1. Introduction.- 1.1 Machine Vision Architectures.- 1.2 The Radon Transform and the PPPE Architecture.- 2. Model and Computation of Digital Projections.- 2.1 Representation of Digital Lines.- 2.2 Generation of Projection Data.- 2.3 Noise Considerations.- 3. Architectures.- 3.1 The Contour Image Generator.- 3.2 The Projection Data Collector.- 3.3 Additional Hardware.- 3.4 Putting It All Together: P3E.- 3.5 Implementation in Commercially Available Pipelines.- 4. Projections Along General Contours.- 5. P3E-Based Image Analysis Algorithms and Techniques.- 5.1 Computing Convex Hulls, Diameters, Enclosing Boxes, Principal Components, and Related Features.- 5.2 Computing Hough Transforms for Line and Curve Detection.- 5.3 Generating Polygonal Masks.- 5.4 Generating Multi-Colored Masks.- 5.5 Non-Linear Masks.- 6. P3E-Based Image Processing Algorithms and Techniques.- 6.1 Non-iterative Reconstruction.- 6.1.1 Convolution Backprojection.- 6.1.2 Filtered Backprojection.- 6.2 Iterative Reconstruction.- 6.2.1 The Kacmarz Method.- 6.3 Two-Dimensional Convolution.- 6.4 Rotation and Translation.- 6.5 Computerized Tomography Reconstruction.- 6.6 Autocorrelation.- 6.7 Polar Fourier Transform and Object Classification.- 7. Radon Transform Theory for Random Fields and Optimum Image Reconstruction from Noisy Projections.- 7.1 Radon Transform Theory of Random Fields.- 7.2 Optimum Reconstruction from Noisy Projections.- 8. Machine Vision Techniques for Visual Inspection.- 9. Conclusion.