We consider stability and approximate reconstruction of Riemannian manifold when the finite number of eigenvalues of the LaplaceBeltrami operator and the boundary values of the corresponding eigenfunctions are given. The reconstruction can be done in stable way when manifold is a priori known to satisfy natural geometrical conditions related to curvature and other invariant quantities.

A class of photoacoustic acquisition geometries in n is considered such that the spherical mean transform admits an exact filtered back projection reconstruction formula. The reconstruction is interpreted as a time reversion mirror that reproduces exactly an arbitrary source distribution in the cavity. A series of examples of non-uniqueness of the inverse potential problem is constructed based ...

This paper concerns modification of the thermal tomography reconstruction algorithm to improve the speed of calculations for faster reconstruction of thermal and geometrical parameters inside a tested structure. We propose to solve the inverse problem in the two step procedure. First, initial rough reconstruction of a tested structure based on the one dimensional (1-D) thermal model. Second, ex...

The quality of attractor reconstruction using the method of delays is known to be sensitive to the delay parameter, τ . Here we develop a new, computationally efficient approach to choosing τ that quantifies reconstruction expansion from the identity line of the embedding space. We show that reconstruction expansion is related to the concept of reconstruction signal strength and that increased ...

The behavioral approach to robot navigation, characterized by a representation of the environment that is topological and robot-environmental interactions that are reactive, is preferable to the pure geometrical navigation because it is far more robust to unpredictable changes of the environment. Nevertheless, there is still a need to obtain geometrical maps. This paper considers a geometrical ...

A new 3D reconstruction method of scoliotic vertebrae of a spine, using two calibrated conventional radiographic images (postero-anterior and lateral), and a global prior knowledge on the geometrical structure of each vertebra is presented. This geometrical knowledge is efficiently captured by a statistical deformable template integrating a set of admissible deformations, expressed by the first...

Most SLAM (Simultaneous Localization and Mapping) algorithms are based on the assumption that scene is static. However, in practice, most real scenes usually contain moving objects. In this letter, we introduce DymSLAM, a dynamic stereo visual system being capable of reconstructing 4D (3D + time) with rigid Unlike previous attempts have considered objects as outliers ignored them, DymSLAM obtai...