Estimation of motion and parameters of heat transport from thermography

In this contribution a technique for measuring motion and parameters of temperature change locally in thermal image sequences will be presented. This leads to the estimation of highly accurate optical flow and parameters of heat transport, such as the constant of diffusivity or the matrix of anisotropic diffusion. Results of the computation are shown on a number of sample applications. 1. Introduction techniques are widely used for non-destructive testing of new materials. These methods have several advantages over other techniques in that they allow for an inspection of relative large surfaces in short time frames. At the same time they offer a robust and reliable detection of defects. Although presenting a number of advantages in the field of NDT, most current techniques are limited to static objects. The reason for this restriction is that motion is not taken into consideration. As an example one might want to look into Lock-In thermography. Here a time series is recorded and a Fourier transform performed at every pixel. Obviously, this technique only makes sense if it is assumed that the scene location mapped onto one pixel remains there during the duration over which the Fourier transform is computed. Otherwise the amplitude and phase information would be a mixture of those from different locations of an object or worse still, from different objects. For a number of potential applications, the observed materials can not be made to remain still during image acquisition. This might be due to the movement of objects on a conveyor belt in industrial applications. Moreover, the observed effect in materials might be due to movement itself, such as the thermo-elastic effect. Here a temperature change is induced by compressing or depressing a material, which can be induced by bending it. By estimating the image velocity, motion compensation can be performed. This allows warping of thermal images, making pixels in subsequent frames to correspond to the same object location. Due to physical transport processes, the objects under observation will change in temperature. This change has to be taken into account when estimating its motion. The transport of heat can usually be described by a differential equation, which turns out to be the diffusion equation in the case of heat transport due to conduction. By incorporating this model into the equation of motion, not only can the object velocity be estimated very accurately, but also the parameters of heat transport. In the following sections it will be demonstrated how image velocity and the constant of diffusion, or the in the case of anisotropic diffusion the whole matrix of diffusivity are accurately retrieved in a single estimation step. Since the estimate is performed on a small spatial temporal neighborhood of the image pixel of interest, both temporally and spatially highly resolved measurements are obtained. These estimates of the constant of diffusion are highly accurate and limited only by the frame rate and resolution of the infrared camera.