In this paper, we present a novel Bayesian classification framework of the matrix variate Bingham distributions with the inclusion of its normalizing constant and develop a consistent general parametric modeling framework based on the Grassmann manifolds. To calculate the normalizing constants of the Bingham model, this paper extends the method of saddle-point approximation (SPA) to a new setting. Furthermore, it employs the standard theory of maximum likelihood estimation (MLE) to evaluate the involved parameters in the used probability density functions. The validity and performance of the proposed approach are tested on 14 real-world visual classification databases. We have compared the classification performance of our proposed approach with the baselines from the previous related approaches. The comparison shows that on most of the databases, the performance of our approach is superior.

Restricted Boltzmann machine (RBM) is a famous model for feature extraction and can be used as an initializer for neural networks. When applying the classic RBM to multidimensional data such as 2D/3D tensors, one needs to vectorize such as high-order data. Vectorizing will result in dimensional disaster and valuable spatial information loss. As RBM is a model with fully connected layers, it requires a large amount of memory. Therefore, it is difficult to use RBM with high-order data on low-end devices. In this article, to utilize classic RBM on tensorial data directly, we propose a new tensorial RBM model parameterized by the tensor train format (TTRBM). In this model, both visible and hidden variables are in tensorial form, which are connected by a parameter matrix in tensor train format. The biggest advantage of the proposed model is that TTRBM can obtain comparable performance compared with the classic RBM with much fewer model parameters and faster training process. To demonstrate the advantages of TTRBM, we conduct three real-world applications, face reconstruction, handwritten digit recognition, and image super-resolution in the experiments.

Matrix manifolds such as Stiefel and Grassmann manifolds have been widely used in modern computer vision. This paper is concerned with the problem of classifying such manifold-valued data, based on the maximum likelihood estimation for the parametric probability density functions defined on the manifolds. By using a new way of computing normalisation constants for the matrix Langevin distribution function, defined for the data on Stiefel manifold, and the Fisher-Bingham density function on Grassmann manifold, we proposed a simple way to estimate the parameters in the distribution and demonstrated on real world datasets that the proposed method is efficient and more accurate. Our method uses asymptotic and Taylor series approximations, with good accuracy estimate.

In this paper, we extend our previously proposed line detection method to line segmentation using a so-called unite-and-divide (UND) approach. The methodology includes two phases, namely the union of spectra in the frequency domain, and the division of the sinogram in Radon space. In the union phase, given an image, its sinogram is obtained by parallel 2D multilayer Fourier transforms, Cartesian-to-polar mapping and 1D inverse Fourier transform. In the division phase, the edges of butterfly wings in the neighborhood of every sinogram peak are firstly specified, with each neighborhood area corresponding to a window in image space. By applying the separated sinogram of each such windowed image, we can extract the line segments. The division Phase identifies the edges of butterfly wings in the neighborhood of every sinogram peak such that each neighborhood area corresponds to a window in image space. Line segments are extracted by applying the separated sinogram of each windowed image. Our experiments are conducted on benchmark images and the results reveal that the UND method yields higher accuracy, has lower computational cost and is more robust to noise, compared to existing state-of-the-art methods.

H.264/MVC multi-view video coding provides a better compression rate compared to the simulcast coding using hierarchical B-picture prediction structure exploiting inter- and intra-view redundancy. However, this technique imposes random access frame delay as well as requiring huge computational time. In this paper a novel technique is proposed using 3D motion estimation (3D-ME) to overcome the problems. In the 3D-ME technique, a 3D frame is formed using the same temporal frames of all views and ME is carried out for the current 3D frame using the immediate previous 3D frame as a reference frame. As the correlation among the intra-view images is higher compared to the correlation among the inter-view images, the proposed 3D-ME technique reduces the overall computational time and eliminates the frame delay with comparable rate-distortion (RD) performance compared to H.264/MVC. Another technique is also proposed in the paper where an extra reference 3D frame comprising dynamic background frames (the most common frame of a scene i.e., McFIS) of each view is used for 3D-ME. Experimental results reveal that the proposed 3D-ME-McFIS technique outperforms the H.264/MVC in terms of improved RD performance by reducing computational time and by eliminating the random access frame delay.

In many machine vision applications, a set of static and Pan-Tilt-Zoom (PTZ) cameras are used to capture a sequence of high-resolution facial images of a moving person. In this paper, we present our implementation of such a system. We emphasis two novelties in our work; the first one is our efficient PTZ camera calibration technique using hand-drawn gridlines. The second one is our head position estimation technique using the Gaussian Mixture Model (GMM) and variance analysis of the foreground blob regions.