Partial volume estimation using continuous representations

This paper presents a new method for partial volume estimation using standard eigenimage method and B-splines. The proposed method is applied on the multi-parameter volumetric images such as MRI. The proposed approach uses the B-spline bases (kernels) to interpolate a continuous 2D surface or 3D density function for a sampled image dataset. It uses the Fourier domain to calculate the interpolation coefficients for each data point. Then, the above interpolation is incorporated into the standard eigenimage method. This incorporation provides a particular mask depending on the B-spline basis used. To estimate the partial volumes, this mask is convolved with the interpolation coefficients and then the eigenimage transformation is applied on the convolution result. To evaluate the method, images scanned from a 3D simulation model are used. The simulation provides images similar to CSF, white matter, and gray matter of the human brain in T1-, T2-, and PDweighted MRI. The performance of the new method is also compared to that of the polynomial estimators. The results show that the new estimators have standard deviations less than that of the eigenimage method (up to 25%) and larger than those of the polynomial estimators (up to 45%). The new estimators have superior capabilities compared to the polynomial ones in that they provide an arbitrary degree of continuity at the boundaries of pixels/voxels. As a result, employing the new method, a continuous, smooth, and very accurate contour/surface of the desired object can be generated. The new B-spline estimators are faster than the polynomial estimators but they are slower than the standard eigenimage method.