5.- Perceptual Level of Detail
We assumed that the scene is represented by a triangular mesh corresponding to the coarsest LOD. For each triangle in the mesh, we calculate the desired LOD and increase the resolution (i.e. generate smaller triangles) accordingly, using adaptive subdivision.
In the calculation of the desired LOD, we are interested in finding the highest spatial frequency that a person can see at a particular location under conditions determined by the triangle's contrast, eccentricity and angular velocity. The spatial frequency of a triangle is found by measuring the maximum angle between the vertices of the triangle projected on the screen plane with respect to the head position. The contrast level for a triangle is obtained by rendering the triangle at the coarsest level and examining the color content of the projection. To calculate the eccentricity, the triangle is represented by its geometric center. Uncertainty estimates mainly affect the eccentricity values.
When the user is looking at the screen, the direction of his (her) head intersects the plane formed by the screen at a point called the Point of Interest (POI). Uncertainty in head orientation affects the location of the POI, which in turn affects the eccentricity values of the triangles. We have incorporated orientation uncertainty in the eccentricity calculations by modifying the triangle's location with respect to the POI. Specifically, given a point P and the orientation uncertainty matrix S, an uncertainty corrected point Pu is calculated as follows:
(1)
where point P is shifted towards POI proportionally to the probability that P itself is the POI.
The highest spatial frequency is determined by solving a system of equations given the contrast, angular velocity and the modified eccentricity values of triangles. Once the highest spatial frequency is known, it can be related to a certain LOD that is determined by the implementation. In our system, the depth of subdivision is taken to be the LOD measure.
Another detail that was changed from the original approach is the use of Hue-Saturation-Intensity as the histogram color space. The reason was that the paper was not very explicit on how to perform the transformation from RGB to their chose of color space. HSI offers the same advantage which is the separation of chroma information from intensity information.