I'm currently designing a curve-matching algorithm and as I already explored many ideas I'm requesting your help. So, if you got some advices about how to handle this problem, feel free to answer!
I got a flash LIDAR spatio-temporal response to one short impulsion. The data acquired is stored in a 3-D matrix:
- First and second dimensions are spatial ones. As in a 2-D image they represent azimuth and elevation of a pixel.
- Third dimension is the temporal one. For each pixel the illumination is recorded for a fixed duration and stored in this dimension. Typically, the curve observed is a Gaussian and its parameters (variance, max amplitude and delay) are affected by the LIDAR surrounding environment.
To be more specific the laser pulse is distorted by the environment. The multi-path of light impacts the Gaussian variance, the object distance to the RADAR impacts the delay and the amplitude and the reflectivity of the object impacts the amplitude of the Gaussian.
As in the real world objects are contiguous and homogeneously distributed in space, neighboring pixels are more likely to have a similar reflectivity and distance to the LIDAR thus neighboring Gaussians are very similar.
What I'm trying to do is to quantify the similarity of a pixel impulse response to its neighborhood (3x3 neighborhood for instance). This is very close to the concept of gradient, I want to detect pixels that are parts of an homogeneous objects and ones at the border of an object where there is a disruption.
For now I've implemented two different algorithms. One that is similar to a an image derivation adapted to the 3-D structure, with a 2-D Laplacian Filter. The second algorithm is based on the measure of similarity using Sum of Absolute Differences, also adapted to the data 3-D structure.
These algorithms work somewhat fine but since the signal can be noisy and sometimes very far from a Gaussian shape I think and I hope better algorithms can be implemented.
My research tracks are focused on curve-fitting before comparison (Levenberg–Marquardt algorithm for instance) for now, but this proved very computationally time-consuming!
If you know about other methods or concepts that can help in resolving my problem, feel free to participate :)
Matrix size is 32x128x128