In our efforts to devise a semi-automated technique for extracting the left ventricular (LV) chamber from a stack of cardiac X-ray CT images, we found that individual regions within the imagery contained blurred surfaces and were corrupted by noise and other small artifacts. To reduce these degradations, we explored image enhancement techniques. While many nonlinear edge-preserving smoothing filters have been proposed for such situations in two dimensions, we have found that the most suitable technique for our three-dimensional application is the maximum-homogeneity filter. Unfortunately, previous implementations of the maximum-homogeneity filter used fixed ad hoc implementations, thereby limiting their utility. We have developed a three-dimensional generalization of the maximum-homogeneity filter. This filter preserves and sharpens region surfaces. It also reduces random noise and small artifacts within uniform regions. We compare this method to 3-D versions of other popular edge-preserving smoothing filters.