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This correspondence details enhancements to previous work on piecewise linear comparametric image registration. The enhancements come in the form of slope constraints and knots' location selection in the comparametric modeling. An analysis of the properties of comparametric functions leads to two general slope constraints that, along with a knot location selection based on the reference image's pixel value distribution, serves to reduce error and sensitivity to the number of segments considered as well as allow for the solution to cases in which there are gaps in the comparagram. Results on real images are presented.