Description

In this section, I will describe the two main stages of the project in more details.

In the first stage, I intend to start by implementing two discrete de-noising filters for the Cartesian (CC) grid. The filters will have a fixed size for this stage of the project. The discrete filters are obtained from spherically shaped continuous filters. Therefore, discrete de-noising filters can also be obtained for the BCC grid from the same spherically shaped continuous filters. Making use of this conceptual framework, I will implement two discrete de-noising filters for the BCC grid, which correspond to the two discrete de-noising filters for the CC grid.

Each filter shall deal with one specific type of noise model. In particular, for the Gaussian noise model, a Gaussian smoothing filter shall be applied. For the salt & pepper noise model, a median filter shall be applied. Both noise models occur in medical imaging. Gaussian noise models the white noise that is present at every sample point. Salt & pepper noise models noise spikes or signal corruptions.

The two noise models and their corresponding discrete de-noising filters will be applied to an analytical dataset for testing. One natural choice is the well-known Marschner Lobb function. Since both these noise models, as well as their corresponding de-noising filters, have been applied to the CC grid, references on de-noising on the CC grid will serve as a basis for this stage of the project.

To visually verify the correctness of the noise models and their corresponding de-noising filters, I shall produce renderings of a noisy dataset, of its corresponding de-noised version, and of its analytical (noise-free) counterpart. I intend to produce renderings both for the BCC and CC grid; the CC renderings will act as the basis of visual correctness.

In the second stage, I intend to compare the quality of de-noising on the BCC grid with that of the CC grid. Whereas the de-noising filters in the first stage have a fixed size, in this second stage, they may be resized according to the radius of their corresponding continuous filters.

For each given radius of a continuous de-noising filter, I shall apply the corresponding pair of discrete filters on a pair of BCC and CC datasets. The pair of datasets shall be sampled from the same analytical function. The effect of noise on the two datasets shall also be comparable. I will then devise a metric for measuring the error due to noise after the de-noising step. For each radius, two pairs of numbers will be computed: 1) the number of samples that the continuous filter covers in the BCC and CC lattices, when the filter is centered on the sample of interest, and 2) the error due to noise on the BCC and CC lattices after the de-noising step.

I intend to then plot the results of the computations with respect to various radii of the continuous filter. The best way to plot these computations is yet to be determined, as is the best way to measure the error due to noise after the de-noising step.

As far as I know, no research has been done on comparing the error due to noise on the CC grid to that of the BCC grid. Therefore, critical thinking becomes the only known basis upon which I can formulate expected results for the second stage.