Sentence examples for manifold lifting problem from inspiring English sources

To inform the design of such an algorithm, we find it helpful to view the general task of reconstruction as what we term a manifold lifting problem: we would like to recover each image x j ∈ ℝ N from its measurements y j ∈ ℝ M j ("lifting" it from the low-dimensional measurement space back to the high-dimensional signal space), while ensuring that all recovered images live along a common IAM.

We combine the discussions provided in Sections 4-A and 4-C to design a manifold lifting algorithm that is specifically tailored to this problem.

We have presented a geometric framework in which many multi-view imaging problems may be cast and explained how this framework can inform the design of effective manifold lifting algorithms for joint reconstruction.

Figure 7 Reconstruction results in manifold lifting demonstration.

Figure 8 Comparative reconstructions for manifold lifting demonstration.

We conclude with a few remarks concerning practical and theoretical aspects of the manifold lifting framework.

c Joint reconstruction using our manifold lifting algorithm with unknown camera positions, PSNR 23.6 dB.

Figure 6c shows the final estimated camera positions after all iterations of our manifold lifting algorithm.

As a proof of concept, we now present a comprehensive multi-view reconstruction algorithm inspired by the manifold lifting viewpoint.

The goal of a manifold lifting algorithm is to recover an ensemble of images from their low-dimensional measurements.

We hope that such discussions will pave the way for the future development of broader classes of manifold lifting algorithms.