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We present a system to recognize underwater plankton images from the shadow image particle profiling evaluation recorder (SIPPER). The challenge of the SIPPER image set is that many images do not have clear contours. To address that, shape features that do not heavily depend on contour information were developed. A soft margin support vector machine (SVM) was used as the classifier. We developed a way to assign probability after multiclass SVM classification. Our approach achieved approximately 90% accuracy on a collection of plankton images. On another larger image set containing manually unidentifiable particles, it also provided 75.6% overall accuracy. The proposed approach was statistically significantly more accurate on the two data sets than a C4.5 decision tree and a cascade correlation neural network. The single SVM significantly outperformed ensembles of decision trees created by bagging and random forests on the smaller data set and was slightly better on the other data set. The 15-feature subset produced by our feature selection approach provided slightly better accuracy than using all 29 features. Our probability model gave us a reasonable rejection curve on the larger data set.