Sharing storage using dirty vectors

Consider a computation F with n inputs (independent variables) and m outputs (dependent variables) and suppose that we wish to evaluate the Jacobian of F. Automatic differentiation commonly performs this evaluation by associating vector storage either with the program variables (in the case of forward-mode automatic differentiation) or with the adjoint variables (in the case of reverse). Each vector component contains a partial derivative with respect to an independent variable, or a partial derivative of a dependent variable, respectively. The vectors may be full vectors, or they may be dynamically managed sparse data structures. In either case, many of these vectors will be scalar multiples of one another. For example, any intermediate variable produced by a unary operation in the forward mode will have a derivative vector that is a multiple of the derivative for the argument. Any computational graph node that is read just once during its lifetime will have an adjoint vector that is a multiple of the adjoint of the node that reads it. It is frequently wasteful to perform component multiplications explicitly. A scalar multiple of another vector can be replaced by a single multiplicative "scale factor" together with a pointer to the other vector. Automated use of this "dirty vector" technique can save considerable memory management overhead and dramatically reduce the number of floating-point operations required. In particular, dirty vectors often allow shared threads of computation to be reverse-accumulated cheaply. The mechanism permits a number of generalizations, some of which give efficient techniques for preaccumulation

A General Framework for Flexible Multi-Cue Photometric Point Cloud Registration

The ability to build maps is a key functionality for the majority of mobile robots. A central ingredient to most mapping systems is the registration or alignment of the recorded sensor data. In this paper, we present a general methodology for photometric registration that can deal with multiple different cues. We provide examples for registering RGBD as well as 3D LIDAR data. In contrast to popular point cloud registration approaches such as ICP our method does not rely on explicit data association and exploits multiple modalities such as raw range and image data streams. Color, depth, and normal information are handled in an uniform manner and the registration is obtained by minimizing the pixel-wise difference between two multi-channel images. We developed a flexible and general framework and implemented our approach inside that framework. We also released our implementation as open source C++ code. The experiments show that our approach allows for an accurate registration of the sensor data without requiring an explicit data association or model-specific adaptations to datasets or sensors. Our approach exploits the different cues in a natural and consistent way and the registration can be done at framerate for a typical range or imaging sensor.Comment: 8 page

Calculation of supersonic viscous flow over delta wings with sharp subsonic leading edges

Two complementary procedures were developed to calculate the viscous supersonic flow over conical shapes at large angles of attack, with application to cones and delta wings. In the first approach the flow is assumed to be conical and the governing equations are solved at a given Reynolds number with a time-marching explicit finite-difference algorithm. In the second method the parabolized Navier-Stokes equations are solved with a space-marching implicit noniterative finite-difference algorithm. This latter approach is not restricted to conical shapes and provides a large improvement in computational efficiency over published methods. Results from the two procedures agree very well with each other and with available experimental data