Mixed Reality (MR) in Surgery

Point clouds as measurements of 3D sensors have many applications in various fields such as object modeling, environment mapping and surface representation. Storage and processing of raw point clouds is time consuming and computationally expensive. In addition, their high dimensionality shall be considered, which results in the well known curse of dimensionality. Conventional methods either apply reduction or approximation to the captured point clouds in order to make the data processing tractable. B-spline curves and surfaces can effectively represent 2D data points and 3D point clouds for most applications. Since processing all available data for B-spline curve or surface fitting is not efficient, based on the Group Testing theory an algorithm is developed that finds salient points sequentially. The B-spline curve or surface models are updated by adding a new salient point to the fitting process iteratively until the Akaike Information Criterion (AIC) is met. Also, it has been proved that the proposed method finds a unique solution so as what is defined in the group testing theory. From the experimental results the applicability and performance improvement of the proposed method in relation to some state-of-the-art B-spline curve and surface fitting methods, may be concluded.

Point clouds as measurements of 3D sensors have many applications in various fields such as object modeling, environment mapping and surface representation. Storage and processing of raw point clouds is time consuming and computationally expensive. In addition, their high dimensionality shall be considered, which results in the well known curse of dimensionality. Conventional methods either apply reduction or approximation to the captured point clouds in order to make the data processing tractable. B-spline curves and surfaces can effectively represent 2D data points and 3D point clouds for most applications. Since processing all available data for B-spline curve or surface fitting is not efficient, based on the Group Testing theory an algorithm is developed that finds salient points sequentially. The B-spline curve or surface models are updated by adding a new salient point to the fitting process iteratively until the Akaike Information Criterion (AIC) is met. Also, it has been proved that the proposed method finds a unique solution so as what is defined in the group testing theory. From the experimental results the applicability and performance improvement of the proposed method in relation to some state-of-the-art B-spline curve and surface fitting methods, may be concluded.

In this paper the problem of 3D scene and object classification from depth data is addressed. In contrast to high-dimensional feature-based representation, the depth data is described in a low dimensional space. In order to remedy the curse of dimensionality problem, the depth data is described by a sparse model over a learned dictionary. Exploiting the algorithmic information theory, a new definition for the Kolmogorov complexity is presented based on the Earth Mover’s Distance (EMD). Finally the classification of 3D scenes and objects is accomplished by means of a normalized complexity distance, where its applicability in practice is proved by some experiments on publicly available datasets. Also, the experimental results are compared to some state-of-the-art 3D object classification methods. Furthermore, it has been shown that the proposed method outperforms FAB-Map 2.0 in detecting loop closures, in the sense of the precision and recall.

In this paper the problem of loop closing from depth or camera image information in an unknown environment is investigated. A sparse model is constructed from a parametric dictionary for every range or camera image as mobile robot observations. In contrast to high-dimensional feature-based representations, in this model, the dimension of the sensor measurements' representations is reduced. Considering the loop closure detection as a clustering problem in high-dimensional space, little attention has been paid to the curse of dimensionality in the existing state-of-the-art algorithms. In this paper, a representation is developed from a sparse model of images, with a lower dimension than original sensor observations. Exploiting the algorithmic information theory, the representation is developed such that it has the geometrically transformation invariant property in the sense of Kolmogorov complexity. A universal normalized metric is used for comparison of complexity based representations of image models. Finally, a distinctive property of normalized compression distance is exploited for detecting similar places and rejecting incorrect loop closure candidates. Experimental results show efficiency and accuracy of the proposed method in comparison to the state-of-the-art algorithms and some recently proposed methods.