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Rapid construction of 3-D Satellite models from limited amounts of 2-D imagery


TECHNOLOGY AREA(S): Space Platforms 

OBJECTIVE: Conceive of and perform R&D on theoretical approaches and associated algorithms that could expedite the modeling of 3-D satellite geometries from limited amounts of 2-D imagery, thereby saving end-user resources for the verification & validation of the ensuing model. 

DESCRIPTION: The need for quickly extracting shape information from a limited number of observational images is growing fast. The observed 2-D images have limited spatial resolution, signal-to-noise ratio (SNR), and viewing aspects. The reality of satellites as complex 3-D shapes with details extending to tiny size scales translates to limited model fidelities as constrained by the observed imagery. This SBIR provides a means to investigate notions for rapidly obtaining satellite models, and associated confidence levels, on the basis of innovative research. For the most part, the point spread function for space-based imagery should be considered known, whereas for ground-based imagery residual effects of atmospheric seeing could be present. Historically, the prowess of the “eye-brain” combination has been unsurpassed up until recent times for determining patterns in imagery and assessing quality of fitted models, and this applies as well to 3-D volumes as they are rotated and aligned during visual fitting processes. Yet, subjectivism, and the lack of quantified uncertainties, limit the attractiveness of this approach. The efforts of the analyst might be more productively used for the quality control and oversight of a continuing flow of new observations and model builds. The challenge of this SBIR is accommodating a vast range of image data set quality and diversity (number of images and their aspects, and image SNR). Approaches that begin with a limited number of degrees of freedom to determine the simplest shapes that are mathematically compatible with the observed data might focus on optimizing chi-squared per parameter, or minimizing parameter uncertainties in the sense of Cramer-Rao bounds (CRB), and are expected to lead to fewer spurious artifacts and not over-represent the information content of the data. Alternatively, approaches that draw from a library of simple shapes with a Principal Component Analysis (PCA) decomposition that includes associated CRBs for the derived eigenvalues are expected to represent more complicated object geometries, possibly at the expense of superfluous or unphysical artifacts. The ultimate goal of the SBIR is for an end user to be able to compare the derived shape and its uncertainties with an independent object library that is not publically available, to facilitate identification or correct library associations. 

PHASE I: Analyze and determine the fundamental performance limits on the proposed approach, as constrained by information theory and in view of the image data set limitations mentioned above. These include Shannon Information Theory as it applies to the information content of images, Cramer-Rao bounds on optimal parameter estimates, Bayesian Estimation Theory, and even PCA approaches if the associated uncertainties in the eigenvalues can be quantified. Imagery examples for test may be either synthesized or requested of the government (AFRL/RD). 

PHASE II: Quantify approach viability through testing with actual image data sets. Quantify speed of processing in a controlled environment simulating an end-users production flow. Additional efforts, should the above basic requirements be realized, include the synthesis of a model with a known format (*.NSM as an example), possibly within a known time interval, and possibly embellished with electro-optical properties. Collaboration with Air Force scientists and engineers for access to object model libraries is possible in Phase II. 

PHASE III: Productize knowledge base and algorithmic approaches with the transitioning of verified and validated algorithms to the Air Force user community for insertion into a national space data center. 


1: Hope and Prasad, "AMA Statistical Information based analysis of a Compressive Imaging System", 2009 AMOS Conference Proceedings

2:  Matson, Charles L., et al. "Fast and optimal multiframe blind deconvolution algorithm for high-resolution ground-based imaging of space objects." Applied Optics 48.1 (2009): A75-A92.

3:  Robinson, Dirk, and Peyman, Milanfar. "Statistical performance analysis of super-resolution." IEEE Transactions on Image Processing 15.6 (2006): 1413-1428.

4:  Helen, Brian J., John R. Valenzuela, and Joel W. LeBlanc (2016). "Theoretical performance assessment and empirical analysis of super-resolution under unknown affine sensor motion. JOSA A 33.4 (2016): 519-526.

KEYWORDS: 3D Models, 2D Imagery, Optics Deconvolution, Tomography, Space Surveillance, Satellites, Space Object Identification 


Paul LeVan 

(505) 846-9959 

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