The Results of the Sub-Pixel Efficacy Region Based B-Spline Interpolation Functions

The Results of the Sub-Pixel Efficacy Region Based B-Spline Interpolation Functions

Carlo Ciulla (Lane College, USA)
DOI: 10.4018/978-1-60566-202-2.ch015
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Abstract

The results obtained processing the MRI database with classic and SRE-based one dimensional quadratic and cubic B-Splines are presented in this chapter. The chapter opens up with information relevant to the image resolution of the MRI database employed for validation. The assessment of the performance of the two classes of interpolators (classic and SRE-based) is conducted both quantitatively and qualitatively. The RSME Ratio is plotted to ascertain which ones of the classic or the SRE-based models deliver the smaller interpolation error. Also, the analysis of error images obtained after processing with either of the two model interpolators and the display of the maps of novel re-sampling locations along with spectral power evolutions corroborates the presentation of the characteristic features of the performances of the interpolation functions treated in this chapter.
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Data

Ciulla and Deek (2005) presented results obtained applying theory and methodology for the improvement of the quadratic B-Spline employing the following 2D images: Lena, T1 MRI and functional MRI. This section extends on what reported earlier presenting results obtained with two-dimensional T1 MRI, T2 MRI and functional MRI data. MRI images’ resolution and matrix size were:

  • T1 MRI (T1-MRI-230 and T1-MRI-450). Matrix resolution: 176 x 208 with 1.00 x 1.00 mm of pixel size, with 75 slices and an inter-slice resolution of 1.00 mm.

  • T2 MRI: matrix resolution was 177 x 182 with 1.00 x 1.00 mm of pixel size, with 19 slices and an inter-slice resolution of 1.00 mm.

  • Functional MRI (fMRI-TS1). Matrix resolution was 128 x 128 with 1.72 x 1.72 mm of pixel size, with 20 slices and an inter-slice resolution of 1.72 mm.

The motion correction paradigm that was applied is described hereto. A misplacement x0 was applied to the signal, then motion correction and interpolation was performed in two different ways: (i) with the classic form of B-Spline and (ii) with SRE-based B-Spline. The latter is the classic B-Spline calculated at the novel re-sampling location as per equation (24) for h3 (x), and equation (43) for h4 (x) respectively (see Chapter XIV for the two equations). For the purpose of simplification, the remainder of this discussion will use the term processed to indicate that the signal or the image was motion corrected and interpolated. At the misplacement x0 the signal or image is termed as processed with classic forms of B-Spline as per equations (3) and (4) of Chapter XIV, whereas at the novel re-sampling location xr0 obtained from equations (24) and (43), the signal or image is termed as processed with SRE-based B-Spline interpolation.

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Results With The Quadratic B-Spline

This section expands what reported earlier (Ciulla & Deek, 2005) presenting additional results that were collected employing T1 MRI, T2 MRI and functional MRI data.

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