CN101398809A - Wavelet transformation processing method of discrete point cloud data - Google Patents

Abstract

The invention relates to a multi-dimensional wavelet transformation processing method, which develops the wavelet transformation from time domain to spatial vector by adopting the multi-dimensional data in a self-variable and function type, changes the multi-dimensional data into the relationship of self-variable and function, samples the data and decomposes the wavelets, thus decomposing the data to different sub-bands. After the data is decomposed by the wavelet, the decomposed coefficient covers the original point data, the data memory quantity is not reduced, but the characteristics after decomposition under different sizes are distributed on different frequency sub-bands, thus facilitating further processing.

Description

The Wavelet transformation processing method of discrete point cloud data

Technical field

The present invention relates to a kind of Wavelet transformation processing method, particularly a kind of Wavelet transformation processing method of multidimensional data.

Background technology

Small echo is a very short damped oscillation of duration, and it is local in time domain, is just being studied by the mathematician decades ago.Wavelet transformation then is relative newer notion, just proposes the notion of wavelet transformation before and after the eighties in 20th century, also is incorporated in the image graphics field by the signal field.Wavelet transformation has good localization property in time domain and frequency field, can be with different resolution approximating functions.The wavelet transformation of signal under low resolution is affected by noise less, can describe the more local message of signal; Wavelet transformation under the high resolving power can reflect the profile than macrostructure.

Discrete point cloud data also can be regarded continuous signal as, and the application wavelet transformation is feasible to the pre-service of discrete point cloud data.Along with the development of laser scanning data technology, the obtaining of discrete point cloud data that comprises the object more information becomes possibility.Based on discrete point cloud data reconstruct, in scientific visualization research, reverse-engineering, computer vision, medical image reconstruction etc. important effect is arranged all, and data processing will directly influence the quality and the efficient of the reconstruct of follow-up data.The data processing that wavelet transformation is applied to discrete point cloud also is in the middle of the research.

Abroad the research focus to the wavelet transformation of discrete point cloud mainly is in order to solve the processing of wavelet transformation to the non-equidistance sampled point; And domestic present research focus is mainly concentrated on the three-dimensionalreconstruction to medical image, on the wavelet transform process to discrete point cloud data, also there is not the disposal route of a cover comparative maturity.

Summary of the invention

The Wavelet transformation processing method that the purpose of this invention is to provide a kind of discrete point cloud data is realized the wavelet decomposition to discrete point cloud, and different features is come out according to the yardstick information Recognition.

A kind of multidimensional Wavelet transformation processing method that this law is bright comprises following steps:

The wave filter of steps A, selected corresponding wavelet basis, correspondence and the yardstick threshold value that each yardstick need proceed to;

Step B, total n dimension raw data, with wherein any n-1 dimension raw data as independent variable, any n-1 dimension raw data in the n dimension raw data is sampled respectively, and with sampled value as initial scale coefficient, determine corresponding initial decomposed class according to described raw data number;

Step C, described sampled value is sorted according to the setting order;

The coefficient that step D, application upper level wavelet decomposition go out and the correlation of small echo, if carry out wavelet decomposition for the first time, then use initial coefficient, coefficient to n-1 dimension direction carries out data filtering and down-sampling one by one, promptly one by one on n-1 dimension direction, ask the coefficient that described upper level wavelet decomposition goes out and the correlation of small echo, promptly the coefficient that one by one described upper level wavelet decomposition is gone out carries out wavelet decomposition;

Step e, judge whether the coefficient that wavelet decomposition goes out reaches each yardstick threshold value, if all reach, then carry out next step, if do not reach entirely, repeating step D then, if there is part not reach, part repeating step D then, the part storage data that reaches or resolve into the different scale that can decompose to not reaching;

Step F, with wavelet decomposition go out but the data of the different yardstick of still undecomposed one-tenth resolve into different yardsticks on request.The inventive method also comprises following feature:

Sampling to described n-1 dimension raw data is carried out is equidistant sampling.

To the ordering that described sampled value is carried out, can be earlier the 1st sampled value of tieing up raw data is sorted, the sampled value to the 2nd dimension raw data sorts again, and by that analogy, the sampled value to n-1 dimension raw data sorts at last.

Described step C specifically can be:

Step C[1], coefficient that the upper level wavelet decomposition is gone out and the correlation of small echo use wavelet decomposition on the 1st dimension direction, obtain its wavelet coefficient and scale coefficient;

Step C[2], the wavelet coefficient and the scale coefficient that solve according to the correlation of the coefficient that goes out of wavelet decomposition on the 1st dimension direction and small echo, tie up on the direction the 2nd and to use wavelet decomposition, obtain 4 yardsticks after the decomposition and the coefficient of colligation of small echo;

Step C[3], 4 yardsticks solving on the direction according to the 2nd dimension and the coefficient of colligation of small echo, the sampled value of the 3rd dimension raw data is used wavelet decomposition, obtain 16 yardsticks after the decomposition and the coefficient of colligation of small echo;

By that analogy, step C[n-1] be: according to solve on the n-2 dimension direction 4 ^N-2The coefficient of colligation of individual yardstick and small echo is used wavelet decomposition to the sampled value of n-1 dimension raw data, obtains 4 after the decomposition ^N-1The coefficient of colligation of individual yardstick and small echo.

Described yardstick threshold value can be selected the value that equates.

If described multidimensional Wavelet transformation processing method is 2 dimensions, concrete steps can be described as:

(1) selectes the wave filter of corresponding wavelet basis, correspondence and the yardstick threshold value that each yardstick need proceed to;

(2) to the discrete point cloud raw data according to equidistantly sampling, sampled value as initial scale coefficient, and is determined corresponding initial decomposed class according to the number of discrete point;

(3) according to a definite sequence to described sampled value sort (according to x coordinate ordering, the y coordinate being carried out wavelet transformation herein);

(4) scale coefficient that the upper level wavelet decomposition is gone out is (if carry out wavelet decomposition for the first time, then be to initial scale coefficient) carry out data filtering and down-sampling, be the correlation of the scale coefficient (scale coefficient that decomposites for y coordinate data value herein) of asking described upper level wavelet decomposition to go out and small echo, just the scale coefficient that described upper level wavelet decomposition is gone out carries out wavelet decomposition;

(5) judge whether the scale coefficient that wavelet decomposition goes out reaches each yardstick threshold value,, then carry out next step if all reach, if do not reach entirely, then repeat (4), if there is part not reach, part repeating step (4) then to not reaching, the part retention data that reaches;

(6), the data that wavelet decomposition is gone out resolve into different yardsticks on request.

If described multidimensional Wavelet transformation processing method 3 dimensions, concrete steps can be described as:

(1) selected corresponding wavelet basis, corresponding wave filter and the yardstick threshold value that need proceed to;

(2) discrete point cloud data is equidistantly sampled respectively according to two coordinate axis, the sampled value of two coordinate axis respectively as the initial scale coefficient of two coordinate axis, is determined corresponding initial decomposed class according to the number of discrete point;

(3) according to a definite sequence to sampled point sort (press earlier the sampled value ordering of x coordinate, the sampled value according to the y coordinate sorts again);

(4) in the horizontal direction on (being the x direction of principal axis), the coefficient that upper level y direction of principal axis wavelet decomposition is gone out is (if carry out wavelet decomposition for the first time, then be to initial coefficient) carry out data filtering and down-sampling, be ask coefficient (coefficient that decomposites for y coordinate data value herein) that described upper level y direction of principal axis wavelet decomposition goes out in the horizontal direction with the correlation of small echo, just the coefficient that described upper level y direction of principal axis wavelet decomposition is gone out carries out wavelet decomposition in the horizontal direction, obtains the wavelet coefficient and the scale coefficient of horizontal direction;

(5) coefficient that step (4) x direction of principal axis wavelet decomposition is gone out, carry out data filtering and down-sampling in vertical direction (being the y direction of principal axis), be ask coefficient (coefficient that decomposites for x coordinate data value herein) that step (4) x direction of principal axis wavelet decomposition goes out in vertical direction with the correlation of small echo, just the scale coefficient that step (4) x direction of principal axis wavelet decomposition is gone out carries out wavelet decomposition, 4 yardsticks after obtaining decomposing and the coefficient of colligation of small echo;

(6) judge whether the coefficient that wavelet decomposition goes out reaches the yardstick threshold value,, then carry out next step,, then jump to step (4) if do not reach if reach;

(7), the data that wavelet decomposition is gone out resolve into different yardsticks on request.

Beneficial effect of the present invention is: discrete point cloud data is through after the wavelet decomposition, coefficient after the decomposition has covered original point data, memory data output does not reduce, but the characteristic distribution under the different scale is convenient to further processing after decomposing on different different frequency sub-bands.

Description of drawings

Fig. 1 is the decomposition and the reconstruct synoptic diagram of two-dimensional discrete cloud data.

Fig. 2 waits the two-dimensional discrete point data decomposition process figure of yardstick threshold value for the present invention.

Fig. 3 is the characteristic dimension decomposing schematic representation of N two-dimensional wavelet transformation of the present invention.

Fig. 4 waits the 3 d-dem point data decomposition process figure of yardstick threshold value for the present invention.

Fig. 5 is the two-dimensional discrete point data distribution plan of a preferred embodiment of the present invention.

The two-dimensional discrete point data of Fig. 6 a preferred embodiment of the present invention is the wavelet decomposition result schematic diagram for the first time.

The two-dimensional discrete point data of Fig. 7 a preferred embodiment of the present invention is the wavelet decomposition result schematic diagram for the second time.

The two-dimensional discrete point data of Fig. 8 a preferred embodiment of the present invention is the wavelet decomposition result schematic diagram for the third time.

Embodiment

If always total n dimension raw data, then wherein n-1 dimension raw data is considered as independent variable, for illustrate simple and clear for the purpose of, below be that two peacekeeping raw data are that the multidimensional discrete point cloud data of three-dimensional is embodiment with raw data, be illustrated.

Embodiment one

The discrete point cloud data of two dimension can be expressed as y _i=f (x _i) form, with x _iBe independent variable, obviously discrete point cloud data satisfies formula 1 condition (square-integrable function), and promptly discrete point cloud data also is the signal of finite energy, wavelet transformation theory can be applied to discrete point cloud data.

${\&Integral;}_a^b{\left|f\left(x\right)\right|}^2\mathrm{dx}<\&infin;---\left(1\right)$

Square-integrable function space is called L ²(R) space, known L ²(R) space can be broken down into the form of a unlimited orthogonal direct sum:

$L^2\left(R\right)={\mathrm{<figure-callout\; id="0"\; label="V"\; filenames="A200810041077E00211.png,A200810041077E00212.png"\; state="\{\{state\}\}">V</figure-callout>}}_0\&CirclePlus;{\mathrm{<figure-callout\; id="0"\; label="W"\; filenames="A200810041077E00211.png,A200810041077E00212.png"\; state="\{\{state\}\}">W</figure-callout>}}_0\&CirclePlus;{\mathrm{<figure-callout\; id="1"\; label="W"\; filenames="A200810041077E00181.png"\; state="\{\{state\}\}">W</figure-callout>}}_1\&CirclePlus;{\mathrm{<figure-callout\; id="2"\; label="W"\; filenames="A200810041077E00181.png,A200810041077E00211.png"\; state="\{\{state\}\}">W</figure-callout>}}_2\&CirclePlus;...---\left(2\right)$

Therefore for discrete point cloud data f (x _i) ∈ L ²(R) can be only be launched into:

$f\left(x\right)=f_0\left(x\right)+\underset{N\&RightArrow;\&infin;}{\mathrm{Lim}}\underset{j=0}{\overset{\&infin;}{\mathrm{\&Sigma;}}}{w}_j\left(x\right)---\left(3\right)$

Wavelet transformation is to use L ²(R) base in space shows function space L ²(R) Nei arbitrary signal also is so for discrete point cloud data, needs to determine mother wavelet function

After the flexible and translation, the analysis wavelet function definition of discrete point cloud is as follows with female small echo:

${\mathrm{\&psi;}}_{s,\mathrm{\&tau;}}\left(x\right)=\frac{1}{\sqrt{s}}\mathrm{\&psi;}\left(\frac{x-\mathrm{\&tau;}}{s}\right)(s\&Element;R+,\mathrm{\&tau;}\&Element;R)---\left(4\right)$

Parameter s and τ are respectively scale parameter and translation parameters in the following formula, and * represents to get conjugate function.Discrete point cloud data (x _i, yi) can be considered the one dimension function, just can be mapped to two-dimensional function W by wavelet transformation _f(s τ), is the Conjoint Analysis to the y value.Equally, discrete point cloud data is carried out contrary continuous wavelet transform then can draw, (s τ) just can show cloud data f (x by ψ _i).

See also Fig. 1, the method for two-dimensional discrete cloud data wavelet decomposition is: given a series of data point coordinate figures, it is launched into the translation and the flexible sum of small echo, and on this process nature the data of representing the cloud data space with wavelet basis.In order to realize cloud data is decomposed the effective ways of expansion, the small echo tectonic block of cloud data should not only satisfy the orthogonality of small echo, also should satisfy the orthogonality of its translation and flexible system.Just can be launched into different characteristic components to discrete point cloud data according to yardstick by such decomposition.

At first, discrete point cloud data is come approximate representation by the linear combination that is called as scaling function, the linear combination of scaling function is called approximate function, and Jin Si precision defines with level like this, and the 0th grade is the highest definition of precision.

Owing to use f ₁(x _i) approach the expression full accuracy discrete point cloud data f ₀(x _i) time have information to come off, so the cloud data information w that needs record to come off ₁(x _i), so that f ₀(x _i) restore, expand to the j level, and because the base that has constituted the higher level space of scaling function and small echo, i.e. V ₀+ W ₀Constituted the base of W1, the rest may be inferred, so following formula is arranged:

f _j(x _i)＝f _j+1(x _i)+w _j+1(x _i) (j＝0，1，2，...) (7)

$w_{j+1}\left(x_i\right)=\underset{k}{\mathrm{\&Sigma;}}{d}_k^{(j+1)}{\mathrm{\&psi;}}_{j+1,k}\left(x\right)(j=\mathrm{0,1,2},...)---\left(8\right)$

C in last two formulas _k ^(j),

And f _j(x _i) be respectively scale coefficient, scaling function and the approximate function of discrete point cloud data j level,

The wavelet coefficient of the discrete point cloud data of j+1 level.To the every j value addition respectively of formula 8, can obtain as shown in the formula:

$f_0\left(x_i\right)=\underset{j=1}{\overset{J}{\mathrm{\&Sigma;}}}{w}_j\left(x_i\right)+f_J\left(x_i\right)(j=\mathrm{0,1,2},...,J)---\left(9\right)$

Formula 9 shows discrete point cloud data f ₀(x _i) with the approximate function f of J level _J(x _i) and rough approximation institute accumulating losses composition all add up, just can recover original cloud data f ₀(x _i).

In addition, the scaling function of discrete point cloud data

Can be expressed as Linear combination, formula 10 is called as two scaling relations of scaling function.

Similar two scaling relations that wavelet function arranged as shown in the formula:

Cjk can be obtained by the dot product of the wavelet function of signal and j level:

Composite type 9,10 and 11 can obtain following two formulas:

$c_j\left(k\right)=\underset{k}{\mathrm{\&Sigma;}}{h}_0(m-2k)c_{j+1}\left(m\right)---\left(13\right)$

$d_j\left(k\right)=\underset{k}{\mathrm{\&Sigma;}}{h}_1(m-2k)c_{j+1}\left(m\right)---\left(14\right)$

According to last two formulas, need selected corresponding wave filter, the wave filter of different small echos is different, normally needs to choose the complete wave filter that can constitute quadrature.If determined filter coefficient h ₀And h ₁Can find out the scale coefficient and the wavelet coefficient that can calculate the j-1 level by the scale coefficient of j level, and the like, just can calculate the coefficient under all low resolutions, can obtain 2 altogether ^N+1-1 each wavelet coefficient and 1 scale coefficient; Similarly restructuring procedure is the inverse process of said process.In sum, and the thought of the multiresolution analysis that proposes with reference to French scientist Mallat, can draw discrete point cloud data f ₀(x _i) can being a plurality of resolution to J resolution of J level with the 1st grade, small echo be represented.Concrete process as shown in Figure 1.

Discrete point cloud data is through above-mentioned decomposition, utilizes the feature of the Conjoint Analysis on the both direction of wavelet transformation, can be divided into different characteristics to cloud data according to scaling relation automatically, thereby provide the foundation for follow-up further application.

The discrete points data of two dimension, can see as with some coordinate axis is the discrete function y of independent variable _i=f (x _i), so just the wavelet transformation of one dimension can be applied on this data set.

Continuous signal need be based on the unlimited integration of scale parameter and translation parameters when reconstruct, and this two parameter of discrete wavelet transformation needs binaryzation.

s＝2 ^j；τ＝k2 ^j (j，k＝0，±1，±2，…) (15)

Parameter s in the formula 4 and τ are got binary segmentation by formula 15, can be to the second order small echo after the continuous wavelet discretize

${\mathrm{\&psi;}}_{j,k}\left(x\right)=2^{-\frac{\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="A200810041077E00181.png,A200810041077E00211.png"\; state="\{\{state\}\}">j</figure-callout>}}{2}}\mathrm{\&psi;}(2^{-j}x-k)---\left(16\right)$

See also Fig. 2, the two-dimensional discrete point is carried out wavelet transformation, the number that requires sampled point usually is 2 ⁿ, and require equidistantly sampling, with convenient follow-up decomposition and reconstruct.According to the basic theories of wavelet transformation, present embodiment proposes according to following step the discrete point of two dimension to be carried out wavelet transformation:

(1) selected corresponding wavelet basis, corresponding wave filter and the yardstick threshold value that need proceed to;

(2) to the discrete point cloud raw data according to equidistantly sampling, sampled value as initial scale coefficient, and is determined corresponding initial decomposed class according to the number of discrete point;

(3) according to a definite sequence to described sampled value sort (according to x coordinate ordering, the y coordinate being carried out wavelet transformation herein);

(4) scale coefficient that the upper level wavelet decomposition is gone out is (if carry out wavelet decomposition for the first time, then be to initial scale coefficient) carry out data filtering and down-sampling, be the correlation of the scale coefficient (scale coefficient that decomposites for y coordinate data value herein) of asking described upper level wavelet decomposition to go out and small echo, just the scale coefficient that described upper level wavelet decomposition is gone out carries out wavelet decomposition;

(5) judge whether the scale coefficient that wavelet decomposition goes out reaches the yardstick threshold value,, then carry out next step,, then repeat (4) if do not reach if reach;

(6), the data decomposition that wavelet decomposition is gone out becomes different yardsticks.

It should be noted that said method, to different yardsticks, selected yardstick threshold value is identical, if will change into different yardstick threshold values is arranged under the different scale, and then said method need be revised as:

(1) selectes the wave filter of corresponding wavelet basis, correspondence and the yardstick threshold value that each yardstick need proceed to;

(2) to the discrete point cloud raw data according to equidistantly sampling, sampled value as initial scale coefficient, and is determined corresponding initial decomposed class according to the number of discrete point;

(3) according to a definite sequence to described sampled value sort (according to x coordinate ordering, the y coordinate being carried out wavelet transformation herein);

(4) scale coefficient that the upper level wavelet decomposition is gone out is (if carry out wavelet decomposition for the first time, then be to initial scale coefficient) carry out data filtering and down-sampling, be the correlation of the scale coefficient (scale coefficient that decomposites for y coordinate data value herein) of asking described upper level wavelet decomposition to go out and small echo, just the scale coefficient that described upper level wavelet decomposition is gone out carries out wavelet decomposition;

(5) judge whether the scale coefficient that wavelet decomposition goes out reaches each yardstick threshold value,, then carry out next step if all reach, if do not reach entirely, then repeat (4), if there is part not reach, part repeating step (4) then to not reaching, the part retention data that reaches;

(6), the data that wavelet decomposition is gone out resolve into different yardsticks on request.

For embodiment one further is elaborated, be example for embodiment two:

Embodiment two

The original test data that present embodiment adopts is to obtain after having the continuous curve equal intervals sampling (128 sampled points) that two radiuses are 1 semi arch.The field of definition of its mid point is [0.208 25.608], and sampling interval is 0.2, the original image of data s signal as shown in Figure 3, and concrete coordinate of data such as following table 1, concrete DATA DISTRIBUTION scatter diagram can be with reference to Fig. 5.

Sequence number	The x coordinate	The y coordinate	Sequence number	The x coordinate	The y coordinate	Sequence number	The x coordinate	The y coordinate
									1	0.208	0.208	44	8.808	7.4474	87	17.408	6.6298
2	0.408	0.4226	45	9.008	7.5317	88	17.608	6.6431
									3	0.608	0.637	46	9.208	7.6111	89	17.808	6.6986
4	0.808	0.851	47	9.408	7.6856	90	18.008	6.8047
									5	1.008	1.0646	48	9.608	7.7553	91	18.208	6.9863
6	1.208	1.2775	49	9.808	7.8199	92	18.408	7.3704
									7	1.408	1.4895	50	10.008	7.8797	93	18.608	7.3131
8	1.608	1.7005	51	10.208	7.9345	94	18.808	7.2546
									9	1.808	1.9103	52	10.408	7.9823	95	19.008	7.195
10	2.008	2.1188	53	10.608	8.0302	96	19.208	7.1344
									11	2.208	2.3257	54	10.808	8.0713	97	19.408	7.0727
12	2.408	2.5311	55	11.008	8.1081	98	19.608	7.0101
									13	2.608	2.7345	56	11.208	8.1407	99	19.808	6.9466
14	2.808	2.936	57	11.408	8.1692	100	20.008	6.8822
									15	3.008	3.1354	58	11.608	8.1939	101	20.208	6.817
16	3.208	3.3325	59	11.808	8.2147	102	20.408	6.7511
									17	3.408	3.5272	60	12.008	8.2318	103	20.608	6.6844
18	3.608	3.7193	61	12.208	8.2453	104	20.808	6.6171
									19	3.808	3.9088	62	12.408	8.2554	105	21.008	6.4806
20	4.008	4.0954	63	12.608	8.2621	106	21.208	6.5491
									21	4.208	4.279	64	12.808	8.2655	107	21.408	6.4115
22	4.408	4.4011	65	13.008	8.2658	108	21.608	6.3419
									23	4.608	4.6369	66	13.208	8.2629	109	21.808	6.2719
24	4.808	4.8109	67	13.408	8.2571	110	22.008	6.2015
									25	5.008	4.9814	68	13.608	8.2484	111	22.208	6.1307
26	5.208	5.1484	69	13.808	8.2369	112	22.408	6.0596
									27	5.408	5.3118	70	14.008	8.2227	113	22.608	5.9882
28	5.608	5.4713	71	14.208	8.2058	114	22.808	5.9166
									29	5.808	5.6271	72	14.408	8.1864	115	23.008	5.8448
30	6.008	5.7788	73	14.608	8.1645	116	23.208	5.7728
									31	6.208	5.9266	74	14.808	8.1402	117	23.408	5.7008
32	6.408	6.0702	75	15.008	8.1135	118	23.608	5.6287
									33	6.608	6.2096	76	15.208	8.0846	119	23.808	5.5566
34	6.808	7.4952	77	15.408	8.0536	120	24.008	5.4845
									35	7.008	7.6491	78	15.608	8.0204	121	24.208	5.4124
36	7.208	7.7384	79	15.808	7.9852	122	24.408	5.3405
									37	7.408	7.7805	80	16.008	7.948	123	24.608	5.2687
38	7.608	7.7815	81	16.208	7.9089	124	24.808	5.1971
									39	7.808	7.7415	82	16.408	7.868	125	25.008	5.1258
40	8.008	7.6549	83	16.608	7.0775	126	25.208	5.0547
									41	8.208	7.5049	84	16.808	6.8559	127	25.408	4.9839

42	8.408	7.2578	85	17.008	6.7283	128	25.608	4.9135
									43	8.608	7.3582	86	17.208	6.657	/	/	/

Table 1 two-dimensional discrete point data

Because number of data points is 128, note y coordinate is c _7kTentatively choosing the yardstick threshold value is 4, promptly discrete points data is launched into different frequency fields according to 3 yardsticks, test target is that raw data is resolved into different compositions according to frequency field, be that 1 half garden arc is considered as noise data with two radiuses herein, be that test target is by wavelet transformation discrete points data to be resolved into point on the smooth curve and the noise point on the half garden arc curve, if once decompose the target that does not reach decomposition, then need the scale component after decomposing is continued to decompose, till reaching target.

Concrete calculation procedure is as follows:

(1) chooses the y of the good discrete point cloud data of ordering _iAs scale coefficient c ₇Initial value;

(2) according to two scaling relation formulas of formula 14 by low-pass filter h ₀And c ₇Convolutional calculation c ₆

$c_6\left(k\right)=\underset{k}{\mathrm{\&Sigma;}}{h}_0(m-2k)c_7\left(m\right)$

Following formula expands into:

c ₆(0)＝h ₀(0)c ₇(0)+h ₀(1)c ₇(1)+h ₀(2)c ₇(2)+h ₀(3)c ₇(3)

c ₆(1)＝h ₀(0)c ₇(2)+h ₀(1)c ₇(3)+h ₀(2)c ₇(4)+h ₀(3)c ₇(5)

c ₆(2)＝h ₀(0)c ₇(4)+h ₀(1)c ₇(5)+h ₀(2)c ₇(6)+h ₀(3)c ₇(7)

……

c ₆(62)＝h ₀(0)c ₇(124)+h ₀(1)c ₇(125)+h ₀(2)c ₇(126)+h ₀(3)c ₇(127)

c ₆(63)＝h ₀(0)c ₇(126)+h ₀(1)c ₇(127)+h ₀(2)c ₇(128)+h ₀(3)c ₇(129)

By on can calculate c ₆(0)=0.3440979, calculates c successively ₆Each component, similarly can calculate d ₆Each component, the mode iterative computation is gone down like this, can calculate c step by step ₅And d ₅, and c ₄And d ₄, up to satisfying the requirement of yardstick threshold value.Decompose to the subordinate yardstick, new wavelet coefficient and scale coefficient component size reduce by half at every turn, according to such step, thereby finish feature decomposition to discrete point cloud data.

According to the introduction of last trifle, in order to simplify loaded down with trivial details calculation procedure, this example is taked to test under matlab7.0, chooses Daubechies (2) wavelet function and wave filter, and wherein the matlab key code of decomposition and reconstruct is as follows respectively:

％...

The % ground floor decomposes code

N＝128；

s ₀＝conv(h ₀，s)；

s ₁conv(h ₁，s)；

s ₀＝s ₀(1，2：N+1)；

s ₁=s ₁(1，2：N+1)；

s ₀=reshape (s ₀, 2, N/2); The % down-sampling

s ₁＝reshape(s1，2，N/2)；

c ₆=s ₀(1 :); %c6 obtains 64 values

d ₆=s ₁(1 :); %d6 obtains 64 values

％...

％...

The last one deck reconfiguration code of %

da＝[d ₆

zeros(size(d ₆))]；

db＝da(：)’；

Dc=conv (db, h ₃); % up-sampling and filtered d ₅

ca＝[c ₆

zeros(size(c ₆))]；

cb＝ca(：)’；

Cc=conv (cb, h ₂); % up-sampling and filtered c ₆

snew＝2*(cc+dc)；

N=length (snew); The odd length that the % up-sampling obtains

Snew=snew (1,3:n-1); % length is reduced to 128

％...

According to shown in Figure 2, can obtain corresponding Wavelet Component and scale component after discrete point cloud decomposes after once decomposing.Through this example of test example is carried out wavelet decomposition 3 times, for the first time raw data is decomposed, obtain c ₆Component and d ₆Component is then to scale component c ₆Thereby continue to decompose and obtain c ₅Component and d ₅Component is at last to scale component c ₅Obtain c thereby decompose ₄Component and d ₄Component, the result after the decomposition is respectively as Fig. 6, Fig. 7 and shown in Figure 8.Comprise four subgraphs among every secondary figure, the initial raw data represented of first subgraph wherein, second son figure expression be data after rebuilding, the scale component of the 3rd other low frequency of the current level of son figure expression, the Wavelet Component of the 4th other high frequency of the current level of son figure expression:

From Fig. 6, Fig. 7 Fig. 8 as can be seen, the discrete point cloud data wavelet decomposition first time of carrying out to input, the characteristic dimension component c6 and the target (the required sampled point that obtains removing 2 semi arch noise datas) of identification are not very identical, think not reach target; Therefore the scale component c6 to this grade decomposes once more, and the c5 component that obtains does not still reach target; Therefore continue to decompose the c5 component, obtained the c4 component, rejected noise data substantially, reached the purpose of decomposing, so stop to continue to decompose, this example test is finished.

Embodiment three

Similar with the two-dimensional discrete point data, 3 d-dem cloud data, the two-dimensional discrete function z that to can be considered with two coordinate axis be independent variable _i=f (x _i, y _i), therefore just two-dimensional wavelet transformation can be applied on the three-dimensional discrete point cloud data collection.Equally, the two-dimensional discrete point is carried out wavelet transformation, need the binaryzation of scale parameter and wavelet parameter equally, also just requiring to satisfy respectively in x and y direction is 2 ^jWith 2 ^kEquidistant sampling, with convenient follow-up decomposition and reconstruct.

See also Fig. 3, according to the basic theories of two-dimensional wavelet transformation, the basis function of two-dimensional wavelet transformation is following respectively to be exactly the expansion of unidimensional scale function and wavelet function, i.e. the combination of scaling function and wavelet function.The wavelet transformation of two dimension is exactly the form that 2D signal is launched into the tensor progression of four kinds of small echos and yardstick, and concrete decomposable process is as follows:

At first carry out the wavelet transform of horizontal direction, p wherein _kAnd q _kRepresent low pass and Hi-pass filter respectively, two formulas specific as follows:

$c_{m,n}^{(j+1,x)}=\underset{k}{\mathrm{\&Sigma;}}{p}_{2k-m}^{*}{c}_{k,n}^{\left(j\right)}---\left(17\right)$

$d_{m,n}^{(j+1,x)}=\underset{k}{\mathrm{\&Sigma;}}{q}_{2k-m}^{*}{c}_{k,n}^{\left(j\right)}---\left(18\right)$

And then coefficient is taked the wavelet transform of vertical direction, is obtained following four formulas:

$c_{m,n}^{(j+1)}=\underset{l}{\mathrm{\&Sigma;}}{p}_{l-2n}^{*}{c}_{m,l}^{(j+1,x)}---\left(19\right)$

$d_{m,n}^{(j+1,h)}=\underset{l}{\mathrm{\&Sigma;}}{q}_{l-2n}^{*}{c}_{n,l}^{(j+1,x)}---\left(20\right)$

$d_{m,n}^{(j+1,v)}=\underset{l}{\mathrm{\&Sigma;}}{p}_{l-2n}^{*}{d}_{m,l}^{(j+1,x)}---\left(21\right)$

$d_{m,n}^{(j+1,d)}=\underset{l}{\mathrm{\&Sigma;}}{q}_{l-2n}^{*}{d}_{m,l}^{(j+1,x)}---\left(22\right)$

At last with 17-28 formula substitutions, 19-22 formulas, and just be launched into and finish decomposition.The once decomposition of 3 d-dem cloud data can produce 4 subbands, repeats to decompose low frequency sub-band, and the subband that can obtain multiple dimensioned 2-d wavelet as shown in Figure 3.

Seeing also Fig. 4, is the 1st dimension sampled value with the sampled value of x coordinate data, is the 2nd dimension sampled value with the sampled value of y coordinate data, and according to above-mentioned basic theories, present embodiment proposes according to the following steps method 3 d-dem cloud data to be decomposed and reconstruct:

(1) selected corresponding wavelet basis, corresponding wave filter and the yardstick threshold value that need proceed to;

(2) discrete point cloud data is equidistantly sampled respectively according to two coordinate axis, the sampled value of two coordinate axis respectively as the initial scale coefficient of two coordinate axis, is determined corresponding initial decomposed class according to the number of discrete point;

(3) according to a definite sequence to sampled point sort (press earlier the sampled value ordering of x coordinate, the sampled value according to the y coordinate sorts again);

(4) in the horizontal direction on (being the x direction of principal axis), the coefficient that upper level y direction of principal axis wavelet decomposition is gone out is (if carry out wavelet decomposition for the first time, then be to initial coefficient) carry out data filtering and down-sampling, be ask coefficient (coefficient that decomposites for y coordinate data value herein) that described upper level y direction of principal axis wavelet decomposition goes out in the horizontal direction with the correlation of small echo, just the coefficient that described upper level y direction of principal axis wavelet decomposition is gone out carries out wavelet decomposition in the horizontal direction, obtains the wavelet coefficient and the scale coefficient of horizontal direction;

(5) coefficient that step (4) x direction of principal axis wavelet decomposition is gone out, carry out data filtering and down-sampling in vertical direction (being the y direction of principal axis), be ask coefficient (coefficient that decomposites for x coordinate data value herein) that step (4) x direction of principal axis wavelet decomposition goes out in vertical direction with the correlation of small echo, just the scale coefficient that step (4) x direction of principal axis wavelet decomposition is gone out carries out wavelet decomposition, 4 yardsticks after obtaining decomposing and the coefficient of colligation of small echo;

(6) judge whether the coefficient that wavelet decomposition goes out reaches the yardstick threshold value,, then carry out next step,, then jump to step (4) if do not reach if reach;

(7), the data that wavelet decomposition is gone out resolve into different yardsticks on request.

Above-mentioned is to carry out under all yardsticks all have the condition of same yardstick threshold value, if different yardsticks has different threshold values, the data that only need to reach the yardstick threshold value keep or decompose to come out, to not reaching the continuation wavelet decomposition of yardstick threshold value, get final product at last, concrete steps can be with reference to the wavelet decomposition step of two dimension.

The data pre-service of discrete point cloud, 3-D display tool for the later stage plays a very important role, present embodiment is with reference to the base conditioning method of wavelet transformation, wavelet transformation is introduced in the processing of discrete point cloud, proposed discrete point cloud data disposal route, and provided concrete calculation procedure based on wavelet transformation.Method according to the present embodiment proposition, 128 two-dimensional discrete point data have simply been enumerated, and one-dimensional discrete is put the cloud small wave converting method be applied to this cloud data, the result shows the wavelet transformation through 3 times, gone out the feature of this cloud data, thereby verified the effective of this method according to the yardstick information extraction.This method is by using wavelet transformation, in processing procedure, cloud data is divided into different frequecy characteristic information according to yardstick, can be according to the different application of later stage cloud data, reducing needs the data volume handled in the three-dimensional visualization process of discrete point cloud data in later stage, have certain scientific research and engineering using value.

Claims (7)

1, a kind of multidimensional Wavelet transformation processing method is characterized in that, comprises following steps:

The wave filter of steps A, selected corresponding wavelet basis, correspondence and the yardstick threshold value that each yardstick need proceed to;

Step B, total n dimension raw data, with wherein any n-1 dimension raw data as independent variable, any n-1 dimension raw data in the n dimension raw data is sampled respectively, and with sampled value as initial scale coefficient, determine corresponding initial decomposed class according to described raw data number;

Step C, described sampled value is sorted according to the setting order;

The coefficient that step D, application upper level wavelet decomposition go out and the correlation of small echo, if carry out wavelet decomposition for the first time, then use initial coefficient, coefficient to n-1 dimension direction carries out data filtering and down-sampling one by one, promptly one by one on n-1 dimension direction, ask the coefficient that described upper level wavelet decomposition goes out and the correlation of small echo, promptly the coefficient that one by one described upper level wavelet decomposition is gone out carries out wavelet decomposition;

Step e, judge whether the coefficient that wavelet decomposition goes out reaches each yardstick threshold value, if all reach, then carry out next step, if do not reach entirely, repeating step D then, if there is part not reach, part repeating step D then, the part storage data that reaches or resolve into the different scale that can decompose to not reaching;

Step F, with wavelet decomposition go out but the data of the different yardstick of still undecomposed one-tenth resolve into different yardsticks on request.

2, multidimensional Wavelet transformation processing method as claimed in claim 1 is characterized in that: the sampling to described n-1 dimension raw data is carried out is equidistant sampling.

3, multidimensional Wavelet transformation processing method as claimed in claim 1, it is characterized in that: the ordering that described sampled value is carried out, sampled value to the 1st dimension raw data sorts earlier, sampled value to the 2nd dimension raw data sorts again, by that analogy, at last the sampled value of n-1 dimension raw data is sorted.

4, multidimensional Wavelet transformation processing method as claimed in claim 1 is characterized in that, described step C specifically can be:

Step C[1], coefficient that the upper level wavelet decomposition is gone out and the correlation of small echo use wavelet decomposition on the 1st dimension direction, obtain its wavelet coefficient and scale coefficient;

Step C[2], the wavelet coefficient and the scale coefficient that solve according to the correlation of the coefficient that goes out of wavelet decomposition on the 1st dimension direction and small echo, tie up on the direction the 2nd and to use wavelet decomposition, obtain 4 yardsticks after the decomposition and the coefficient of colligation of small echo;

Step C[3], 4 yardsticks solving on the direction according to the 2nd dimension and the coefficient of colligation of small echo, the sampled value of the 3rd dimension raw data is used wavelet decomposition, obtain 16 yardsticks after the decomposition and the coefficient of colligation of small echo;

By that analogy, step C[n-1] be: according to solve on the n-2 dimension direction 4 ^N-2The coefficient of colligation of individual yardstick and small echo is used wavelet decomposition to the sampled value of n-1 dimension raw data, obtains 4 after the decomposition ^N-1The coefficient of colligation of individual yardstick and small echo.

5, multidimensional Wavelet transformation processing method as claimed in claim 1 is characterized in that: described yardstick threshold value can be selected the value that equates.

6, multidimensional Wavelet transformation processing method as claimed in claim 1 is characterized in that: described multidimensional Wavelet transformation processing method is 2 dimensions, and concrete steps are described as:

(1) selectes the wave filter of corresponding wavelet basis, correspondence and the yardstick threshold value that each yardstick need proceed to;

(2) to the discrete point cloud raw data according to equidistantly sampling, sampled value as initial scale coefficient, and is determined corresponding initial decomposed class according to the number of discrete point;

(3) according to a definite sequence to described sampled value sort (according to x coordinate ordering, the y coordinate being carried out wavelet transformation herein);

(4) scale coefficient that the upper level wavelet decomposition is gone out is (if carry out wavelet decomposition for the first time, then be to initial scale coefficient) carry out data filtering and down-sampling, be the correlation of the scale coefficient (scale coefficient that decomposites for y coordinate data value herein) of asking described upper level wavelet decomposition to go out and small echo, just the scale coefficient that described upper level wavelet decomposition is gone out carries out wavelet decomposition;

(5) judge whether the scale coefficient that wavelet decomposition goes out reaches each yardstick threshold value,, then carry out next step if all reach, if do not reach entirely, then repeat (4), if there is part not reach, part repeating step (4) then to not reaching, the part retention data that reaches;

(6) data that wavelet decomposition is gone out resolve into different yardsticks on request.

7, multidimensional Wavelet transformation processing method as claimed in claim 1 is characterized in that: described multidimensional Wavelet transformation processing method is 3 dimensions, and concrete steps are described as:

(1) selected corresponding wavelet basis, corresponding wave filter and the yardstick threshold value that need proceed to;

(2) discrete point cloud data is equidistantly sampled respectively according to two coordinate axis, the sampled value of two coordinate axis respectively as the initial scale coefficient of two coordinate axis, is determined corresponding initial decomposed class according to the number of discrete point;

(3) according to a definite sequence to sampled point sort (press earlier the sampled value ordering of x coordinate, the sampled value according to the y coordinate sorts again);

(4) in the horizontal direction on (being the x direction of principal axis), the coefficient that upper level y direction of principal axis wavelet decomposition is gone out is (if carry out wavelet decomposition for the first time, then be to initial coefficient) carry out data filtering and down-sampling, be ask coefficient (coefficient that decomposites for y coordinate data value herein) that described upper level y direction of principal axis wavelet decomposition goes out in the horizontal direction with the correlation of small echo, just the coefficient that described upper level y direction of principal axis wavelet decomposition is gone out carries out wavelet decomposition in the horizontal direction, obtains the wavelet coefficient and the scale coefficient of horizontal direction;

(5) coefficient that step (4) x direction of principal axis wavelet decomposition is gone out, carry out data filtering and down-sampling in vertical direction (being the y direction of principal axis), be ask coefficient (coefficient that decomposites for x coordinate data value herein) that step (4) x direction of principal axis wavelet decomposition goes out in vertical direction with the correlation of small echo, just the scale coefficient that step (4) x direction of principal axis wavelet decomposition is gone out carries out wavelet decomposition, 4 yardsticks after obtaining decomposing and the coefficient of colligation of small echo;

(6) judge whether the coefficient that wavelet decomposition goes out reaches the yardstick threshold value,, then carry out next step,, then jump to step (4) if do not reach if reach;

(7) data that wavelet decomposition is gone out resolve into different yardsticks on request.

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