CN102684703A - Efficient lossless compression method for digital elevation model data - Google Patents

Abstract

The invention achieves an effect of carrying out rapid lossless compression on digital elevation models by using an optimal linear square forecast model and an adaptive arithmetic coding technology. Under the condition of keeping that digital elevation model data information is not lost before and after being compressed, an effect that digital elevation model data is higher in compression ratio and shorter in compression time is achieved. The compression process is divided into two steps: 1, identifying and eliminating information redundancies between adjacent elevations of a digital elevation model by using the optimal linear square forecast model, extracting independent space information, and reducing information entropies, namely that after carrying out decorrelation by using the optimal linear square forecast model, carrying out replacement by using an array without redundancy or with a small redundancy rate; and 2, for the array, carrying out encoding on the extracted information by using the adaptive arithmetic coding technology, so that the reduced information entropies are specifically implemented, thereby further reducing the data quantity. After the two steps, a binary data stream with a higher compression ratio is obtained.

Description

A kind of method of the data lossless of digital elevation model efficiently compression

One, technical field

The present invention relates to a kind of method of the data lossless of digital elevation model efficiently compression, belong to the Spatial Information Technology field.

Two, background technology

Development along with Spatial Information Technology.It is increasingly high that people obtain the automaticity of high-resolution digital elevation model (DEM); Resolution and the data volume of DEM increase rapidly; The DEM of a system handles reaches a hundreds of Gbtyte; Even several TB, the storage of these data takies a large amount of hard drive spaces, has surpassed the development speed of computer hardware; Having is exactly that the present network bandwidth and transmission rate is all limited again, and in order to accelerate the transmission of DEM on network, the compress technique of data provides a kind of effective solution.Compress technique also is one of the important means of the fail safe of service data in addition.

Data compression is according to having or not information dropout to be divided in the process of reconstruction: lossless compress and lossy compression method.Though lossy compression method can obtain the compression ratio higher than lossless compress; The transmission time that takes up room with network to reducing memory device has wide significance; But it can not rebuild the content of original DEM accurately, meeting lost part information, and compression process is irreversible.Require data to have very high confidence level some field people; Like boundary line that relates to national sovereignty among the DEM and the elevation information that reflects the physical features variation etc.; This part information that lossy compression method is lost is vital to us, and therefore lossless compression algorithm has very important realistic meaning to precision, storage, transmission and the information processing that guarantees data efficiently.About document has proposed a lot of diminishing and lossless compression algorithm about text, image; Though these algorithms obtain very high compression ratio when image compression; Because the height value among the DEM is a floating number; And have certain correlation between the consecutive value, these algorithms often are difficult to be applied on the lossless compress of dem data or compression ratio is not high, compression time is longer.

The present invention has realized taking advantage of forecast model and adaptive arithmetic code technology to realize the quick nondestructive compression of DEM with optimum linearity two.

Three, summary of the invention

1, purpose: the purpose of this invention is to provide a kind of method of dem data efficient lossless compression, keeping under the situation that nothing is lost before and after the dem data Information Compression, realize that dem data higher compression ratio, compression time are shorter.

2, technical scheme: the present invention relates to a kind of method of the data lossless of digital elevation model efficiently compression, the steps flow chart of this method is as shown in Figure 1.

The compression of DEM is divided into two processes: the first step, and take advantage of forecast model identification and eliminate information redundancy between the adjacent elevation of DEM through optimum linearity two, extract independently spatial information; Reduce comentropy; That is, to the digital elevation model H [i * n+j] of a m * n through array pVar [i * n+j] replacement irredundant after the forecast model decorrelation or that redundancy is less, wherein 1≤i≤n with one; 1≤j≤m, m, n are positive integer; Next step adopts the adaptive arithmetic code technology that the information of being extracted is encoded to pVar [i * n+j], makes the comentropy after the minimizing be able to concrete realization, further reduces data volume.After this two step, the binary data stream that can obtain having high compression ratio.Concrete implementation procedure is following:

Step 1: set up optimum linearity two and take advantage of forecast model

Prediction is exactly to utilize the correlation between adjacent data among the DEM, estimates the information of any down.Because the data compression and decompression process adopts same rule to predict, so can recover original dem data accurately from the information behind the coding.

The adaptive arithmetic code that the present invention adopts is a kind of entropy coding, and entropy coding has higher description efficient to the data of Gaussian distributed than equally distributed data.Altitude data is generally disobeyed Gaussian distribution; If each data in the discrete data are stochastic variables; Then whole data set Gaussian distributed is eliminated the correlation between the DEM so at first introduce a linear prediction model, the approximate Gaussian distributed of the DEM correction that generates at last.Because dem data is a tactic two-dimensional matrix, the conditional probability distribution of a back point can be obtained by the last collection of coded data.Make C={x _Mn: n＜j, 0≤m＜N; N=j, 0≤m＜i}, wherein the size of DEM is n * m, x _I+1It is the height value that the next one will be encoded.In order to obtain last compression effectiveness, hope x _I+1Probability P in whole two-dimensional matrix (formula 1) maximum.

$P\left\{x_{i+1}\right|i,j\∈(N,M)\}=\underset{i,j=0}{\overset{N-1,M-1}{\mathrm{\Π}}}P\left(x_{i+1}\right|S_{\mathrm{ij}}),S_{\mathrm{ij}}\⊆C---\left(1\right)$

S in the formula (1) _IjBe the context of specified requirements, x _I+1Code length be-log ₂P{x _I+1| i, j ∈ (N, M) } position be the mean value of probabilistic model entropy, conditional probability P{x _I+1| i, and j ∈ (N, M) } be that encoded radio from the front calculates, so decoder can be decoded to it according to identical order equally.

Know that from last surface analysis when using the statistical coding packed data, if the distance of the frequency departure equilibrium locations of elevation correction is more little, compression effectiveness is just good more.(i j) is the stochastic variable of Normal Distribution to elevation variable H, and its predicted value error can have the elevation of consecutive points to obtain, and is as shown in Figure 2, (i, vertical error ν j) among the DEM _{I, j}Calculate by formula (2).

ν _i，j＝H _i，j-κ ₁H _i-1，j-κ ₂H _i-1，j-1-κ ₃H _i，j-1 (2)

In the formula (2), κ ₁, κ ₂, κ ₃Be real number, k ₁+ k ₂+ k ₃=1; ν _{I, j}The two-dimensional matrix V that forms one (m-1) * (n-1).The important precision index of weighing error matrix V is mathematic expectaion μ and variances sigma, and μ representes the mathematical feature of V concentrated position; σ representes the numerical characteristic around the concentrated position dispersion degree, and σ is more little, and the dispersion of V is more little, otherwise dispersion degree is big more.In order to make forecast model optimum, should satisfy formula (3):

$\left\{\begin{array}{c}u=0\\ \mathrm{\σ}=\mathrm{Min}\end{array}\right.$ Promptly $\left\{\begin{array}{c}\underset{i=1}{\overset{m}{\mathrm{\Σ}}}\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{v}_{i,j}=0\\ \underset{i=1}{\overset{m}{\mathrm{\Σ}}}\underset{j=1}{\overset{m}{\mathrm{\Σ}}}\left({\mathrm{\α}}_{i,j}{v}_{i,j}^2\right)=\mathrm{Min}\\ v_{i,j}=H_{i,j}-{\mathrm{\κ}}_1{H}_{i,j}-{\mathrm{\κ}}_2{H}_{i-1,j-1}-{\mathrm{\κ}}_3{H}_{i,j-1}\end{array}\right.---\left(3\right)$

Formula (3) is exactly that optimum linearity two is taken advantage of forecast model, wherein, and α _{I, j}Be coefficient correlation, α _{I, j}=1; Order

ρ is the Lagrange multiplier, with Φ to κ ₁, κ ₂, κ ₃Ask first derivative and order:

$\left\{\begin{array}{c}\underset{i,j}{\mathrm{\Σ}}v=0\\ \∂\mathrm{\ψ}/\∂{\mathrm{\κ}}_1=0\\ \∂\mathrm{\ψ}/\∂{\mathrm{\κ}}_2=0\\ \∂\mathrm{\ψ}/\∂{\mathrm{\κ}}_3/=0\\ \∂\mathrm{\ψ}/\∂\mathrm{\λ}=0\end{array}\right.---\left(4\right)$

$\left(\begin{array}{cccc}\underset{i=1}{\overset{m}{\mathrm{\Σ}}}\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{H}_{i-1,j}^2& \underset{i=1}{\overset{m}{\mathrm{\Σ}}}\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{H}_{i-1,j}{H}_{i-1,j-1}& \underset{i=1}{\overset{m}{\mathrm{\Σ}}}\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{H}_{i-1,j}{H}_{i,j-1}& -\frac{1}{2}\underset{i=1}{\overset{m}{\mathrm{\Σ}}}\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{H}_{i-1,j}\\ \underset{i=1}{\overset{m}{\mathrm{\Σ}}}\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{H}_{i-1,j}{H}_{i-1,j-1}& \underset{i=1}{\overset{m}{\mathrm{\Σ}}}\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{H}_{i-1,j-1}^2& \underset{i=1}{\overset{m}{\mathrm{\Σ}}}\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{H}_{i-1,j-1}{H}_{i-1,j}& -\frac{1}{2}\underset{i=1}{\overset{m}{\mathrm{\Σ}}}\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{H}_{i-1,j-1}\\ \underset{i=1}{\overset{m}{\mathrm{\Σ}}}\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{H}_{i-1,j-1}{H}_{i,j-1}& \underset{i=1}{\overset{m}{\mathrm{\Σ}}}\underset{j-1}{\overset{n}{\mathrm{\Σ}}}{H}_{i-1,j}{H}_{i,j-1}& \underset{i=1}{\overset{m}{\mathrm{\Σ}}}\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{H}_{i,j-1}^2& -\frac{1}{2}\underset{i=1}{\overset{m}{\mathrm{\Σ}}}\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{H}_{i,j-1}\\ \underset{i=1}{\overset{m}{\mathrm{\Σ}}}\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{H}_{i-1,j}& \underset{i=1}{\overset{m}{\mathrm{\Σ}}}\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{H}_{i-1,j-1}& \underset{i=1}{\overset{m}{\mathrm{\Σ}}}\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{H}_{i,j-1}& 0\end{array}\right)\left(\begin{array}{c}{\mathrm{\κ}}_1\\ {\mathrm{\κ}}_2\\ {\mathrm{\κ}}_3\\ \mathrm{\ρ}\end{array}\right)=\left(\begin{array}{c}\underset{i=1}{\overset{m}{\mathrm{\Σ}}}\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{H}_{i,j}{H}_{i-1,j}\\ \underset{i=1}{\overset{m}{\mathrm{\Σ}}}\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{H}_{i,j}{H}_{i-1.,j-1}\\ \underset{i=1}{\overset{m}{\mathrm{\Σ}}}\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{H}_{i,j}{H}_{i,j-1}\\ \underset{i=1}{\overset{m}{\mathrm{\Σ}}}\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{H}_{i,j}\end{array}\right)---\left(5\right)$

Order $A=\left\{a_{\mathrm{ij}}\right\}=\left(\begin{array}{cccc}\underset{i=1}{\overset{m}{\mathrm{\Σ}}}\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{H}_{i-1,j}^2& \underset{i=1}{\overset{m}{\mathrm{\Σ}}}\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{H}_{i-1,j}{H}_{i-1,j-1}& \underset{i=1}{\overset{m}{\mathrm{\Σ}}}\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{H}_{i-1,j}{H}_{i,j-1}& -\frac{1}{2}\underset{i=1}{\overset{m}{\mathrm{\Σ}}}\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{H}_{i-1,j}\\ \underset{i=1}{\overset{m}{\mathrm{\Σ}}}\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{H}_{i-1,j}{H}_{i-1,j-1}& \underset{i=1}{\overset{m}{\mathrm{\Σ}}}\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{H}_{i-1,j-1}^2& \underset{i=1}{\overset{m}{\mathrm{\Σ}}}\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{H}_{i-1,j-1}{H}_{i-1,j}& -\frac{1}{2}\underset{i=1}{\overset{m}{\mathrm{\Σ}}}\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{H}_{i-1,j-1}\\ \underset{i=1}{\overset{m}{\mathrm{\Σ}}}\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{H}_{i-1,j-1}{H}_{i,j-1}& \underset{i=1}{\overset{m}{\mathrm{\Σ}}}\underset{j-1}{\overset{n}{\mathrm{\Σ}}}{H}_{i-1,j}{H}_{i,j-1}& \underset{i=1}{\overset{m}{\mathrm{\Σ}}}\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{H}_{i,j-1}^2& -\frac{1}{2}\underset{i=1}{\overset{m}{\mathrm{\Σ}}}\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{H}_{i,j-1}\\ \underset{i=1}{\overset{m}{\mathrm{\Σ}}}\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{H}_{i-1,j}& \underset{i=1}{\overset{m}{\mathrm{\Σ}}}\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{H}_{i-1,j-1}& \underset{i=1}{\overset{m}{\mathrm{\Σ}}}\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{H}_{i,j-1}& 0\end{array}\right),$ $B=\left\{b_i\right\}=\left(\begin{array}{c}\underset{i=1}{\overset{m}{\mathrm{\Σ}}}\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{H}_{i,j}{H}_{i-1,j}\\ \underset{i=1}{\overset{m}{\mathrm{\Σ}}}\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{H}_{i,j}{H}_{i-1,j-1}\\ \underset{i=1}{\overset{m}{\mathrm{\Σ}}}\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{H}_{i,j}{H}_{i,j-1}\\ \underset{i=1}{\overset{m}{\mathrm{\Σ}}}\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{H}_{i,j}\end{array}\right)$

Wherein, i, j=1,2,3,4.

Separate above-mentioned equation (5) through the Doolittle decomposition method, obtain:

$\left\{\begin{array}{c}{u}_{\mathrm{kj}}=a_{\mathrm{kj}}-\underset{t=1}{\overset{k-1}{\mathrm{\Σ}}}{l}_{\mathrm{kt}}{u}_{\mathrm{tj}}\\ l_{ik}=(a_{ik}-\underset{t=1}{\overset{k-1}{\mathrm{\Σ}}}{l}_{it}{u}_{\mathrm{tk}})/u_{\mathrm{kk}}\end{array}\right.$

k＝1，2，3，4；j＝k，k+1，...，3；i＝k+1，...，n (6)

$\left\{\begin{array}{c}{y}_i=b_i-\underset{t=1}{\overset{i-1}{\mathrm{\Σ}}}{l}_{\mathrm{it}}{y}_t\\ {\mathrm{\κ}}_j=(y_j-\underset{t=j+1}{\overset{n}{\mathrm{\Σ}}}{u}_{it}{\mathrm{\κ}}_t)/u_{\mathrm{jj}}\end{array}\right.$ I=1 wherein ..., 4; J=3,2,1 (7)

Through following formula (6) and (7), can be in the hope of κ ₁, κ ₂, κ ₃Value.(i, first row j) and the value of first row are constant, utilize ν to keep H _{I, j}=int (H _{I, j}-κ ₁H _{I-1, j}-κ ₂H _{I-1, j-1}-κ ₃H _{I, j-1}) calculate elevation correction, the result be stored in pVar (i, j), this moment 1≤i≤n, 1≤j≤m.

Step 2: arithmetic coding compression DEM corrects error

(i j) adopts adaptive arithmetic code to encode, and finally realizes data compression to predicated error matrix pVar.Basic thought is that each different sequences is videoed in the respective digital zone between 0 and 1 according to the frequency of occurrences, and this region list is shown as the binary fraction that can change precision, and the data that wherein frequency of occurrences is low are more utilized the high more fractional representation of precision.The compression effectiveness of this algorithm of frequency of occurrences decision of source data also determines the corresponding interval range of source data in the cataloged procedure simultaneously, then determines the dateout that the arithmetic compression algorithm is final between the code area.

In the realization of arithmetic coding high-order context model, along with the linearity increase of model order, the model committed memory is the speed increment of index, and needing the contextual number of storage is m ⁿ, wherein, m is mutual unduplicated symbol numbers, n is the exponent number of model.Utilize the high-order context always to be based upon this rule on the contextual basis of low order; 0 rank context table is stored in the linear linked list; Each element in the chained list has comprised the pointer that points to corresponding 1 rank context table; Comprise the pointer that points to 2 rank context table again in the 1 rank context table, comprised the pointer that points to 3 rank context table again in the 2 rank context table, constituted the whole context tree thus.Have only the literary talent up and down that occurred to have the node that has distributed in the tree, the context that did not occur needn't the committed memory space, only just has count value at the character that this context occurred at the back, can reduce space consuming to greatest extent thus.Through after this process, obtain the binary data stream that DEM has high compression ratio.

3, advantage and effect: about document has proposed a lot of diminishing and lossless compression algorithm about image; Though these algorithms obtain very high compression ratio when text, image compression, be difficult to be applied on the lossless compress of dem data or compression ratio is not high, compression time is longer.The present invention proposes to take advantage of forecast model and adaptive arithmetic code technology to realize the quick nondestructive compression of DEM with optimum linearity two.Keeping under the situation that nothing is lost before and after the dem data Information Compression, realizing that dem data higher compression ratio, compression time are shorter.

Four, description of drawings

Fig. 1 DEM lossless compress process sketch map

The position relation of Fig. 2 grid DEM consecutive points

Five, embodiment

The present invention relates to a kind of method of the data lossless of digital elevation model efficiently compression, the steps flow chart of this method is as shown in Figure 1.

The compression of DEM is divided into two processes: the first step, and take advantage of forecast model identification and eliminate information redundancy between the adjacent elevation of DEM through optimum linearity two, extract independently spatial information; Reduce comentropy; That is, to the digital elevation model H [i * n+j] of a m * n through array pVar [i * n+j] replacement irredundant after the forecast model decorrelation or that redundancy is less, wherein 1≤i≤n with one; 1≤j≤m, m, n are positive integer; Next step adopts the adaptive arithmetic code technology that the information of being extracted is encoded to pVar [i * n+j], makes the comentropy after the minimizing be able to concrete realization, further reduces data volume.After this two step, can obtain having the more binary data stream of high compression ratio.Concrete implementation procedure is following:

Step 1: set up optimum linearity two and take advantage of forecast model

Prediction is exactly to utilize the correlation between adjacent data among the DEM, estimates the information of any down.Because the data compression and decompression process adopts same rule to predict, so can recover original dem data accurately from the information behind the coding.

The adaptive arithmetic code that the present invention adopts is a kind of entropy coding, and entropy coding has higher description efficient to the data of Gaussian distributed than equally distributed data.Altitude data is generally disobeyed Gaussian distribution; If each data in the discrete data are stochastic variables; Then whole data set Gaussian distributed is eliminated the correlation between the DEM so at first introduce a linear prediction model, the approximate Gaussian distributed of the DEM correction that generates at last.Because dem data is a tactic two-dimensional matrix, the conditional probability distribution of a back point can be obtained by the last collection of coded data.Make C={x _Mn: n＜j and 0≤m＜N; N=j and 0≤m＜i}, wherein the size of DEM is n * m, x _I+1It is the height value that the next one will be encoded.In order to obtain last compression effectiveness, hope x _I+1Probability P in whole two-dimensional matrix (formula 1) maximum.

$P\left\{x_{i+1}\right|i,j\∈(N,M)\}=\underset{i,j=0}{\overset{N-1,M-1}{\mathrm{\Π}}}P\left(x_{i+1}\right|S_{\mathrm{ij}}),S_{\mathrm{ij}}\⊆C---\left(1\right)$

S in the formula (1) _IjBe the context of specified requirements, x _I+1Code length be-log ₂P{x _I+1| i, j ∈ (N, M) } position be the mean value of probabilistic model entropy, conditional probability P{x _I+1| i, and j ∈ (N, M) } be that encoded radio from the front calculates, so decoder can be decoded to it according to identical order equally.

The present invention proposes a kind of optimum linearity two of better performances and takes advantage of forecast model.Know that from last surface analysis when using the statistical coding packed data, if the distance of the frequency departure equilibrium locations of elevation correction is more little, compression effectiveness is just good more.(i j) is the stochastic variable of Normal Distribution to elevation variable H, and its predicted value error can have the elevation of consecutive points to obtain, and is as shown in Figure 2, (i, vertical error ν j) among the DEM _{I, j}Calculate by formula (2).

ν _i，j＝H _i，j-κ ₁H _i-1，j-κ ₂H _i-1，j-1-κ ₃H _i，j-1 (2)

In the formula (2), κ ₁, κ ₂, κ ₃Be real number, k ₁+ k ₂+ k ₃=1; ν _{I, j}The two-dimensional matrix V that forms one (m-1) * (n-1).The important precision index of weighing error matrix V is mathematic expectaion μ and variances sigma, and μ representes the mathematical feature of V concentrated position; σ representes the numerical characteristic around the concentrated position dispersion degree, and σ is more little, and the dispersion of V is more little, otherwise dispersion degree is big more.In order to make forecast model optimum, should satisfy formula (3):

$\left\{\begin{array}{c}u=0\\ \mathrm{\σ}=\mathrm{Min}\end{array}\right.$ Promptly $\left\{\begin{array}{c}\underset{i=1}{\overset{m}{\mathrm{\Σ}}}\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{v}_{i,j}=0\\ \underset{i=1}{\overset{m}{\mathrm{\Σ}}}\underset{j=1}{\overset{m}{\mathrm{\Σ}}}\left({\mathrm{\α}}_{i,j}{v}_{i,j}^2\right)=\mathrm{Min}\\ v_{i,j}=H_{i,j}-{\mathrm{\κ}}_1{H}_{i,j}-{\mathrm{\κ}}_2{H}_{i-1,j-1}-{\mathrm{\κ}}_3{H}_{i,j-1}\end{array}\right.---\left(3\right)$

Formula (3) is exactly that optimum linearity two is taken advantage of forecast model, wherein, and α _{I, j}Be coefficient correlation, α _{I, j}=1; Order

ρ is the Lagrange multiplier, with Φ to κ ₁, κ ₂, κ ₃Ask first derivative and order:

$\left\{\begin{array}{c}\underset{i,j}{\mathrm{\Σ}}v=0\\ \∂\mathrm{\ψ}/\∂{\mathrm{\κ}}_1=0\\ \∂\mathrm{\ψ}/\∂{\mathrm{\κ}}_2=0\\ \∂\mathrm{\ψ}/\∂{\mathrm{\κ}}_3/=0\\ \∂\mathrm{\ψ}/\∂\mathrm{\λ}=0\end{array}\right.---\left(4\right)$

$\left(\begin{array}{cccc}\underset{i=1}{\overset{m}{\mathrm{\Σ}}}\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{H}_{i-1,j}^2& \underset{i=1}{\overset{m}{\mathrm{\Σ}}}\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{H}_{i-1,j}{H}_{i-1,j-1}& \underset{i=1}{\overset{m}{\mathrm{\Σ}}}\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{H}_{i-1,j}{H}_{i,j-1}& -\frac{1}{2}\underset{i=1}{\overset{m}{\mathrm{\Σ}}}\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{H}_{i-1,j}\\ \underset{i=1}{\overset{m}{\mathrm{\Σ}}}\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{H}_{i-1,j}{H}_{i-1,j-1}& \underset{i=1}{\overset{m}{\mathrm{\Σ}}}\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{H}_{i-1,j-1}^2& \underset{i=1}{\overset{m}{\mathrm{\Σ}}}\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{H}_{i-1,j-1}{H}_{i-1,j}& -\frac{1}{2}\underset{i=1}{\overset{m}{\mathrm{\Σ}}}\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{H}_{i-1,j-1}\\ \underset{i=1}{\overset{m}{\mathrm{\Σ}}}\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{H}_{i-1,j-1}{H}_{i,j-1}& \underset{i=1}{\overset{m}{\mathrm{\Σ}}}\underset{j-1}{\overset{n}{\mathrm{\Σ}}}{H}_{i-1,j}{H}_{i,j-1}& \underset{i=1}{\overset{m}{\mathrm{\Σ}}}\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{H}_{i,j-1}^2& -\frac{1}{2}\underset{i=1}{\overset{m}{\mathrm{\Σ}}}\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{H}_{i,j-1}\\ \underset{i=1}{\overset{m}{\mathrm{\Σ}}}\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{H}_{i-1,j}& \underset{i=1}{\overset{m}{\mathrm{\Σ}}}\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{H}_{i-1,j-1}& \underset{i=1}{\overset{m}{\mathrm{\Σ}}}\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{H}_{i,j-1}& 0\end{array}\right)\left(\begin{array}{c}{\mathrm{\κ}}_1\\ {\mathrm{\κ}}_2\\ {\mathrm{\κ}}_3\\ \mathrm{\ρ}\end{array}\right)=\left(\begin{array}{c}\underset{i=1}{\overset{m}{\mathrm{\Σ}}}\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{H}_{i,j}{H}_{i-1,j}\\ \underset{i=1}{\overset{m}{\mathrm{\Σ}}}\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{H}_{i,j}{H}_{i-1.,j-1}\\ \underset{i=1}{\overset{m}{\mathrm{\Σ}}}\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{H}_{i,j}{H}_{i,j-1}\\ \underset{i=1}{\overset{m}{\mathrm{\Σ}}}\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{H}_{i,j}\end{array}\right)---\left(5\right)$

Order $A=\left\{a_{\mathrm{ij}}\right\}=\left(\begin{array}{cccc}\underset{i=1}{\overset{m}{\mathrm{\Σ}}}\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{H}_{i-1,j}^2& \underset{i=1}{\overset{m}{\mathrm{\Σ}}}\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{H}_{i-1,j}{H}_{i-1,j-1}& \underset{i=1}{\overset{m}{\mathrm{\Σ}}}\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{H}_{i-1,j}{H}_{i,j-1}& -\frac{1}{2}\underset{i=1}{\overset{m}{\mathrm{\Σ}}}\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{H}_{i-1,j}\\ \underset{i=1}{\overset{m}{\mathrm{\Σ}}}\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{H}_{i-1,j}{H}_{i-1,j-1}& \underset{i=1}{\overset{m}{\mathrm{\Σ}}}\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{H}_{i-1,j-1}^2& \underset{i=1}{\overset{m}{\mathrm{\Σ}}}\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{H}_{i-1,j-1}{H}_{i-1,j}& -\frac{1}{2}\underset{i=1}{\overset{m}{\mathrm{\Σ}}}\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{H}_{i-1,j-1}\\ \underset{i=1}{\overset{m}{\mathrm{\Σ}}}\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{H}_{i-1,j-1}{H}_{i,j-1}& \underset{i=1}{\overset{m}{\mathrm{\Σ}}}\underset{j-1}{\overset{n}{\mathrm{\Σ}}}{H}_{i-1,j}{H}_{i,j-1}& \underset{i=1}{\overset{m}{\mathrm{\Σ}}}\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{H}_{i,j-1}^2& -\frac{1}{2}\underset{i=1}{\overset{m}{\mathrm{\Σ}}}\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{H}_{i,j-1}\\ \underset{i=1}{\overset{m}{\mathrm{\Σ}}}\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{H}_{i-1,j}& \underset{i=1}{\overset{m}{\mathrm{\Σ}}}\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{H}_{i-1,j-1}& \underset{i=1}{\overset{m}{\mathrm{\Σ}}}\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{H}_{i,j-1}& 0\end{array}\right),$ $B=\left\{b_i\right\}=\left(\begin{array}{c}\underset{i=1}{\overset{m}{\mathrm{\Σ}}}\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{H}_{i,j}{H}_{i-1,j}\\ \underset{i=1}{\overset{m}{\mathrm{\Σ}}}\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{H}_{i,j}{H}_{i-1,j-1}\\ \underset{i=1}{\overset{m}{\mathrm{\Σ}}}\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{H}_{i,j}{H}_{i,j-1}\\ \underset{i=1}{\overset{m}{\mathrm{\Σ}}}\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{H}_{i,j}\end{array}\right)$

Wherein, i, j=1,2,3,4.

Separate above-mentioned equation (5) through the Doolittle decomposition method, obtain:

$\left\{\begin{array}{c}{u}_{\mathrm{kj}}=a_{\mathrm{kj}}-\underset{t=1}{\overset{k-1}{\mathrm{\Σ}}}{l}_{\mathrm{kt}}{u}_{\mathrm{tj}}\\ l_{ik}=(a_{ik}-\underset{t=1}{\overset{k-1}{\mathrm{\Σ}}}{l}_{it}{u}_{\mathrm{tk}})/u_{\mathrm{kk}}\end{array}\right.$ k＝1，2，3，4；j＝k，k+1，...，3；i＝k+1，...，n (6)

$\left\{\begin{array}{c}{y}_i=b_i-\underset{t=1}{\overset{i-1}{\mathrm{\Σ}}}{l}_{\mathrm{it}}{y}_t\\ {\mathrm{\κ}}_j=(y_j-\underset{t=j+1}{\overset{n}{\mathrm{\Σ}}}{u}_{it}{\mathrm{\κ}}_t)/u_{\mathrm{jj}}\end{array}\right.$ I=1 wherein ..., 4; J=3,2,1 (7)

Through following formula (6) and (7), can be in the hope of κ ₁, κ ₂, κ ₃Value.(i, first row j) and the value of first row are constant, utilize ν to keep H _{I, j}=int (H _{I, j}-κ ₁H _{I-1, j}-κ ₂H _{I-1, j-1}-κ ₃H _{I, j-1}) calculate elevation correction, the result be stored in pVar (i, j), this moment 1≤i＜n, 1≤j＜m.

Step 2: arithmetic coding compression DEM corrects error

(i j) adopts adaptive arithmetic code to encode, and finally realizes data compression to predicated error matrix pVar.Basic thought is that each different sequences is videoed in the respective digital zone between 0 and 1 according to the frequency of occurrences, and this region list is shown as the binary fraction that can change precision, and the data that wherein frequency of occurrences is low are more utilized the high more fractional representation of precision.The compression effectiveness of this algorithm of frequency of occurrences decision of source data also determines the corresponding interval range of source data in the cataloged procedure simultaneously, then determines the dateout that the arithmetic compression algorithm is final between the code area.

In the realization of arithmetic coding high-order context model, along with the linearity increase of model order, the model committed memory is the speed increment of index, and needing the contextual number of storage is m ⁿ, wherein, m is mutual unduplicated symbol numbers, n is the exponent number of model.Utilize the high-order context always to be based upon this rule on the contextual basis of low order; 0 rank context table is stored in the linear linked list; Each element in the chained list has comprised the pointer that points to corresponding 1 rank context table; Comprise the pointer that points to 2 rank context table again in the 1 rank context table, comprised the pointer that points to 3 rank context table again in the 2 rank context table, constituted the whole context tree thus.Have only the literary talent up and down that occurred to have the node that has distributed in the tree, the context that did not occur needn't the committed memory space, only just has count value at the character that this context occurred at the back, can reduce space consuming to greatest extent thus.Through after this process, obtain the binary data stream that DEM has high compression ratio.

Embodiment 1:

Dispose Intel (R) Core at one ^TM2.4GHz 2 processors, the 2G internal memory is implemented on the computer of ATI Radeon HD figure video card.Select three width of cloth dem data Asia, ChinaPart and JingPart, represent different landform: Asia to comprise the mountain area that ocean and relief are very big respectively; The ChinaPart overwhelming majority is area, the mountain ridge; JingPart is the flat-bottomed land.Table 1 has been listed the relevant information of this three width of cloth verification msg.

The information of table 1.DEM

Table 2 has been listed DEM compression method of the present invention and Winrar, the CAB performance index to three width of cloth DEM compression respectively.The formula of compression ratio is like (8):

Compression ratio:

From table 2, can find out: the compression time that the present invention obtains DEM to be significantly less than the back both, and also exceed 10%-20% than the compression ratio of WINRAR or CAB.

Three kinds of distinct methods algorithms of table 2. are to the comparison of DEM compression ratio and compression time performance

Claims (1)

1. the method step of a digital elevation model data lossless compression efficiently comprises:

Step 1: set up optimum linearity two and take advantage of forecast model

Because (i, (i j) is the stochastic variable of Normal Distribution to elevation variable H j) to any point in the digital elevation model (DEM), and its predicted value error can be obtained (i, vertical error ν j) among the DEM by the consecutive points elevation _{I, j}Calculate by formula (1).

ν _i，j＝H _i，j-κ ₁H _i-1，j-κ ₂H _i-1，j-1-κ ₃H _i，j-1 (1)

In the formula (1), κ ₁, κ ₂, κ ₃Be real number, k ₁+ k ₂+ k ₃=1; ν _{I, j}The two-dimensional matrix V that forms one (m-1) * (n-1), the important precision index of weighing error matrix V is mathematic expectaion μ and variances sigma, and σ is more little, and the dispersion of V is more little, on the contrary dispersion degree is big more, and optimum in order to make forecast model, should satisfy formula (2):

$\left\{\begin{array}{c}u=0\\ \mathrm{\σ}=\mathrm{Min}\end{array}\right.,$ Promptly $\left\{\begin{array}{c}\underset{i=1}{\overset{m}{\mathrm{\Σ}}}\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{v}_{i,j}=0\\ \underset{i=1}{\overset{m}{\mathrm{\Σ}}}\underset{j=1}{\overset{m}{\mathrm{\Σ}}}\left({\mathrm{\α}}_{i,j}{v}_{i,j}^2\right)=\mathrm{Min}\\ v_{i,j}=H_{i,j}-{\mathrm{\κ}}_1{H}_{i,j}-{\mathrm{\κ}}_2{H}_{i-1,j-1}-{\mathrm{\κ}}_3{H}_{i,j-1}\end{array}\right.---\left(2\right)$

Formula (2) is exactly that optimum linearity two is taken advantage of forecast model, wherein, and α _{I, j}Be coefficient correlation, α _{I, j}=1; Order

ρ is the Lagrange multiplier, with Φ to κ ₁, κ ₂, κ ₃Ask first derivative and order:

$\left\{\begin{array}{c}\underset{i,j}{\mathrm{\Σ}}v=0\\ \∂\mathrm{\ψ}/\∂{\mathrm{\κ}}_1=0\\ \∂\mathrm{\ψ}/\∂{\mathrm{\κ}}_2=0\\ \∂\mathrm{\ψ}/\∂{\mathrm{\κ}}_3/=0\\ \∂\mathrm{\ψ}/\∂\mathrm{\λ}=0\end{array}\right.---\left(3\right)$

$\left(\begin{array}{cccc}\underset{i=1}{\overset{m}{\mathrm{\Σ}}}\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{H}_{i-1,j}^2& \underset{i=1}{\overset{m}{\mathrm{\Σ}}}\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{H}_{i-1,j}{H}_{i-1,j-1}& \underset{i=1}{\overset{m}{\mathrm{\Σ}}}\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{H}_{i-1,j}{H}_{i,j-1}& -\frac{1}{2}\underset{i=1}{\overset{m}{\mathrm{\Σ}}}\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{H}_{i-1,j}\\ \underset{i=1}{\overset{m}{\mathrm{\Σ}}}\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{H}_{i-1,j}{H}_{i-1,j-1}& \underset{i=1}{\overset{m}{\mathrm{\Σ}}}\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{H}_{i-1,j-1}^2& \underset{i=1}{\overset{m}{\mathrm{\Σ}}}\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{H}_{i-1,j-1}{H}_{i-1,j}& -\frac{1}{2}\underset{i=1}{\overset{m}{\mathrm{\Σ}}}\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{H}_{i-1,j-1}\\ \underset{i=1}{\overset{m}{\mathrm{\Σ}}}\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{H}_{i-1,j-1}{H}_{i,j-1}& \underset{i=1}{\overset{m}{\mathrm{\Σ}}}\underset{j-1}{\overset{n}{\mathrm{\Σ}}}{H}_{i-1,j}{H}_{i,j-1}& \underset{i=1}{\overset{m}{\mathrm{\Σ}}}\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{H}_{i,j-1}^2& -\frac{1}{2}\underset{i=1}{\overset{m}{\mathrm{\Σ}}}\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{H}_{i,j-1}\\ \underset{i=1}{\overset{m}{\mathrm{\Σ}}}\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{H}_{i-1,j}& \underset{i=1}{\overset{m}{\mathrm{\Σ}}}\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{H}_{i-1,j-1}& \underset{i=1}{\overset{m}{\mathrm{\Σ}}}\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{H}_{i,j-1}& 0\end{array}\right)\left(\begin{array}{c}{\mathrm{\κ}}_1\\ {\mathrm{\κ}}_2\\ {\mathrm{\κ}}_3\\ \mathrm{\ρ}\end{array}\right)=\left(\begin{array}{c}\underset{i=1}{\overset{m}{\mathrm{\Σ}}}\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{H}_{i,j}{H}_{i-1,j}\\ \underset{i=1}{\overset{m}{\mathrm{\Σ}}}\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{H}_{i,j}{H}_{i-1.,j-1}\\ \underset{i=1}{\overset{m}{\mathrm{\Σ}}}\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{H}_{i,j}{H}_{i,j-1}\\ \underset{i=1}{\overset{m}{\mathrm{\Σ}}}\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{H}_{i,j}\end{array}\right)---\left(4\right)$

Order $A=\left\{a_{\mathrm{ij}}\right\}=\left(\begin{array}{cccc}\underset{i=1}{\overset{m}{\mathrm{\Σ}}}\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{H}_{i-1,j}^2& \underset{i=1}{\overset{m}{\mathrm{\Σ}}}\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{H}_{i-1,j}{H}_{i-1,j-1}& \underset{i=1}{\overset{m}{\mathrm{\Σ}}}\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{H}_{i-1,j}{H}_{i,j-1}& -\frac{1}{2}\underset{i=1}{\overset{m}{\mathrm{\Σ}}}\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{H}_{i-1,j}\\ \underset{i=1}{\overset{m}{\mathrm{\Σ}}}\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{H}_{i-1,j}{H}_{i-1,j-1}& \underset{i=1}{\overset{m}{\mathrm{\Σ}}}\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{H}_{i-1,j-1}^2& \underset{i=1}{\overset{m}{\mathrm{\Σ}}}\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{H}_{i-1,j-1}{H}_{i-1,j}& -\frac{1}{2}\underset{i=1}{\overset{m}{\mathrm{\Σ}}}\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{H}_{i-1,j-1}\\ \underset{i=1}{\overset{m}{\mathrm{\Σ}}}\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{H}_{i-1,j-1}{H}_{i,j-1}& \underset{i=1}{\overset{m}{\mathrm{\Σ}}}\underset{j-1}{\overset{n}{\mathrm{\Σ}}}{H}_{i-1,j}{H}_{i,j-1}& \underset{i=1}{\overset{m}{\mathrm{\Σ}}}\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{H}_{i,j-1}^2& -\frac{1}{2}\underset{i=1}{\overset{m}{\mathrm{\Σ}}}\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{H}_{i,j-1}\\ \underset{i=1}{\overset{m}{\mathrm{\Σ}}}\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{H}_{i-1,j}& \underset{i=1}{\overset{m}{\mathrm{\Σ}}}\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{H}_{i-1,j-1}& \underset{i=1}{\overset{m}{\mathrm{\Σ}}}\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{H}_{i,j-1}& 0\end{array}\right),$ $B=\left\{b_i\right\}=\left(\begin{array}{c}\underset{i=1}{\overset{m}{\mathrm{\Σ}}}\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{H}_{i,j}{H}_{i-1,j}\\ \underset{i=1}{\overset{m}{\mathrm{\Σ}}}\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{H}_{i,j}{H}_{i-1,j-1}\\ \underset{i=1}{\overset{m}{\mathrm{\Σ}}}\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{H}_{i,j}{H}_{i,j-1}\\ \underset{i=1}{\overset{m}{\mathrm{\Σ}}}\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{H}_{i,j}\end{array}\right)$

Wherein, i, j=1,2,3,4.

Separate above-mentioned equation (4) through the Doolittle decomposition method, obtain:

$\left\{\begin{array}{c}{u}_{\mathrm{kj}}=a_{\mathrm{kj}}-\underset{t=1}{\overset{k-1}{\mathrm{\Σ}}}{l}_{\mathrm{kt}}{u}_{\mathrm{tj}}\\ l_{ik}=(a_{ik}-\underset{t=1}{\overset{k-1}{\mathrm{\Σ}}}{l}_{it}{u}_{\mathrm{tk}})/u_{\mathrm{kk}}\end{array}\right.$ k＝1，2，3，4；j＝k，k+1，...，3；i＝k+1，...，n (5)

$\left\{\begin{array}{c}{y}_i=b_i-\underset{t=1}{\overset{i-1}{\mathrm{\Σ}}}{l}_{\mathrm{it}}{y}_t\\ {\mathrm{\κ}}_j=(y_j-\underset{t=j+1}{\overset{n}{\mathrm{\Σ}}}{u}_{it}{\mathrm{\κ}}_t)/u_{\mathrm{jj}}\end{array}\right.$ I=1 wherein ..., 4; J=3,2,1 (6)

Through following formula (5) and (6), try to achieve κ ₁, κ ₂, κ ₃Value, (i, the values that first row and first j) is listed as are constant, utilize ν to keep H _{I, j}=int (H _{I, j}-κ ₁H _{I-1, j}-κ ₂H _{I-1, j-1}-κ ₃H _{I, j-1}) calculate elevation correction, the result be stored in pVar (i, j), this moment 1≤i≤n, 1≤j≤m.

Step 2: adaptive arithmetic code compression DEM corrects error

In the realization of adaptive arithmetic code high-order context model; 0 rank context table is stored in the linear linked list, and each element in the chained list has comprised the pointer that points to corresponding 1 rank context table, has comprised the pointer that points to 2 rank context table again in the 1 rank context table; Comprised the pointer that points to 3 rank context table again in the 2 rank context table; Constitute whole context tree thus, have only the literary talent up and down that occurred to have the node that has distributed in the tree, the context that did not occur needn't the committed memory space; The character that only occurred at the back at this context just has count value; Can reduce space consuming to greatest extent thus,, obtain the binary data stream that DEM has high compression ratio through after this process.

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