A new weighted bivariate blending rational spline with parameters is constructed based on function values of a function only. The interpolation is C1 in the whole interpolating region under the condition which free parameters is not limited. This study deals with the bounded property of the interpolation. In order to meet the needs of practical design, an interpolation technique is employed to control the shape of surfaces. This rational interpolation with parameters is used in the medical image enhancement. The value of the interpolating function at any point in the interpolating region can be modified under the condition that the interpolating data are not changed by selecting the suitable parameters. Using the surface control, the local enhancement of the image is implemented. The experimentations show that this algorithm is efficient.
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