Abstract-Intra-operative imaging techniques for obtaining the shape and morphology of soft-tissue surfaces in vivo are a key enabling technology for advanced surgical systems. Different optical techniques for 3D surface reconstruction in laparoscopy have been proposed, however, so far no quantitative and comparative validation has been performed. Furthermore, robustness of the methods to clinically important factors like smoke or bleeding has not yet been assessed. To address these issues, we have formed a joint international initiative with the aim of validating different state-of-the-art passive and active reconstruction methods in a comparative manner. In this comprehensive in vitro study, we investigated reconstruction accuracy using different organs with various shape and texture and also tested reconstruction robustness with respect to a number of factors like the pose of the endoscope as well as the amount of blood or smoke present in the scene. The study suggests complementary advantages of the different techniques with respect to accuracy, robustness, point density, hardware complexity and computation time. While reconstruction accuracy under ideal conditions was generally high, robustness is a remaining issue to be addressed. Future work should include sensor fusion and in vivo validation studies in a specific clinical context.

Supervised and unsupervised vector quantization methods for classification and clustering traditionally use dissimilarities, frequently taken as Euclidean distances. In this article, we investigate the applicability of divergences instead, focusing on online learning. We deduce the mathematical fundamentals for its utilization in gradient-based online vector quantization algorithms. It bears on the generalized derivatives of the divergences known as Fréchet derivatives in functional analysis, which reduces in finite-dimensional problems to partial derivatives in a natural way. We demonstrate the application of this methodology for widely applied supervised and unsupervised online vector quantization schemes, including self-organizing maps, neural gas, and learning vector quantization. Additionally, principles for hyperparameter optimization and relevance learning for parameterized divergences in the case of supervised vector quantization are given to achieve improved classification accuracy.

We present a systematic approach to the mathematical treatment of the t-distributed stochastic neighbor embedding (t-SNE) and the stochastic neighbor embedding (SNE) method. This allows an easy adaptation of the methods or exchange of their respective modules. In particular, the divergence which measures the difference between probability distributions in the original and the embedding space can be treated independently from other components like, e.g. the similarity of data points or the data distribution. We focus on the extension for different divergences and propose a general framework based on the consideration of Fré chet-derivatives. This way the general approach can be adapted to the user specific needs.

We discuss the use of divergences in dissimilarity based classification. Divergences can be employed whenever vectorial data consists of non-negative, potentially normalized features. This is, for instance, the case in spectral data or histograms. In particular, we introduce and study Divergence Based Learning Vector Quantization (DLVQ). We derive cost function based DLVQ schemes for the family of γ-divergences which includes the well-known Kullback-Leibler divergence and the so-called Cauchy-Schwarz divergence as special cases. The corresponding training schemes are applied to two different real world data sets. The first one, a benchmark data set (Wisconsin Breast Cancer) is available in the public domain. In the second problem, color histograms of leaf images are used to detect the presence of Cassava Mosaic Disease in cassava plants. We compare the use of standard Euclidean distances with DLVQ for different parameter settings. We show that DLVQ can yield superior classification accuracies and Receiver Operating Characteristics.

The system is mobile, markerless, intuitive and real-time capable with sufficient accuracy. It can support the forensic pathologist during autopsy with augmented reality and textured surfaces. Furthermore, the system enables multimodal documentation for presentation in court. Despite its preliminary prototype status, it has high potential due to its low price and simplicity.