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The advent of the Hubble Space Telescope (HST) has provided images ofgalaxies at moderate and high redshifts and changed the scope of galaxymorphologies considerably. It is evident that the Hubble Sequence requiresmodifications in order to incorporate all the various morphologies oneencounters at such redshifts. We investigate and compare different approachesto quantifying peculiar galaxy morphologies on images obtained from the MediumDeep 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 forpeculiarity and put them to use on a sample of 978 galaxies, classifying themby eye as either normal or peculiar. Based on our criteria and on conceptsborrowed from digital image processing we design a set of four purelymorphological parameters, which comprise the overall texture (or``blobbiness'') of the image; the distortion of isophotes; the filling-factorof isophotes; and the skeleta of detected structures. We also examine theparameters suggested by Abraham et al. (1995). An artificial neural network(ANN) is trained to distinguish between normal and peculiar galaxies. While themajority of peculiar galaxies are disk-dominated, we also find evidence for asignificant population of bulge-dominated peculiars. Consequently, peculiargalaxies do not all form a ``natural'' continuation of the Hubble sequencebeyond the late spirals and the irregulars. The trained neural network isapplied to a second, larger sample of 1999 WFPC2 images and its probabilisticcapabilities are used to estimate the frequency of peculiar galaxies atmoderate redshifts as $35 \pm 15 %$.Comment: 32 pages, latex and 9 figures, Ap. J., accepte

Quantitative Morphology of Moderate‐Redshift Galaxies: How Many Peculiar Galaxies Are There?