Concepts inA new energy minimization framework and sparse linear system for path planning and shape from shading

Photometric stereo

Photometric stereo is a technique in computer vision for estimating the surface normals of objects by observing that object under different lighting conditions. The technique was originally introduced by Woodham in 1980. The special case where the data is a single image is known as shape from shading, and was analyzed by B. K. P. Horn in 1989.  more from Wikipedia

Energy minimization

In computational chemistry, energy minimization (also called energy optimization or geometry optimization) methods are used to compute the equilibrium configuration of molecules and solids. Stable states of molecular systems correspond to global and local minima on their potential energy surface.  more from Wikipedia

Linear system

A linear system is a mathematical model of a system based on the use of a linear operator. Linear systems typically exhibit features and properties that are much simpler than the general, nonlinear case. As a mathematical abstraction or idealization, linear systems find important applications in automatic control theory, signal processing, and telecommunications. For example, the propagation medium for wireless communication systems can often be modeled by linear systems.  more from Wikipedia

Motion planning

Motion planning (a.k.a. , the "navigation problem", the "piano mover's problem") is a term used in robotics for the process of detailing a task into discrete motions. For example, consider navigating a mobile robot inside a building to a distant waypoint. It should execute this task while avoiding walls and not falling down stairs. A motion planning algorithm would take a description of these tasks as input, and produce the speed and turning commands sent to the robot's wheels.  more from Wikipedia

Eikonal equation

The eikonal equation (from German Eikonal, which is from Greek ¿¿¿¿¿, image) is a non-linear partial differential equation encountered in problems of wave propagation, when the wave equation is approximated using the WKB theory. It is derivable from Maxwell's equations of electromagnetics, and provides a link between physical (wave) optics and geometric (ray) optics.  more from Wikipedia

Fast marching method

The fast marching method is introduced by James A. Sethian as a numerical method for solving boundary value problems of the Eikonal equation: Typically, such a problem describes the evolution of a closed curve as a function of time with speed in the normal direction at a point on the curve. The speed function is specified, and the time at which the contour crosses a point is obtained by solving the equation.  more from Wikipedia

Euler¿Lagrange equation

In calculus of variations, the Euler¿Lagrange equation, Euler's equation, or Lagrange's equation, is a differential equation whose solutions are the functions for which a given functional is stationary. It was developed by Swiss mathematician Leonhard Euler and Italian mathematician Joseph Louis Lagrange in the 1750s.  more from Wikipedia