# Morphological Pyramids in Multiresolution MIP Rendering

## Project goal

The goal is to extend nonlinear signal decompositions based on morphological pyramids, and apply these decompositions to multiresolution maximum intensity projection (MIP) volume rendering with progressive refinement and perfect reconstruction. The structure of the resulting multiresolution rendering algorithm is very similar to wavelet splatting. To enhance the approximation quality of visualizations from reduced data (higher levels of the pyramid), two approaches are explored. First, a new class of morphological pyramids, involving connectivity enhancing operators, is considered. In the pyramidal analysis phase, a conditional dilation operator is used, with a given number n of iterations. The corresponding pyramids for n=0 and n=1 are known as the adjunction pyramid and Sun-Maragos pyramid, respectively. The approximation quality when rendering from higher levels of the pyramid increases as a function of the number of iterations n of the conditional dilation operator, but the improvement for n>1 is limited. The second new approach, called streaming MIP-splatting, again starts from the adjunction pyramid. The new element is that detail coefficients of all levels are considered simultaneously and are resorted with respect to decreasing magnitude of a suitable error measure. All resorted coefficients are projected successively, until a desired accuracy of the resulting MIP image is obtained. We show that this method outperforms the previous methods based on morphological pyramids, both with respect to image quality with a fixed amount of detail data, and in terms of flexibility of controlling approximation error or computation time.

Multiresolution MIP reconstruction from a 2-level morphological pyramid, neuron data.

Left column: level-2 reconstruction; right
column: level-1 reconstruction. First row: adjunction pyramid; second row:
Sun-Maragos pyramid; third row: conditional dilation pyramid with n=25; fourth row: trivial pyramid.

## Selected publications

- Jos B. T. M. Roerdink (2005) Morphological Pyramids in Multiresolution MIP Rendering of Large Volume Data: Survey and New Results. J. Math. Imag. Vision, 22(2/3):143–157, 2005.
- Jos B. T. M. Roerdink (2003) Multiresolution Maximum Intensity Volume Rendering by Morphological Adjunction Pyramids. IEEE Trans. Image Processing, 12(6):653–660, June 2003.
- Jos B. T. M. Roerdink (2002) Comparison of Morphological Pyramids for Multiresolution MIP Volume Rendering. In D. Ebert, P. Brunet, and I. Navazo, eds., Data Visualization 2002. Proc. Eurographics – IEEE TCVG Symposium, May 27-29, 2002, Barcelona, Spain. ACM, New York, pages 61–70, 2002.
- Jos B. T. M. Roerdink (2001) Multiresolution Maximum Intensity Volume Rendering by Morphological Pyramids. In D. Ebert, J. M. Favre, and R. Peikert, eds., Data Visualization 2001. Proc. Joint Eurographics – IEEE TCVG Symposium on Visualization, May 28-30, 2001, Ascona, Switzerland. Springer, Wien, New York, pages 45–54, 2001.