curve Operators corresponding positioning respective aspects and positioning of each of the curved path of Hilbert aspect; (f) according to the path of the Hilbert Curve and the corresponding positioning aspects, N ₁ value, close to the minimum relative ordering of the Hilbert curve and the starting point of the path The query window information calculates an upper-level query information; (g) according to the upper-level query information and the corresponding positioning manner of the corresponding sub-Hilbert curve, the window mode, the sub-window information of each sub-window, and the relative of the corresponding query regions The minimum ordering calculates the corresponding lower order query information; (h) divides the query area near the starting point of the Hilbert curve path and includes the sub-window into new four-partition query areas, each new query area containing a new sub-Hilbert Curve, and define the sub-window located in the new query area as a new query window, and calculate the block of each new query area according to the minimum order and N ₁ value in the upper query information of each new query window. New relative minimum ordering; (i) repeat steps (d) through (h), when the height and width of the new query window are equal to the number of blocks in the height and width of the new query area, define the last The query area is a terminal query area and defines a relative minimum order thereof as a terminal minimum order, and calculates a terminal maximum order according to the terminal minimum order and the height and width of the terminal query area; and (j) according to the path direction of the Hilbert curve, Repeat steps (d) through (i) to sequentially calculate the terminal minimum order and terminal maximum order corresponding to the query area containing the sub-window. The method of claim 1, wherein in step (a), the positioning modes comprise a first positioning aspect, a second positioning aspect, a third positioning aspect, and a fourth positioning aspect, and The corresponding starting and ending points are located in the lower, left, upper and right directions respectively. The method of claim 2, wherein in step (e), according to the path direction of the Hilbert curve, the sub-Hilbert curves sequentially correspond to the second positioning mode, the first positioning mode, and the first positioning. The aspect and the fourth positioning aspect. The method of claim 2, wherein in step (e), according to the path direction of the Hilbert curve, the sub-Hilbert curves sequentially correspond to the first positioning mode, the second positioning mode, and the second positioning. The aspect and the third positioning aspect. The method of claim 2, wherein in step (e), according to the path direction of the Hilbert curve, the sub-Hilbert curves sequentially correspond to the fourth positioning mode, the third positioning mode, and the third positioning. The aspect and the second positioning aspect. The method of claim 2, wherein in the step (e), according to the path direction of the Hilbert curve, the sub-Hilbert curves sequentially correspond to the third positioning mode, the fourth positioning mode, and the fourth positioning. The aspect and the first positioning aspect. The method of claim 1, wherein the N ₁ value is 2 ^r , and in step (c), the relative minimum order in the blocks of the query regions is the minimum order, and the minimum order is added (2 ^{r- 1} × 2 ^r-1 ) × 1, the minimum order is added by (2 ^{r - 1} × 2 ^{r - 1} ) × 2 and the minimum order is added by (2 ^{r - 1} × 2 ^{r - 1} ) × 3. The method of claim 1, wherein in the step (d), the window modes are divided into nine aspects, wherein the query windows in the window modes are respectively covered by: four query areas, lower left and lower right query areas , the lower right and upper right query areas, the upper right query area, the lower right query area, the upper left and upper right query areas, the lower left and upper left query areas, the upper left query area and the lower left query area; the query window information includes the coordinates of the lower left corner of the query window, Height and width, each sub-window information contains the coordinates, height and width of the lower left corner of the sub-window.