CONCLUSIONS

The classification of the galaxies and a mathematical quantity fractal dimension are both, at some level, related to the complexity of shapes. In the expectation of devising an automated scheme of classifying galaxies, fractal dimensions of 89 spiral galaxies and 14 elliptical galaxies were studied in this project. Two of the fractal dimensions, the capacity dimension and the correlation dimension were calculated for the contours generated around different intensity levels of the galaxy images. Average fractal dimensions for the elliptical galaxies were expected to have lower values compared to the average fractal dimensions for the spiral galaxies because of their less complex shapes. It was found that neither the capacity dimension nor the correlation dimension can be used for a reliable automation of galaxy classification when one computes their averages for an entire possible range of intensity contours around the galaxies. Computing the average of the correlation dimension for a selected range of intensities around the center of the entire intensity range, however, could be useful for galaxy classification.

In recent years, the use of Artificial Neural Networks has grown significantly for classifications. They are also being used for classifying galaxies. When constructing an Artificial Neural Network, one has to specify a number of input parameters using which the network is designed to generate outputs. For galaxy classification, the number of input parameters depends on how we choose to describe a galaxy. Correlation dimension could be used as one such parameter. The correlation dimension is computed using the correlation integral C(r), as described in Chapter 3. Computation of C(r) is very sensitive to the presence of foreground stars in the galaxy images. It is very crucial that proper care is taken in the data reduction process to ensure that the only data remaining in the image is from the galaxy itself.

It would be interesting to derive additional parameters from the function C(r) which could be used as inputs to an Artificial Neural Network.