The advent of the Hubble Space Telescope ( HST ) has provided images of galaxies at moderate and high redshifts and changed the scope of galaxy morphologies considerably . It is evident that the Hubble Sequence requires modifications in order to incorporate all the various morphologies one encounters at such redshifts . We investigate and compare different approaches to quantifying peculiar galaxy morphologies on images obtained from the Medium Deep Survey ( MDS ) and other surveys using the Wide Field Planetary Camera 2 ( WFPC2 ) on board the HST , in the I band ( filter F814W ) . We define criteria for peculiarity and put them to use on a sample of 978 galaxies , classifying them by eye as either normal or peculiar . Based on our criteria and on concepts borrowed from digital image processing we design a set of four purely morphological parameters , which comprise the overall texture ( or “ blobbiness ” ) of the image ; the distortion of isophotes ; the filling-factor of isophotes ; and the skeleta of detected structures . We also examine the parameters suggested by Abraham et al . ( 1995 ) . An artificial neural network ( ANN ) is trained to distinguish between normal and peculiar galaxies . While the majority of peculiar galaxies are disk-dominated , we also find evidence for a significant population of bulge-dominated peculiars . Consequently , peculiar galaxies do not all form a “ natural ” continuation of the Hubble sequence beyond the late spirals and the irregulars . The trained neural network is applied to a second , larger sample of 1999 WFPC2 images and its probabilistic capabilities are used to estimate the frequency of peculiar galaxies at moderate redshifts as 35 \pm 15 \% .