Riasati V R, Abushagur M A
Appl Opt. 1997 May 10;36(14):3022-34. doi: 10.1364/ao.36.003022.
The projection-slice synthetic discriminant function (PSDF) filter is introduced and proposed for distortion-invariant pattern-recognition applications. The projection-slice theorem, often used in tomographic applications for medical imaging, is utilized to implement a distortion-invariant filter. Taking M projections from one training image and combining them with (N - 1)M projections taken from another N - 1 training image accomplishes this. With the projection-slice theorem, each set of these M projections can be represented as M one-dimensional slices of the two-dimensional Fourier transform of the particular training image. Therefore, the PSDF filter has the advantage of matching each of the training images with at least M slices of their respective Fourier transforms. This filter is theoretically analyzed, numerically simulated, and experimentally implemented and tested to verify the simulation results. These tests show that the PSDF filter significantly outperforms the matched-filter and the basic synthetic discriminant function technique for the particular images used.
提出并引入投影切片合成判别函数（PSDF）滤波器用于畸变不变模式识别应用。常用于医学成像断层扫描应用的投影切片定理被用于实现一个畸变不变滤波器。从一幅训练图像中获取M个投影，并将它们与从另外N - 1幅训练图像中获取的(N - 1)M个投影相结合来实现这一点。根据投影切片定理，这些M个投影的每一组都可以表示为特定训练图像二维傅里叶变换的M个一维切片。因此，PSDF滤波器具有将每幅训练图像与其各自傅里叶变换的至少M个切片进行匹配的优势。对该滤波器进行了理论分析、数值模拟以及实验实现和测试，以验证模拟结果。这些测试表明，对于所使用的特定图像，PSDF滤波器显著优于匹配滤波器和基本合成判别函数技术。
