US20060171567A1  System for geometrically accurate compression and decompression  Google Patents
System for geometrically accurate compression and decompression Download PDFInfo
 Publication number
 US20060171567A1 US20060171567A1 US11/327,645 US32764506A US2006171567A1 US 20060171567 A1 US20060171567 A1 US 20060171567A1 US 32764506 A US32764506 A US 32764506A US 2006171567 A1 US2006171567 A1 US 2006171567A1
 Authority
 US
 United States
 Prior art keywords
 signal
 gradient
 system
 reconstructed
 data
 Prior art date
 Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
 Abandoned
Links
 238000007906 compression Methods 0 abstract claims description title 28
 238000000034 methods Methods 0 claims description 16
 238000003860 storage Methods 0 abstract description 6
 238000004891 communication Methods 0 claims description 4
 230000015654 memory Effects 0 description 5
 238000004422 calculation algorithm Methods 0 description 4
 239000000203 mixtures Substances 0 description 4
 230000014509 gene expression Effects 0 description 3
 230000001965 increased Effects 0 description 3
 239000011133 lead Substances 0 description 3
 230000036961 partial Effects 0 description 3
 238000004458 analytical methods Methods 0 description 2
 230000001976 improved Effects 0 description 2
 239000002609 media Substances 0 description 2
 239000011805 balls Substances 0 description 1
 230000001276 controlling effects Effects 0 description 1
 230000000875 corresponding Effects 0 description 1
 230000036545 exercise Effects 0 description 1
 238000006011 modification Methods 0 description 1
 230000004048 modification Effects 0 description 1
 230000002093 peripheral Effects 0 description 1
 230000001902 propagating Effects 0 description 1
 230000002104 routine Effects 0 description 1
 230000001702 transmitter Effects 0 description 1
Images
Classifications

 G—PHYSICS
 G06—COMPUTING; CALCULATING; COUNTING
 G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
 G06T9/00—Image coding
 G06T9/004—Predictors, e.g. intraframe, interframe coding
Abstract
A system is disclosed providing accurate compression, storage, transmission and reconstruction of both simulated and empirical data representing terrain and other physical or hypothetical signals or surfaces, in one or multiple dimensions. In one embodiment, a gradient of an original surface is generated, and the data representing that gradient is compressed, then stored and/or transmitted. Reconstruction of the gradient yields an accurate representation of the original gradient. An alternative embodiment includes taking a second gradient of the original surface before compression, in which case reconstruction yields the second gradient, from which the first gradient can also be recovered.
Description
 This application claims the benefit of U.S. Provisional Application No. 60/257,210, of Osher et al., filed Dec. 20, 2000, entitled “Geometrically Accurate Compression and Decompression”, which is incorporated herein by reference.
 The present invention relates to a system for compressing and reconstructing (decompressing) signals, including signals representing physical data such as terrain. Such signals may be computerconstructed data, empirically derived images or signals, or in general any information or data representing actual or simulated phenomena.
 After compression of data representing a terrain, digital terrain elevation (or images, indeed any graph) data (“DTED”), a common problem is accurate reconstruction of terrain features, such as the slope. Given digitized data representing terrain elevation, or indeed any graph in two or more dimensions at a data point (x,y) (or the multiple dimension extension at a data point (x_{1}, . . . ,x_{n})), it is highly useful to be able to compress and decompress the data in such a way that terrain—or, more generally, graph or image features—are accurately reconstructed.
 Conventional systems in current use compress the data, store or transmit it as needed, and at a later point reconstruct the data from the compresseddata files. This can lead to large errors in derived quantities obtained from the reconstructed data, in particular when the gradient of the reconstructed data is taken.
 The gradient of the original data is often of considerable interest. In the case of DTED, it may be important for aircraft to be aware of the precise terrain slopes, and the errors introduced by determining gradients from reconstructed data may be too great to be of practical use for many applications.
 Especially for lossy compression techniques, a reconstructed image generally does not have the same values for the norm of the gradient that the original image had. In fact, errors in the gradient are often quite large for higher compression ratios. These errors are quite significant since the accuracy of the terrain slope is crucial in many areas, e.g. landing of aircraft in navigation exercises.
 Accordingly, a system is needed that can compress and reconstruct multidimensional data, such as terrain data or other signals, with an increased accuracy in the reconstructed information, and in particular in the gradients that are determined from the reconstructed data, and the norms of those gradients.
 An apparatus and method according to one embodiment of the present invention are implemented in a processorbased system. A method according to the invention provides an accurately compressed and reconstructed signal, and in particular accurately reconstructed gradients of the original signal, by applying compression procedures to the gradient of the original signal. An alternative embodiment further involves the process of generating a second gradient of the original signal, and compressing that second gradient, which upon decompression provides an accurate reconstruction of the second gradient of the original signal. The methods of the invention are suitable for compressing, storing, transmitting and reconstructing both simulated and empirical data representing terrain and other physical or hypothetical signals or surfaces, in one or multiple dimensions.

FIG. 1 is a block showing a processorbased system suitable for an implementation of the present invention. 
FIG. 2 is a representation of a signal that can be compressed and reconstructed according to the present invention. 
FIG. 3 is a representation of a gradient of the signal ofFIG. 2 . 
FIG. 4 is a representation of another signal that can be compressed and reconstructed according to the present invention. 
FIG. 5 is a representation of a gradient of the signal ofFIG. 4 . 
FIG. 6 is a representation of a gradient of the signal ofFIG. 5 . 
FIGS. 78 are flow charts representing methods implementing aspects of the present invention. 
FIG. 1 illustrates a processorbased system 100, such as a workstation or a server, in connection with the present invention may be implemented. The system 100 is coupled to a display 110 and one or more user interface devices 120 (such as a mouse, keyboard, track ball, etc.), and operates under control of at least one microprocessor 130 (though it may be a multiprocessor system).  The processor 130 is connected to a local device control circuitry 140, which includes circuitry that controls data and command exchanges with local devices such as the display 110 via an accelerated graphics processor (AGP) 150 and memory 160, which may in a typical system will include multiple DIMMs (dual inline memory modules) or other suitable memory modules or media.
 The local device control circuitry 140 is connected to a peripheral device control circuit 170 via a bus such as PCI bus 180. The system 100 additionally is connected to local internal and/or external storage 190.
 Input/output (I/O) channels 200 are connected to or in communication with the system 100, and may include conventional network connections, wireless communications devices, and/or other conventional apparatus for exchanging data with the system 100. In addition, transmitters, receivers or in general transceivers 210 may be connected to or in communication with the system 100, which are suitable for remote or isolated operations include weather stations or other telemetry stations, on aircraft, etc.
 The compression and decompression operations of the present invention are in one embodiment carried out under the control of program modules stored in the memory 160 and executing on the processor 130. These operations may be implemented in and/or executed by software, hardware (e.g. in configured field gate arrays, custom logic, etc.), firmware or some combination thereof. In this application, the term “logic” will be used to refer to any such appropriate combination of software, hardware, firmware or other manner of implementing the invention.
 The image, terrain, or other data relating to the invention will typically take the form of data files stored in memory or in some storage medium, which can be read, modified, stored, output, displayed and printed by the computer system, either under automatic (or program) control or under the direction of a user.
 Compression and Reconstruction of Gradient Data
 The system of the invention is applicable to many types of compression procedures presently in use, with improved accuracy of the reconstructed signals, and in particular of their gradients (or slopes) and corresponding norms of those gradients. An example of one appropriate compression procedure is a histogram equalization procedure, as described, for instance, in Sapiro, G. and Caselles, V., “Histogram Modification via Differential Equations”, Journal of Differential Equations, Vol. 135, No. 2, pp. 238268 (1997), which is incorporated herein by reference. Generally, appropriate compression procedures include those that are exact for constant signals, but are lossy in the general case (such as JPEG or histogram equalization).
 Thus, the inventive methods may be applied to signals processed according to any compression procedures. In addition, the inventive methods may be applied to signals representing data of many dimensions. However, for the sake of the following discussion a twodimensional signal will be taken as an example.
 The normal vector to the signal or graph representing a surface or terrain is given by:
$\frac{\left({u}_{x},{u}_{y},1\right)}{\sqrt{(1+{u}_{x}^{2}+{u}_{y}^{2}}}.$
It follows that the steepness (or slope) of the terrain surface is determined by the gradient of that signal, namely:
∇u=√{square root over (u _{ x } ^{ 2 } +u _{ y } ^{ 2 } )}.  A method according to the present invention compresses the gradient ∇u, rather than the signal u itself. The basic framework of such a method is carry out the following operations:
 Operation #1: Compute ∇u either analytically or numerically. (It may be done analytically for simulated data, and numerically for empirical data, or even analytically for empirical data that has been approximated by mathematical representations.)
 Operation #2: Use any suitable compression technique to compress and store (or transmit) ∇u as {double overscore (∇u)}.
 Operation #3: Recover a reconstructed signal v by solving the equation:
∇v={double overscore (∇u)}. EquationA:
In particular, this can be solved using fast numerical level set based procedures for solving the Eikonal equation ∇v={double overscore (∇u)}. 
FIG. 7 is a flow chart according to this series of operations.  An Eikonal equation is one of the form
√{square root over (v _{x} ^{2} =v _{y} ^{2})}=C(x,y) for C(x,y)>0.
This gives a generalized distance to a set. If C=1, then the distance is a real distance. Examples of this may include: (a) distance to the origin of a coordinate system, and (b) distance to a set defined by the equation x=0.  (a) Distance to the Origin.
 If v=√{square root over (x^{2}+y^{2})}, the distance is to the origin x=y=0, with:
${v}_{x}=\frac{x}{\sqrt{{x}^{2}+{y}^{2}}};{v}_{y}=\frac{y}{\sqrt{{x}^{2}+{y}^{2}}};\mathrm{and}\text{\hspace{1em}}{v}_{x}^{2}+{v}_{y}^{2}=\frac{{x}^{2}+{y}^{2}}{{x}^{2}+{y}^{2}}=1$  b) Distance to a Set x=0.
 If v=x, the distance represents a distance to the set x=0, with:

 v_{x}=1 if x>0;
 v_{x}=−1 if x<0; and
 v_{y}=0;
and thus v_{x} ^{2}+v_{y} ^{2}=1. At least a few values of v=u at a few data points are input, including certain boundary points and points of extrema of u.
 A system according to the present invention can take advantage of fast methods to compute the unique viscosity solution to this HamiltonJacobi nonlinear partial differential equation, i.e. the Eikonal Equation A above. The viscosity solution is used because {double overscore (∇u)} represents
$\frac{1}{\mathrm{velocity}}$
in the Eikonal Equation. Thus, we can view Equation A above as finding the distance v in that variable metric.  Operation #3 above involves the solution of
∇v=f(x,y),
where f(x,y)={double overscore (∇u)} is the compressed quantity. As mentioned above, this may be a numerical or an analytical solution.  It has been proven that there exists a unique viscosity solution to this equation, given the values of u at appropriate data points. See Rouy, E. and Tourin, A., A viscosity solutions approach to shape from shading, SIAM Journal of Numerical Analysis, Vol. 29, No. 3, pp. 867884 (1992). There are fast Dijkstralike algorithms and/or sweeping algorithms that are designed for this purpose. On Dijkstralike algorithms, see: J. N. Tsitsiklis, “Efficient Algorithms for Globally Optimal Trajectories”, IEEE Transactions on Automatic Control, Vol. 40, No. 9, September 1995, pp. 15281538, which is incorporated herein by reference.
 To solve the Eikonal equation in any number of independent variables (x, y, z, . . . ) on a distance grid with n points and values of u assigned at isolated points, there is a shortestpath type of algorithm given by Tsitsiklis, which runs in optimal time O(n log n), with n being the number of pixels. Dijkstra approach is a classical algorithm which computes the “taxicab” distance metric, i.e. which solves:
max(u _{x} ,u _{y})=C(x,y)
in this optimal time. Tsitsiklis generalized it to the true geodesic distance (as the crow flies). The classical algorithm and its generalization update each grid point once in increasing order of distance, and may use an O(log n) heapsort search.  Fast sweeping algorithms solve the same algebraic expression as the Dijkstralike algorithms on the grid at each point—however, not in increasing order of distance, but rather in an iterative fashion, updating points as often as needed until convergence within a predetermined tolerance. Fast sweeping methods can involve simplified programming and can be faster, e.g. if C(x,y)=1 and a leftright, updown procedure is used. See, e.g., M. Boue and P. Dupuis, Markov chain approximations for deterministic control problems with affine dynamics and quadratic cost in the control, SLAM J. Numer. Analysis, Vol. 36, No. 3, pp. 667695 (1999).
 Input used for these fast solution techniques (which can be referred to as “fast solvers”) are the numerical values of f(x,y) and the values of u at grid points where ∇u is less than some very small tolerance (i.e. where u might be an extremum).
 This present invention is thus useful in combination with any compression routine.
 One might consider the approach of compressing the vector ∇u=(u_{x},u_{y}) to get {double overscore (∇u)}=({double overscore (u_{x})},{double overscore (u_{y})}), and then recover u. There are two conditions that must be considered to avoid inaccuracies in the reconstruction of the gradient:
 (i) There is a need for compatibility, i.e.
({double overscore (u_{x})})_{y}=({double overscore (u_{y})})_{x},
at least approximately, and this is generally false for the recovered u, using this simplified procedure.  (ii) Reconstructing u from one compressed derivative, e.g. solving numerically v_{x}={double overscore (u_{x})} can lead to large errors in the resulting v_{y}.
 Reconstruction of the signal from the decompressed gradient is effectively an integration process, which can be carried out numerically or can be carried out analytically for a function derived from or representing the decompressed signal (within some predetermined level of accuracy). Such integration can be carried out for each level of gradient operation (e.g. for second gradients—see Alternative Method I, below).
 Other implementations of the basic method for solving ∇u={double overscore (∇u)} can be enhanced in several ways.
FIG. 8 is a flow chart illustrating an Alternative Method I, as follows.  Alternative Method I
 (1) Compute numerically ∇u.
 (2) Compute numerically ∇∇u.
 (3) Compress and store ∇∇u, obtaining {double overscore (∇∇u)}.
 (4) Recover v using fast a Eikonal solver twice. First solve for w in
∇w={double overscore (∇∇u)}.  Then solve for v in
∇v=w.  Wherever numerical computation or data generation is called for herein, it should be understood that under appropriate circumstances an analytical solution may be generated, and viceversa. In either case, a predetermined level of accuracy may be used a controlling factor, e.g. for the compression, gradient, integration and/or reconstruction operations.
 The extra data storage that would be used for this algorithm is the storage of v=u and ∇v=∇u at extrema, i.e. those points for which ∇u and ∇∇u, respectively, have values below a small predefined tolerance.
 This method can be generated recursively to N Eikonal solvers. The extra storage is minimal, but the decompression step would be approximately N times slower.
 Alternative Method II
 (1) Solve ∇w={double overscore (∇u)}.
 (2) Compress ∇(u−w), and obtain ∇{double overscore ((u−w))}.
 (3) Solve ∇z=∇{double overscore ((u−w)}).
 In steps (1) and (3), use the values of u and u−w, respectively, at their approximate extrema, as usual.
 (4) Then obtain v, the reconstruction of u, via v=w+z.
 This method adds a correction to the basic method by compressing and reconstructing errors in ∇u.
 Recovering Curvature
 Additionally, other geometric features of the terrain, for example mean curvature of the surface, can be recovered from compressed data in a similar manner. Following is a procedure for recovering curvature.
 For a surface defined by
z=u(x,y),
its mean curvature is:$k=\frac{{u}_{\mathrm{xx}}\left({u}_{y}^{2}+1\right)2{u}_{\mathrm{xy}}{u}_{x}{u}_{y}+{u}_{\mathrm{yy}}\left({u}_{x}^{2}+1\right)}{{\left(1+{u}_{x}^{2}+{u}_{y}^{2}\right)}^{3/2}}.$
See S. Osher and J. A. Sethian, “Fronts Propagating with CurvatureDependent Speed: Algorithms Based on Hamilton—Jacobi Formulations”, Osher, S., and Sethian, J. A., Journal of Computational Physics, Vol. 79, pp. 1249 (1988), which is incorporated herein by reference.  This involves first and second partial derivatives of u. Thus, in order to recover curvature from compressed data, Alternative Method I above can be used, with N≧2. This allows the recovery of a signal v whose second and first derivatives are accurate approximations to those of u. Then a numerical implementation for the expression defining k above may be used, where v replaces u.
 Higher derivatives of curvature—in fact all geometric features—can be recovered in an analogous fashion, which will be clear from the foregoing to those skilled in the art. For instance, instead of using the Eikonal equation, one can take any elliptic differential operator of second or higher order, for example the Laplacian
(v)=u _{xx} +u _{yy},
and solve numerically
(v)={double overscore ((v))}
for v, where appropriate boundary conditions are imposed. Then geometric features can be recovered as above.  The inventive methods provide improved compression ratios for DTED, images or graphs which have large flat regions where ∇u or any desired feature will be zero, hence easy to compress. Thus the inventive methods are highly accurate in these situations in retrieving the data, as well as the desired feature or features.
 Pseudocode Appropriate for Method Involving Compressing Normals to Gradients
 The following pseudocode relates to compressing a quantity, e.g. the norm of the gradient, from an original set of data, and recovering the original data from the compressed quantity.

 // Read in the original file and store it as quantity u[i][j]
 // Compute the derived quantity, e.g. norm of grad u[i][j]
 // Store the norm as a separate quantity v[i][j]
 %% Compression routines are completely up to the users' preference.
 %% Possible compression techniques include JPEGLS, JPEG, LSS (Level Set
 % % Systems of Los Angeles, Calif.).
 %% LSS' technique can used with lossy compression techniques, wherein
 %% there are errors between the original and restored image.
 // Compress the original file
 // Compress the normal vectors file
 // Decompress the compressed original file
 // Decompress the compressed normal vectors file
 // Read in the compressed/decompressed original file—store it as quantity uc[i][j]
 // Read in the compressed/decompressed normal vectors file—store it as quantity vc[i][j]
 // Reconstruct an approximation to the original image u[i][j], from the compressed/decompressed quantity vc[i][j]. This reconstruction is based upon numerically solving the partial differential equation:
 grad w=vc[i][j] for w[i][j]
 // As an initial guess, you may used w=uc[i][j], or set w=stored values of u[i][j] at isolated extrema.
 From this procedure, it can result that w[i][j] will be a better approximation to u[i][j] than uc[i][j], because the relevant quantity v[i][j] will be better approximated by w[i][j] than it will be by uc[i][j].
 The Level Set Systems approach mentioned above can be found in applicant's copending patent application, “Method and Apparatus for FeatureBased Quantization and Compression of Data”, Ser. No. 09/737,834 filed Dec. 14, 2000, which is incorporated herein by reference.
 Examples of Application of Methods According to the Invention
 Examples 1 and 2 below will be discussed in connection with
FIGS. 26 . 
FIG. 2 illustrates a onedimensional signal that may be divided into N pixels in this manner, where N=10 for the sake of the example. Thus, inFIGS. 26 , the xcoordinates indicating the N pixels are labeled j=1, 2, . . . , 10, and the signal may be expressed as:
u={u _{j}}_{j1} ^{N}.  In general in the present description, an original signal will be denoted as u and its components as u_{j}. A reconstructed signal (i.e. data that has been regenerated from compressed data) will be denoted as v (and its components as v_{j}) or w (and its components as w_{j}), as will be seen below. In addition, a compressed signal or data will be denoted by a double bar over the compressed quantity; so {double overscore (u)} would indicate the compressed form of the data or signal u, and similarly with any other quantities or expressions.
 This simple signal is sufficient to illustrate the operation of the present invention, and it is straightforward to generalize the procedures of the invention to signals of two or more dimensions, and to realworld settings of threedimensional phenomena.
 The quantity ∇u (rather than u) is compressed according to the present invention, and can be computed by standard finite difference methods. Thus,
${\uf603\nabla u\uf604}_{j}=\frac{\uf603{u}_{j}{u}_{j1}\uf604}{\left(1/N\right)}=\uf603{u}_{j}{u}_{j1}\uf604\times N\text{\hspace{1em}}\mathrm{for}\text{\hspace{1em}}j\ge 2;\mathrm{and}$ ${\uf603\nabla u\uf604}_{1}=\frac{\uf603{u}_{2}{u}_{1}\uf604}{\left(1/N\right)}=\uf603{u}_{2}{u}_{1}\uf604\times N.$  For simplicity, in these examples, we may take u_{j}≧u_{j1 }for all j, so we can remove the absolute value notation shown above.

FIG. 2 shows an example of a onedimensional linear signal u, expressible as vector of data u={U_{j}}, where:
u _{j} =j/N (j=1, 2, . . . , N).
Then ∇u_{j}=1 for all j, as shown inFIG. 3 . Note that ∇u is a constant, independent of j. Thus, the compressed value of ∇u is the same as the uncompressed value, as inFIG. 3 . In this example, then, there is no error in the compressed and uncompressed values of ∇u, nor is there any error in u or the reconstructed v.  In general, in this description the variable u will be used to refer to the original signal or data, and the variables v and w will be used to indicate the data after reconstruction (after of the first or second gradient or derivative, as will be discussed below).
 Generally, lossy compression procedures will result in errors in signals u that do not comprise constant values, so earlier methods (which compress the signals u, and not the gradient of u as in the present invention) will lead to larger errors in the gradient of the reconstructed signal, i.e. ∇u, than in the present system. As mentioned above, the methods of the invention involving compression of gradient values instead of the original signal data are applicable in one dimension or in multiple dimensions.

FIG. 4 shows an example onedimensional signal, expressible as:${u}_{j}=\frac{j\text{\hspace{1em}}\left(j+1\right)}{2{N}^{2}}\text{\hspace{1em}}\left(j=1,2,\dots \text{\hspace{1em}},N\right)$
Thus, for this signal ∇u_{j}=j/N as shown inFIG. 5 . (Note that the values of ∇u_{j }in Example 2 are the same as the values of u_{j }in Example 1, which follows since the above function for u_{j }in Example 2 was obtained by integrating the value u_{j}=j/N from Example 1.)  If the approach of compressing the derivative (or gradient) of the function is used, rather than compressing the function itself, then we compute ∇∇u, and obtain:

 ∇∇u_{j}=1 for all j (as shown in
FIG. 6 ).
 ∇∇u_{j}=1 for all j (as shown in
 The compression of this is errorfree (for this example), and hence the errors in the reconstructed w (which approximates ∇u) and v (which approximates u) are also zero, as is the error in the curvature approximating the curvature of z=u(x). Here,
$k=\frac{{u}_{\mathrm{xx}}}{{\left(1+{u}_{x}^{2}\right)}^{3/2}},$
since there is no dependence on y. Thus, the method ofFIG. 7 reduces the resulting error in this example. 
 In apparatus implementations of the present invention, each of the steps or operations involved can be carried out by executing one or more program or logic modules. The terrain, signal or surface data can, as discussed above, be simulated or realworld (e.g. empirically gathered) data.
 A processorbased system according to the invention can thus be connected to input or receiving devices (including sensors, satellite receivers, etc.) 210 and I/O channels 200 as shown in
FIG. 1 , and the I/O channels may communicate with other apparatus that use the processed surface and gradient signals, such as avionics (not separately shown) or other user interface equipment.
Claims (28)
1. A method for compressing and decompressing digital terrain elevation data, images, or graphs in at least two dimensions, including the steps of:
computing a numerical approximation to at least one of the slope, curvature, and/or another predetermined geometric feature, and storing the numerical approximation together with data values prescribed at certain predetermined locations;
applying a suitable compression technique to the geometric feature; and
retrieving the image.
24. (canceled)
5. The method of claim 1 , wherein the retrieving step is carried out by numerically solving an elliptic differential equation using a source term derived from a compressed version of the elliptic operator applied to the image, where appropriate boundary conditions are stored and used.
6. A system for compressing and decompressing surface data, including:
a gradient module configured to receive the surface data and generate a gradient signal;
a compression module configured to receive the gradient signal and generate a compressed signal; and
a reconstruction module configured to decompress the compressed signal to recover the gradient signal as a reconstructed signal.
7. The system of claim 6 , further including a module configured to store the compressed signal.
8. The system of claim 6 , further including a module configured to transmit the compressed signal.
9. The system of claim 6 , configured to operate in cooperation with a processorbased computer system.
10. The system of claim 6 , wherein the surface data comprises digital terrain elevation data.
11. The system of claim 6 , further including an input/output channel in communication with avionics equipment, and configured to provide elevation data to the avionics equipment generated from the reconstructed signal.
12. The system of claim 6 , further including an integration module configured to generate reconstructed surface data from the reconstructed signal.
13. A system for compressing and. decompressing surface data, including:
a first gradient module configured to receive the surface data and generate a first gradient signal;
a second gradient module configured to receive the surface data and generate a second gradient signal;
a compression module configured to receive the second gradient signal and generate a compressed signal; and
a reconstruction module configured to decompress the compressed signal to recover the second gradient signal as a reconstructed signal.
14. The system of claim 13 , further including an integration module to generate reconstructed surface data from the reconstructed signal.
15. The system of claim 13 , further including a module configured to store the compressed signal.
16. The system of claim 13 , further including a module configured to transmit the compressed signal.
17. The system of claim 13 , configured to operate in cooperation with a processorbased computer system.
18. The system of claim 13 , Wherein the surface data comprises digital terrain elevation data.
19. The system of claim 13 , further including an input/output channel in communication with, avionics equipment, and configured to provide elevation data to the avionics equipment generated from the reconstructed signal.
20. A program storage device readable by a computer the device containing instructions executable by the computer to perform method steps for compressing and reconstructing a signal of at least one dimension, the method including the steps of:
generating a gradient of the signal;
compressing the gradient of the signal to generate a compressed signal; and
decompressing the compressed signal to generate a reconstructed signal.
21. The program storage device of claim 20 , wherein said method further includes the step of generating an integrated signal from the reconstructed signal.
22. The program storage device of claim 21 , wherein at least one of the steps of generating the gradient of the signal and generating the integrated signal is carried out by a numerical process.
23. The program storage device of claim 22 , wherein at least one of the gradient and the integrated signal is generated to within a predetermined level of accuracy.
24. The program storage device of claim 21 , wherein at least one of the steps of generating the gradient of the signal and generating the integrated signal is carried out by analytically.
25. The program storage device of claim 24 , wherein at least one of the gradient and the integrated signal is generated to within a predetermined level of accuracy.
26. The program storage device of claim 20 , wherein the signal relates to terrain data.
27. The program storage device of claim 26 , wherein said method further includes the step of transmitting the reconstructed signal as input to avionics equipment for providing relative elevation data.
28. A program storage device readable by a computer, the device containing instructions executable by the computer to perform method steps for compressing and reconstructing a signal of at least one dimension, the method including the steps of:
generating a first gradient of the signal;
generating a second gradient from the first gradient;
compressing the second gradient to generate a compressed signal; and
decompressing the compressed signal to generate a reconstructed second gradient signal.
29. The program storage device of claim 28 , wherein said method further includes the step of generating an integrated signal from the reconstructed second gradient signal.
30. The program storage device of claim 29 , wherein said method further includes the step of transmitting the integrated signal as input to avionics equipment for providing relative elevation data.
Priority Applications (3)
Application Number  Priority Date  Filing Date  Title 

US25721000P true  20001220  20001220  
US10/039,748 US7027658B2 (en)  20001220  20011218  System for geometrically accurate compression and decompression 
US11/327,645 US20060171567A1 (en)  20001220  20060109  System for geometrically accurate compression and decompression 
Applications Claiming Priority (1)
Application Number  Priority Date  Filing Date  Title 

US11/327,645 US20060171567A1 (en)  20001220  20060109  System for geometrically accurate compression and decompression 
Related Parent Applications (1)
Application Number  Title  Priority Date  Filing Date  

US10/039,748 Continuation US7027658B2 (en)  20001220  20011218  System for geometrically accurate compression and decompression 
Publications (1)
Publication Number  Publication Date 

US20060171567A1 true US20060171567A1 (en)  20060803 
Family
ID=26716415
Family Applications (2)
Application Number  Title  Priority Date  Filing Date 

US10/039,748 Expired  Fee Related US7027658B2 (en)  20001220  20011218  System for geometrically accurate compression and decompression 
US11/327,645 Abandoned US20060171567A1 (en)  20001220  20060109  System for geometrically accurate compression and decompression 
Family Applications Before (1)
Application Number  Title  Priority Date  Filing Date 

US10/039,748 Expired  Fee Related US7027658B2 (en)  20001220  20011218  System for geometrically accurate compression and decompression 
Country Status (1)
Country  Link 

US (2)  US7027658B2 (en) 
Cited By (3)
Publication number  Priority date  Publication date  Assignee  Title 

US20080273753A1 (en) *  20070501  20081106  Frank Giuffrida  System for Detecting Image Abnormalities 
US20100240060A1 (en) *  20000804  20100923  Board Of Regents, The University Of Texas System  Detection and Diagnosis of Smoking Related Cancers 
US9262818B2 (en)  20070501  20160216  Pictometry International Corp.  System for detecting image abnormalities 
Families Citing this family (13)
Publication number  Priority date  Publication date  Assignee  Title 

US7480889B2 (en) *  20030406  20090120  Luminescent Technologies, Inc.  Optimized photomasks for photolithography 
US7698665B2 (en) *  20030406  20100413  Luminescent Technologies, Inc.  Systems, masks, and methods for manufacturable masks using a functional representation of polygon pattern 
US7124394B1 (en) *  20030406  20061017  Luminescent Technologies, Inc.  Method for timeevolving rectilinear contours representing photo masks 
KR101330344B1 (en) *  20050913  20131115  루미네슨트 테크놀로지, 인크.  Systems, masks, and methods for photolithography 
WO2007041602A2 (en) *  20051003  20070412  Luminescent Technologies, Inc.  Lithography verification using guard bands 
WO2007041600A2 (en) *  20051003  20070412  Luminescent Technologies, Inc.  Maskpattern determination using topology types 
US7793253B2 (en) *  20051004  20100907  Luminescent Technologies, Inc.  Maskpatterns including intentional breaks 
WO2007044557A2 (en)  20051006  20070419  Luminescent Technologies, Inc.  System, masks, and methods for photomasks optimized with approximate and accurate merit functions 
US7769730B2 (en) *  20051024  20100803  Softjin Technologies Private Limited  Method and system for data compression and decompression 
IL182367A (en) *  20070401  20130324  Boaz Ben Moshe  Method for compressing elevation maps 
KR101379255B1 (en) *  20070406  20140328  삼성전자주식회사  Method and apparatus for encoding and decoding based on intra prediction using differential equation 
US7653258B2 (en) *  20070417  20100126  Saudi Arabian Oil Company  Enhanced isotropic 2D and 3D gradient method 
US8731313B2 (en) *  20090323  20140520  Level Set Systems, Inc.  Method and apparatus for accurate compression and decompression of threedimensional point cloud data 
Family Cites Families (9)
Publication number  Priority date  Publication date  Assignee  Title 

US4729127A (en) *  19811020  19880301  The United States Of America As Represented By The Secretary Of The Army  Method and system for compression and reconstruction of cultural data for use in a digital moving map display 
US4906940A (en) *  19870824  19900306  Science Applications International Corporation  Process and apparatus for the automatic detection and extraction of features in images and displays 
US4890249A (en) *  19880316  19891226  Hughes Simulation Systems, Inc.  Data compression and decompression for digital radar landmass simulation 
US5546084A (en) *  19920717  19960813  Trw Inc.  Synthetic aperture radar clutter reduction system 
US5649032A (en) *  19941114  19970715  David Sarnoff Research Center, Inc.  System for automatically aligning images to form a mosaic image 
US6092009A (en) *  19950731  20000718  Alliedsignal  Aircraft terrain information system 
US5552787A (en) *  19951010  19960903  The United States Of America As Represented By The Secretary Of The Navy  Measurement of topography using polarimetric synthetic aperture radar (SAR) 
US6404431B1 (en) *  19980413  20020611  Northrop Grumman Corporation  Virtual map store/cartographic processor 
US6507660B1 (en) *  19990527  20030114  The United States Of America As Represented By The Secretary Of The Navy  Method for enhancing airtoground target detection, acquisition and terminal guidance and an image correlation system 

2001
 20011218 US US10/039,748 patent/US7027658B2/en not_active Expired  Fee Related

2006
 20060109 US US11/327,645 patent/US20060171567A1/en not_active Abandoned
Cited By (8)
Publication number  Priority date  Publication date  Assignee  Title 

US20100240060A1 (en) *  20000804  20100923  Board Of Regents, The University Of Texas System  Detection and Diagnosis of Smoking Related Cancers 
US8093001B2 (en)  20000804  20120110  Board Of Regents, The University Of Texas System  Detection and diagnosis of smoking related cancers 
US20080273753A1 (en) *  20070501  20081106  Frank Giuffrida  System for Detecting Image Abnormalities 
US8385672B2 (en) *  20070501  20130226  Pictometry International Corp.  System for detecting image abnormalities 
US9262818B2 (en)  20070501  20160216  Pictometry International Corp.  System for detecting image abnormalities 
US9633425B2 (en)  20070501  20170425  Pictometry International Corp.  System for detecting image abnormalities 
US9959609B2 (en)  20070501  20180501  Pictometry International Corporation  System for detecting image abnormalities 
US10198803B2 (en)  20070501  20190205  Pictometry International Corp.  System for detecting image abnormalities 
Also Published As
Publication number  Publication date 

US7027658B2 (en)  20060411 
US20030025703A1 (en)  20030206 
Similar Documents
Publication  Publication Date  Title 

Weickert  Applications of nonlinear diffusion in image processing and computer vision  
Min et al.  Fast global image smoothing based on weighted least squares  
Brand  Incremental singular value decomposition of uncertain data with missing values  
Yarlagadda et al.  Fast algorithms for l p deconvolution  
JP4384813B2 (en)  Timedependent geometry compression  
Simoncelli et al.  Probability distributions of optical flow  
CA2375412C (en)  An improved simulation method and apparatus  
Farnebäck  Twoframe motion estimation based on polynomial expansion  
Chan et al.  The digital TV filter and nonlinear denoising  
Teboul et al.  Variational approach for edgepreserving regularization using coupled PDEs  
EP0750203B1 (en)  Subsurface modeling from seismic data and secondary measurements  
US7542036B2 (en)  Level set surface editing operators  
US4941193A (en)  Methods and apparatus for image compression by iterated function system  
Terzopoulos et al.  Sampling and reconstruction with adaptive meshes  
US6009435A (en)  Progressive compression of clustered multiresolution polygonal models  
EP0506327A2 (en)  A system and method for ranking and extracting salient contours for target recognition  
US5727080A (en)  Dynamic histogram warping of image histograms for constant image brightness, histogram matching and histogram specification  
EP1081649B1 (en)  Apparatus and method for image compression  
US5577130A (en)  Method and apparatus for determining the distance between an image and an object  
US5563960A (en)  Apparatus and method for emphasizing a selected region in the compressed representation of an image  
US6052124A (en)  System and method for directly estimating threedimensional structure of objects in a scene and camera motion from three twodimensional views of the scene  
US20020082813A1 (en)  Method and system for coordinate transformation to model radial flow near a singularity  
Mullen et al.  Signing the unsigned: Robust surface reconstruction from raw pointsets  
Gilboa et al.  Estimation of optimal PDEbased denoising in the SNR sense  
Nevatia et al.  Linear feature extraction and description 
Legal Events
Date  Code  Title  Description 

AS  Assignment 
Owner name: LEVEL SET SYSTEMS, INC., CALIFORNIA Free format text: ASSIGNMENT OF ASSIGNORS INTEREST;ASSIGNORS:OSHER, STANLEY J.;ZHAO, HONGKAI;REEL/FRAME:017463/0283;SIGNING DATES FROM 20060401 TO 20060404 

STCB  Information on status: application discontinuation 
Free format text: ABANDONED  FAILURE TO RESPOND TO AN OFFICE ACTION 