The problem is how to reconstruct tiny relative velocity changes (say, 0.001% to 0.01%) due to pressure or thermal variations and detect opening/closing or development of microcracks in the concrete from measurements of few transducers as sources and receivers (say, 15 sources and 15 receivers on a 2m*2m surface). Examples are the concrete containment of wind tunnel or nuclear power plant. Temperature or pressure changes cause the expansion or contraction of the structure and therefore changes of wave speed and scattering property. Is it possible to reconstruct the change between two nearby states provided the same experiment?

Ultrasound and why. Since the relative velocity change is very small, waves should go through a long enough trajectory to show the difference, usually the dilation or shrinking of the waveform. The cracks are micrometer or millimeter scale, the scale of the background heterogeneity. It has been observed that it is hard to find the mismatch of waveforms on directly arrival waveforms. To be able to reconstruct such small changes, we need to take the advantage of multiple reflection, that is, ultrasonic frequency (KHz to MHz) and late arrival waves (coda waves).

Relative velocity change and scattering change are related to dilation and decorrelation of the two waveforms through similar integral equations, respectively. Combining several source-receiver pairs we are able to discretize the integral equation and solve a least squares problem with a suitable regularization. For more detail of the method, please refer to our paper.

This technique has been used to monitor the deterioration and aging of VeRCoRs, a 1/3 replica of the nuclear power plant containment wall. Our paper has been submitted to Structural Health Monitoring and the preprint version can be found here.

We code a Matlab toolbox to solve the whole problem, including the raw data processing, numerical solution of PDEs, regularized least squares solvers with nonnegative constraint, result demonstration, etc. The code is under certain authority protection. You can contact Eric LAROSE if you are interested in our code.

To complete

You can download the code from here.

To complete

In animations an object is represented by thousands of points or faces. Assume that we have a horse in an animation. We want to simulate the running of the horse. It’s impossible to move each point separately. Instead, a few points called cage is chosen outside of the horse. And all the points composing the horse is represented based on the cage (e.g., mean value coordinate). We only need to move the cage to have the animation of a running horse.

This active cage idea is used to image segmentation. Using the Chan and Vese energy, the image segmentation problem is formulated into a minimization problem. The variables are locations of those cage points. The gradient descent method is used to solve the minimization problem.

The result of the active cage segmentation method is dramatically improved with a technique called “restart”. During the experiments, we find out that after several steps of minimization the cage points are too far away from the approximate boundary. This means that the affect of cage points to the represented points is very weak and the program terminatese before a reasonable segmentation result. We come up with a method to choose the cage automatically from the present result and restart the whole minimization process.

You could find detail information here.