CN101123000B - Three-dimensional graphic data compression processing method - Google Patents

Abstract

The invention discloses a method of three-dimension image data compressing and processing. Regular quadrilateral surfaces are used instead of triangle surfaces, and the steps of re-gridding, subdivided wavelet construction, zero-tree compressing and entropy coding are used for compressing the image data, so a quadrilateral surface based geometric image compressing method is provided. The invention can better adapt and fulfill the requirements of quick development of the three-dimension displaying data collecting technologies and application of the technologies. The invention can help achieving a better compressing effect for complex models, the models can be gradually transmitted, and the distortion ratio is small, controllable and adjustable. Prior available storing and transmitting capacities can be better used to reduce limits and influences of prior hardware and network facilities to three-dimension display technologies.

Description

A kind of compression processing method of 3 D graphic data

Technical field

The present invention relates to a kind of data compression process technical field, relate in particular to a kind of compression processing method of 3 D graphic data.

Background technology

The development of computer graphics and hardware technology is for people bring visual revolution.Along with the development of technology, the manifestation mode of conventional two-dimensional can not satisfy people's demand, and people have higher requirement to the interaction capabilities and the expressive ability of computing machine, and adopting the three-dimensional information technology to show various scenes has been trend of the times.Compare with two-dimensional medium forms of expression such as literal, image, videos, three-dimensional picture shows better and alternately flexible characteristic more of realistic stronger, intuitive, particularly in the occasion of emphasizing intuitive and interaction capabilities, as aspects such as engineering design, machine-building, analog simulation, city planning, historical relic reparation and Entertainments, dimension display technologies has played irreplaceable effect, therefore is widely used in every field.Demands of applications has driven the development of acquisition technique, and corresponding model becomes increasingly complex, and is also more and more meticulousr, but has also caused the sharp increase of model data.The Digital Michelangelo Project project of Stanford University for example, maximum sculpture model data amount has surpassed 32G unexpectedly, and common model data amount is also very considerable.

But at present the storage and the network capacity of computing machine are relatively limited, and Network Transmission bandwidth particularly can not satisfy the real-time Transmission of model data far away.The development of dimension display technologies and popularization have been subjected to the restriction of transmission bandwidth and storage space, because the quantity of information that three-dimensional model can hold head and shoulders above two dimensional form can hold, storage and transmission to these models need a large amount of space and bandwidth, and this point has exceeded present hardware and networks development level.For this reason, also 3-D display data compression process technology is had higher requirement.And aspect data compression technique, what adopt usually at present is to utilize the gore slice graticule to compress the method for processing, and its compression performance and transmission performance can not adapt to and satisfy the fast development and the demands of applications of current acquisition technique well.Especially for complicated model, need better compression and handle means.

In order to solve above-mentioned contradiction, satisfy demands of applications, the compression problem that how to solve three-dimensional modeling data is that pendulum is in our problem anxious to be solved in front to utilize the development of present existing storage and transmittability and adaptation and promotion 3-D technology as much as possible.

Summary of the invention

The objective of the invention is to solve the problem that prior art exists, provide a kind of based on the segmentation model, based on wavelet transformation, utilize quad patch 3 D graphic data to be compressed the method for processing, be intended to improve the compressibility of 3 D graphic data, the quantity of information that reduces three-dimensional model as far as possible and held, to save storage space and transmission bandwidth, can not reduce the distortion rate of three-dimensional picture simultaneously again, with the sense of reality and the intuitive of guaranteeing figure.

Purpose of the present invention is achieved by the following technical programs:

The compression processing method of a kind of 3 D graphic data provided by the invention may further comprise the steps:

A) obtain the preliminary sweep grid of model outward appearance;

B) by heavily gridding module, described preliminary sweep grid is carried out regular processing and obtains regular quadrilateral surface slice graticule, this quadrilateral surface slice graticule has the segmentation continuity and supports topology information to simplify the operation;

C) by segmentation small echo constructing module, described new gridding information data are divided, predict, upgrade and merge processing, with the decomposition and the restructuring procedure of realization gridding information data, thus the image behind the acquisition wavelet transformation;

D), make up wavelet zero-tree with two-layer, the quaternary tree form up and down relevant with wavelet coefficient by zero tree compression module; For quad patch, the corresponding relation of employing face, limit, point, and the 1-4 corresponding relation can be set up in the face of upper and lower two-layer quadrilateral surface slice graticule, limit, can set up the 1-1 corresponding relation between the summit of lower floor and the limit of last layer, so between the levels summit, set up the 1-4 corresponding relation by transfer function;

E) by the EZW method wavelet zero-tree that obtains is quantized and compression, thereby obtain Wavelet image zero tree compressed encoding;

F), described zero tree compressed encoding is carried out further data compression, thereby obtain the three-dimensional picture packed data by the entropy coding module;

The present invention is based on the segmentation model, through the quad patch replacement triangle surface of overweight gridding with regularization, by segment the compression of little wave structure, wavelet zero-tree, the entropy coding step is carried out the geometric figure compression, can effectively improve the compression performance of figure and the transmission performance of data.

Setting up zero tree in geometric model is the prerequisite that makes wavelet coefficient can utilize remainder coding to carry out data compression.For making zero of foundation set balance as much as possible, promptly the leaf node quantity difference of adjacent node is less, and the present invention can further take following mode to make up zero tree:

Two limits in the middle of the limit of upper strata of the present invention quadrilateral surface slice graticule, corresponding lower floor grid and both sides and two limits interlacing parallel with the limit of described centre; The summit of described upper strata quadrilateral surface slice graticule, is the mid point on 90 limits of spending and the intermediate point of each dough sheet with the integral body on the limit of getting at the mid point on corresponding lower floor limit that grid is got.This kind situation, in the centre of dough sheet, what limit and point all formed is the corresponding relation of 1-4; Work as the appearance sky at once at the boundary of dough sheet, what the point on limit and the limit then formed is the corresponding relation of 1-3, and the point in the middle of the dough sheet still is the corresponding relation of 1-4.

Select and operation for convenient, the present invention also can take following mode aspect the zero tree structure in addition:

Two limits in the middle of the limit of upper strata of the present invention quadrilateral surface slice graticule, corresponding lower floor grid and homonymy two limits parallel with the limit of described centre; The summit of described upper strata quadrilateral surface slice graticule, is the mid point on 90 limits of spending and the intermediate point of each dough sheet with the integral body on the limit of getting at the mid point on corresponding lower floor limit that grid is got.This kind situation, in the centre of dough sheet, what limit and point all formed is the corresponding relation of 1-4; Boundary at dough sheet is empty at once when occurring, and what limit and point then formed is the corresponding relation of 1-2.

The present invention utilizes the quad patch of regularization to replace triangle surface to compress processing, in the heavily gridding process of described step b), can adopt QR (quadrilateral remesh) method that Hormann proposes to be the regular quadrilateral patch grids with the triangular mesh of arbitrary mess is regular particularly.

And in the little wave structure of the segmentation of described step c), its decomposable process is division-prediction-renewal, and is specific as follows:

Division-with original information c ⁿBe decomposed into two mutually disjoint information subset c ^N-1And d ^N-1, c wherein ^N-1Be new information set, d ^N-1It then is the small echo collection; All summits are divided into two set: one is even number set Even (n-1), this set record be all control vertexs when anterior layer, corresponding c ^N-1Another is odd number set Odd (n-1), this set record be by the generation point when anterior layer control mesh segmentation gained, corresponding d ^N-1

The prediction-with the segmentation model be that the basis utilizes the geometric transformation rule of Kobbelt model as predictive operator P, d in the following manner ^N-1-=P (c ^N-1) pair set odd number Odd (n-1) carries out conversion, makes the odd number set be converted to wavelet coefficient set M (n-1);

Upgrade-utilize the rule of quantity of information balance, adopt the odd point that makes a circle in even number point week, also promptly changed the wavelet coefficient of formation, upgrade the even number point through prediction;

Its restructuring procedure is renewal-prediction-merging, and wherein merging is the process of and contrary corresponding with division, with the information subset c that obtains ^N-1And d ^N-1Merging is got up, and reduction reconstructs original information set c ⁿ

The present invention has following beneficial effect:

(1) adopts the quad patch of regularization to replace triangle surface, the geometric figure compression method based on quad patch is provided, can adapt to and satisfy the fast development and the demands of applications of 3-D display data acquisition technology better.

(2) more reasonable on the structure of zero tree, balance is better, can reduce the distortion rate of compression effectiveness as much as possible, helps guaranteeing the sense of reality and the intuitive of figure.

(3) have better slickness, can obtain better compression effectiveness for complex model,

(4) the compression efficiency height of 3-D display data of the present invention, can be by progressive transmission, the compression effectiveness distortion rate is less and may command and adjusting, present existing storage and transmittability be can utilize better, the present hardware and the network facilities reduced restriction and influence that dimension display technologies caused.

Description of drawings

The present invention is described in further detail below in conjunction with embodiment and accompanying drawing:

Fig. 1 is the workflow block diagram of the embodiment of the invention one;

Fig. 2 is the once resulting result schematic diagram of quadrilateral surface slice graticule segmentation in the embodiment of the invention one;

Fig. 3 is the fission process synoptic diagram of local quad patch in the embodiment of the invention one;

Fig. 4 is a Kobbelt pattern segmentation mask artwork in the embodiment of the invention one;

Fig. 5 is a predictive operator summit sign picture in the embodiment of the invention one;

Fig. 6 is the basic procedure block diagram of small echo picture coding in the embodiment of the invention one;

Fig. 7 is the corresponding relation synoptic diagram of the face of structure wavelet zero-tree method in the embodiment of the invention one;

Fig. 8 is the corresponding relation synoptic diagram on the limit of structure wavelet zero-tree method in the embodiment of the invention one;

Fig. 9 is the corresponding relation synoptic diagram of the point of structure wavelet zero-tree method in the embodiment of the invention one;

Figure 10 is the corresponding relation synoptic diagram on the limit of structure wavelet zero-tree method in the embodiment of the invention two;

Figure 11 is the corresponding relation synoptic diagram of the point of structure wavelet zero-tree method in the embodiment of the invention two.

Embodiment

Embodiment one:

Fig. 1～Figure 9 shows that as shown in Figure 1, to may further comprise the steps one of embodiment of 3 D graphic data compression processing method of the present invention:

A) obtain the preliminary sweep grid of model outward appearance;

B) by heavily gridding module, the preliminary sweep grid is carried out regular processing, make the new grid of acquisition have the segmentation continuity and support topology information to simplify the operation;

C) by segmentation small echo constructing module, new gridding information data are divided, predict, upgrade and merge processing, with the decomposition and the restructuring procedure of realization gridding information data, thus the image behind the acquisition wavelet transformation;

D), make up wavelet zero-tree with two-layer, the quaternary tree form up and down relevant with wavelet coefficient by zero tree compression module;

E) by the EZW method wavelet zero-tree that obtains is quantized and compression, thereby obtain Wavelet image zero tree compressed encoding;

F), zero tree compressed encoding is carried out further data compression, thereby obtain the three-dimensional picture packed data by the entropy coding module.

It below is concrete elaboration to above steps.

Heavily gridding

Simplify process based on the dough sheet of algorithm of subdivision and suppose that always each grid of simplifying level all has the segmentation connectivity, can both satisfy the Changing Pattern of segmentation topology information in the simplification process, not the situation that can occur conflicting.But, in the production process of realistic model, because the scrambling of model outward appearance, the grid that produces all is not have the successional grid at random of segmentation usually, therefore need do certain regular processing of heavily gridding (remeshing), can make grid support that really topology information simplifies the operation.

QR (quadrilateral remesh) method that present embodiment adopts Hormann to propose, at first carry out parametrization (Parameterization), utilize the whole grid of semicircular canal to resample then, thereby be one and have the successional regular quadrilateral patch grids of segmentation the triangular mesh of arbitrary mess is regular.Wherein, be in the middle of the dough sheet grid vertex all be degree be four canonical summit, the grid vertex that border one is enclosed then is non-regular.In non-canonical summit, having only the degree on the summit on four angles of dough sheet is 2, and other non-canonical summit degree of being is 3 summit.

Segment little wave structure

Structure segmentation small echo need relate to four operations usually: divide (Split), prediction (Predict), upgrade (Update), merge (Merge).

Division (Split)

The operating process of division can be adopted multiple implementation, and fairly simple can adopt Lazy small echo, Haar small echo, also can adopt other complicated wavelet function to handle.It mainly acts on the information c that is original ⁿBe decomposed into two mutually disjoint information subset c ^N-1And d ^N-1, c wherein ^N-1Be new information set, d ^N-1Then be the small echo collection, the wavelet coefficient collection in the similar wavelet analysis of its meaning.All summits are divided into two set: one is even number set Even (n-1), this set record be all control vertexs when anterior layer, corresponding c ^N-1Another is odd number set Odd (n-1), this set record be by the generation point when anterior layer control mesh segmentation gained, corresponding d ^N-1

As shown in Figures 2 and 3, for the grid of n layer, all summits (comprising solid dot and hollow dots) all belong to the even number set, are designated as Even (n), corresponding to c ⁿAll solid dot in the grid are the control vertexs when anterior layer, so belong to the even number collection of n layer, are designated as Even (n-1), corresponding to c ^N-1All hollow dots in the grid can be obtained by Even (n-1) segmentation, are designated as odd number set Odd (n-1).Like this, just, can obtain mutually disjointing between odd number collection and the even number collection and satisfying following formula 1:

Even(n)＝Even(n-1)+Odd(n-1)

Formula 1

$\mathrm{Even}(n-1)\⋐\mathrm{Even}\left(n\right)$

Prediction (Predict)

Through the division of the first step, original information set c ⁿBe broken down into two parts, these two parts have higher correlativity.For the result who makes structure has the characteristic of small echo, need the process of analog wavelet converting, at information subset c ^N-1And d ^N-1Between set up a kind of projected relationship, make two parts be converted into low frequency and the HFS in the wavelet transformation.

, will segment model and affact c as the basis with the segmentation model as a fallout predictor ^N-1On, and with its result as d ^N-1Predict the outcome, thereby set up both projected relationships.Predicted value and d ^N-1Difference then be called details, perhaps copy wavelet transformation to be called wavelet coefficient.

Two set Even (n-1) that division forms and Odd (n-1), the n-1 layer control mesh of in fact corresponding dough sheet and through the new edge point millet cake of segmentation back formation.Present embodiment utilizes the geometric transformation rule of Kobbelt model as predictive operator P, its concrete computation rule as shown in Figure 4, being calculated as follows of each coefficient:

$\mathrm{\&alpha;}=-\frac{\mathrm{\&omega;}}{16},$ $\mathrm{\&beta;}=\frac{8+\mathrm{\&omega;}}{16},$ σ＝α ²，μ＝αβ， $v={\mathrm{\&beta;}}^2,0<\mathrm{\&omega;}<2(\sqrt{5}-1)$

And d in the following manner ^N-1-=P (c ^N-1) pair set odd number Odd (n-1) carries out conversion, makes the odd number set be converted to wavelet coefficient set M (n-1), thereby realize the construction process of wavelet coefficient.

Upgrade (Update)

In the fission process of the first step, the division of information set adopts sample mode to handle, and promptly adopts a certain fixing preference pattern from c ⁿThe middle c that extracts ^N-1And d ^N-1, and not will consider c ⁿThe characteristic of itself.In this manner, a large amount of information characteristics may appear to being drawn into d ^N-1Among, make c ^N-1The situation that can't keep original information collection feature.

For this reason, need be by upgrading operation with d ^N-1In the Partial Feature information transfer to c ^N-1In, make feature that original information concentrates at c ^N-1Can access reservation.Present embodiment adopts the rule of quantity of information balance to realize upgrading operation, in conjunction with the process of vertex split, adopts the odd point that makes a circle in even number point week, has also promptly changed the wavelet coefficient of formation through prediction, upgrades the even number point.As shown in Figure 5, for vertex v ₁₂ ^N-1, adopt the wavelet coefficient m that makes a circle in its week _i ^N-1Upgrade, upgrading formula is formula 2:

${v_{12}}^{n-1}={v_{12}}^{n-1}+A\underset{i=0}{\overset{7}{\mathrm{\&Sigma;}}}{m_l}^{n-1}$ (wherein $A=\frac{1}{10}$ ) formula 2

Merge (Merge)

Merging is the process of and contrary corresponding with division, and it mainly acts on the information subset c that is obtaining ^N-1And d ^N-1Merging is got up, and reduction reconstructs original information set c ⁿThereby, reach the purpose of signal reconstruct.

The operating process that merges Merge is: for Even that obtains (n-1) and Odd (n-1), the topological transformation rule merging of segmenting pattern according to Kobbelt becomes Even (n); In the processing of geological information, adopt formula 1 directly to merge geological information.

Adopt Split, Merge, P, U to represent above-mentioned division, merging, prediction, four operations of renewal respectively, then can make up the decomposition and the restructuring procedure of small echo in the following way:

Decomposable process: $\left\{\begin{array}{c}\{c^{n-1},d^{n-1}\}:=\mathrm{Split}\left(c^n\right)\\ d^{n-1}-=P\left(c^{n-1}\right)\\ c^{n-1}+=U\left(d^{n-1}\right)\end{array}\right.$ Formula 3

Process of reconstruction: $\left\{\begin{array}{c}{c}^{n-1}-=U\left(d^{n-1}\right)\\ d^{n-1}+=P\left(c^{n-1}\right)\\ c^n:=\mathrm{Merge}(c^{n-1},d^{n-1})\end{array}\right.$ Formula 4

Zero tree compressed encoding

The basic framework of Wavelet image coding as shown in Figure 6.Framework is divided into three parts, and wherein quantization modules also promptly zero is set compressed encoding, it is the compression basis of whole framework, also be the source of data degradation, need relate to the content of two aspects: one is the building mode of zero tree, and another then is the quantification manner of wavelet coefficient.EZW mainly is meant the algorithm of this module.In EZW algorithm original text, their respectively corresponding Embedding and Zerotree modules.

The structure of zero tree

Setting up zero tree on geometric model is to make wavelet coefficient can utilize the zerotree image technology to carry out the prerequisite of data compression.Wavelet coefficient for forming in the dough sheet simplification process exists the level corresponding relation between them.But this is not enough, because in the zerotree image of classics, wavelet coefficient all is to adopt the quaternary tree form to organize, if the wavelet coefficient that model simplification is generated compresses, equally also need between the wavelet coefficient of each level, seek a kind of corresponding relation, make and to travel through the quaternary tree all levels wavelet coefficient, that have uniqueness thereby can construct by two-layer formation 1-4 corresponding relation up and down.

Present embodiment utilizes the 1-4 division relation in the Kobbelt segmentation model to handle and sets up the 1-4 corresponding relation.

The corresponding relation of face as shown in Figure 7.

The corresponding relation on limit as shown in Figure 8, the limit of upper strata quadrilateral surface slice graticule A, two limits 1,2 in the middle of the corresponding grid B of lower floor, and the limit 1,2 of both sides and centre is parallel and two limits 3,4 of interlacing.

The corresponding relation of point as shown in Figure 9, the summit of upper strata quadrilateral surface slice graticule A, is the mid point 8 on 90 limits of spending and the intermediate point 7 of each dough sheet with the integral body on the limit of getting at the mid point 6 on corresponding lower floor grid limit that B gets.As shown in Figure 9, in the process of simplifying, be labeled as hollow summit and all can be deleted and be converted into wavelet coefficient, the summit of its hollow core is the child node on solid summit, exists the 1-4 corresponding relation between them.

In the centre of dough sheet, what limit and point all formed is the corresponding relation of 1-4.And empty at once when occurring at the boundary of dough sheet, what the point on limit and the limit (square hollow point and circular hollow point) then formed is the corresponding relation of 1-3, and the point (triangle hollow dots) in the middle of the dough sheet still is the corresponding relation of 1-4.

Quantize

Present embodiment uses the EZW method to carry out the quantification of wavelet zero-tree.Comprehensive compressibility, two factors of distortion rate consider, adopt four times, six times and eight quantification reconstruct all is comparatively desirable selection of times.Consider that in conjunction with visual effect six times is the most suitable quantification reconstruct number of times.

Entropy coding

Entropy coding (entropy encoding) is the lossless coding that a class is utilized the no semantic data stream that the statistical information of data compresses, it is a kind of statistical property according to information itself, number of times and probability that particularly same character repeats come compress informational data, a kind of data compression technique that the feasible information data that repeats adopts a comparatively simple indications to represent.In the process of entropy coding, do not adopt any mode approximate or that cast out to handle, so itself can recover this compression process fully, that is to say, can not cause losing of data precision in the entropy coding process, general all is that correlation technique with lossy compression method combines, and earlier data is carried out lossy compression method, and then adopts entropy coding to do further entropy coding and do further data compression.Present embodiment adopts the Haffman coding to carry out entropy coding, and the data that will repeat are continuously exactly encoded to reduce data redudancy in simple terms.

Embodiment two:

Figure 10 and two of the embodiment that Figure 11 shows that 3 D graphic data compression processing method of the present invention, be with embodiment one difference: in the structure of zero tree, the corresponding relation on limit as shown in figure 10, the limit of upper strata quadrilateral surface slice graticule A, two limits 3,5 that the limit 1,2 of two limits 1,2 in the middle of the corresponding grid B of lower floor and homonymy and centre is parallel.The corresponding relation of point as shown in figure 11, the summit of upper strata quadrilateral surface slice graticule A, is the mid point 8 on 90 limits of spending and the intermediate point 7 of each dough sheet with the integral body on the limit of getting at the mid point 6 on corresponding lower floor grid limit that B gets.This kind situation, in the centre of dough sheet, what limit and point all formed is the corresponding relation of 1-4; Boundary at dough sheet is empty at once when occurring, and what limit and point then formed all is corresponding relations of 1-2.

Claims (5)

1. the compression processing method of a 3 D graphic data may further comprise the steps:

A) obtain the preliminary sweep grid of model outward appearance;

B) by heavily gridding module, described preliminary sweep grid is carried out regular processing, make the new grid of acquisition have the segmentation continuity and support topology information to simplify the operation;

C) by segmentation small echo constructing module, described new gridding information data are divided, predict, upgrade and merge processing, with the decomposition and the restructuring procedure of realization gridding information data, thus the image behind the acquisition wavelet transformation;

D), make up wavelet zero-tree with two-layer, the quaternary tree form up and down relevant with wavelet coefficient by zero tree compression module;

E) by the EZW method wavelet zero-tree that obtains is quantized and compression, thereby obtain Wavelet image zero tree compressed encoding;

F), described zero tree compressed encoding is carried out further data compression, thereby obtain the three-dimensional picture packed data by the entropy coding module;

It is characterized in that:

The new grid that obtains in the described step b) is regular quadrilateral surface slice graticule;

In the zero tree building process of described step d), for quad patch, the corresponding relation of employing face, limit, point, and between the face and face of the non-boundary of upper and lower two-layer quadrilateral surface slice graticule, can set up the 1-4 corresponding relation between limit and the limit, can set up the 1-1 corresponding relation between the summit of lower floor and the limit of last layer, so between non-boundary levels summit, set up the 1-4 corresponding relation by transfer function.

2. the compression processing method of 3 D graphic data according to claim 1, it is characterized in that: the limit of described upper strata quadrilateral surface slice graticule (A), two limits (1,2) of the centre that corresponding lower floor grid (B) is got and both sides and two limits (3,4) that interlace parallel with the limit (1,2) of described centre; The summit of described upper strata quadrilateral surface slice graticule (A), is the mid point (8) on 90 limits of spending and the intermediate point (7) of each dough sheet with the integral body on the limit of getting at the mid point (6) on corresponding lower floor grid (B) limit of getting.

3. the compression processing method of 3 D graphic data according to claim 1, it is characterized in that: the limit of described upper strata quad patch (A) grid, two limits (3,5) that two limits (1,2) of the centre that corresponding lower floor grid (B) is got and homonymy are parallel with the limit (1,2) of described centre; The summit of described upper strata quadrilateral surface slice graticule (A), is the mid point (8) on 90 limits of spending and the intermediate point (7) of each dough sheet with the integral body on the limit of getting at the mid point (6) on corresponding lower floor grid (B) limit of getting.

4. according to the compression processing method of claim 1 or 2 or 3 described 3 D graphic datas, it is characterized in that: adopt QR method that Hormann proposes to be the regular quadrilateral patch grids with the triangular mesh of arbitrary mess is regular in the described step b).

5. according to the compression processing method of claim 1 or 2 or 3 described 3 D graphic datas, it is characterized in that in the described step c), its decomposable process is division-prediction-renewal, and is specific as follows:

Division-with original information c ⁿBe decomposed into two mutually disjoint information subset c ^N-1And d ^N-1, c wherein ^N-1Be new information set, d ^N-1It then is the small echo collection; All summits are divided into two set: one is even number set Even (n-1), this set record be all control vertexs when anterior layer, corresponding c ^N-1Another is odd number set Odd (n-1), this set record be by the generation point when anterior layer control mesh segmentation gained, corresponding d ^N-1Described n is current n layer grid;

The prediction-with the segmentation model be that the basis utilizes the geometric transformation rule of Kobbelt model as predictive operator P, d in the following manner ^N-1-=P (c ^N-1) pair set odd number Odd (n-1) carries out conversion, makes the odd number set be converted to wavelet coefficient set M (n-1);

Upgrade-utilize the rule of quantity of information balance, adopt the odd point that makes a circle in even number point week, also promptly changed the wavelet coefficient of formation, upgrade the even number point through prediction;

Its restructuring procedure is renewal-prediction-merging, and wherein merging is the process of and contrary corresponding with division, with the information subset c that obtains ^N-1And d ^N-1Merging is got up, and reduction reconstructs original information set c ⁿ

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