Considering the graph of a feature function as an embedded surface in three dimensions is a standard device in computer vision. When multiple feature functions (eg. multiple images) are available, the natural extension of the above concept is to a higher-dimensional embedded surface. This has received surprisingly little attention. In this paper, we advocate for this view by showing the utility of surface area for estimating spatial transformations between images for the purposes of registration. In contrast to the entropy of the stack of images (when represented as continuous and differentiable functions) being zero, the surface area turns out to be useful measure for image registration. We show that during the progression of standard registration algorithms like Congealing, the area of the stack of images being registered decreases. Our own algorithm for affine registration based on image stack surface area (ISSA) minimization has several advantages compared with Congealing and Mutual Information (MI) registration. Finally, we highlight the generality of our framework by also showcasing experiments on affine point-set registration.

Urban neighborhood classification using very high resolution (VHR) remote sensing imagery is a challenging and {\em emerging} application. A semi-supervised learning approach for identifying neighborhoods is presented which employs superpixel tessellation representations of VHR imagery. The image representation utilizes homogeneous and irregularly shaped regions termed superpixels and derives novel features based on intensity histograms, geometry, corner and superpixel density and scale of tessellation. The semi-supervised learning approach uses a support vector machine (SVM) to obtain a preliminary classification which is then subsequently refined using graph Laplacian propagation. Several intermediate stages in the pipeline are presented to showcase the important features of this approach. We evaluated this approach on four different geographic settings with varying neighborhood types and compared it with the recent Gaussian Multiple Learning algorithm. This evaluation shows several advantages, including model building, accuracy, and efficiency which makes it a great choice for deployment in large scale applications like global human settlement mapping and population distribution (e.g., LandScan), and change detection.

Despite the ubiquitous use of distance transforms in the shape analysis literature and the popularity of fast marching and fast sweeping methods - essentially Hamilton-Jacobi solvers, there is very little recent work leveraging the Hamilton-Jacobi to Schrödinger connection for representational and computational purposes. In this work, we exploit the linearity of the Schrödinger equation to (i) design fast discrete convolution methods using the FFT to compute the distance transform, (ii) derive the histogram of oriented gradients (HOG) via the squared magnitude of the Fourier transform of the wave function, (iii) extend the Schrödinger formalism to cover the case of curves parametrized as line segments as opposed to point-sets, (iv) demonstrate that the Schrödinger formalism permits the addition of wave functions - an operation that is not allowed for distance transforms, and finally (v) construct a fundamentally new Schrödinger equation and show that it can represent both the distance transform and its gradient density - not possible in earlier efforts.