Noise characteristics for the Microsoft Kinect sensor are presented. Horizontal (x) and vertical (y) stochastic noise are measured using a novel 3D checker board. Results show that the noise is affected mostly by the depth at which the object is sensed and by the radial distance from the center of the field of view. Measurement-based models for the noise in horizontal and vertical axes are presented. The proposed model is compared against existing models in literature and shows better results by considering the horizontal and vertical location of the depth measurement.

Since the emergence of the commodity-priced, small-sized Microsoft Kinect™ sensor, 3D object pose estimation has become prevalent in many applications across a wide variety of disciplines. However, because most current methods require a hard assignment between a measurement point cloud and a given CAD model point cloud for alignment, accurate pose estimation is limited to a small range of sensor noise and resolution, and CAD model precision. This paper therefore presents a MLE algorithm that achieves a statistically optimal global maximum likelihood on the surface of the continuous 6D pose domain by soft assigning all measurement points to all model points. The accuracy in estimation of orientation and position of the MLE algorithm is then compared to a variant of the ICP method that accounts for an anisotropie Gaussian measurement noise distribution. It is finally shown through a series of simulated measurement point clouds and depth images that MLE outperforms the ICP variant, and achieves a monotonie increase in performance with an increase in either points on target or CAD model precision.

We derive approximate expressions for the probability of error in a two-class hypothesis testing problem in which the two hypotheses are characterized by zero-mean complex Gaussian distributions. These error expressions are given in terms of the moments of the test statistic employed and we derive these moments for both the likelihood ratio test, appropriate when class densities are known, and the generalized likelihood ratio test, appropriate when class densities must be estimated from training data. These moments are functions of class distribution parameters which are generally unknown so we develop unbiased moment estimators in terms of the training data. With these, accurate estimates of probability of error can be calculated quickly for both the optimal and plug-in rules from available training data. We present a detailed example of the behavior of these estimators and demonstrate their application to common pattern recognition problems, which include quantifying the incremental value of larger training data collections, evaluating relative geometry in data fusion from multiple sensors, and selecting a good subset of available features.

Many applications of object recognition in the presence of pose uncertainty rely on statistical models-conditioned on pose-for observations. The image statistics of three-dimensional (3-D) objects are often assumed to belong to a family of distributions with unknown model parameters that vary with one or more continuous-valued pose parameters. Many methods for statistical model assessment, for example the tests of Kolmogorov-Smirnov and K. Pearson, require that all model parameters be fully specified or that sample sizes be large. Assessing pose-dependent models from a finite number of observations over a variety of poses can violate these requirements. However, a large number of small samples, corresponding to unique combinations of object, pose, and pixel location, are often available. We develop methods for model testing which assume a large number of small samples and apply them to the comparison of three models for synthetic aperture radar images of 3-D objects with varying pose. Each model is directly related to the Gaussian distribution and is assessed both in terms of goodness-of-fit and underlying model assumptions, such as independence, known mean, and homoscedasticity. Test results are presented in terms of the functional relationship between a given significance level and the percentage of samples that wold fail a test at that level.

The implementation of computational systems to perform challenging operations often involves balancing the performance specification, system throughput, and available system resources. For problems of automatic target recognition (ATR), these three quantities of interest are the probability of classification error, the rate at which regions of interest are processed, and the capabilities of the underlying hardware (which is a function of the available computational resources and available power). An understanding of the inter-relationships between these factors can be an aid in making informed choices while exploring competing design possibilities. Combining characterizations of ATR performance, which yield probability of classification error as a function of target model complexity, with analytical models of computational performance, which yield throughput as a function of target model complexity and available resources, we can form a set of parametric curves which relate the quality of the results to the resources consumed.