Reconstruction projections images

The system uses a remote controlled manipulator system whieh scans the volume of interest. It also positions the x-ray source and x-ray camera at different angles relative the crack and create projection images of the craek. By using a tomographic reconstruction of these images a 3-D representation of the crack can be used for analysis and sizing. 

Due to the large unit cell of v- AlCrFe, many atoms overlap in every projection. Images have to be combined to obtain a 3D potential map in order to resolve the individual atoms. Two important steps are needed for 3D reconstruction converting the 2D indices into 3D indices and putting all images into a common origin. 

From the standpoint of image projection, it is important to recognize that a lens can reconstruct an image only from light that has been diffracted and that diffraction in turn limits the maximum resolution which can be attained. Thus an understanding of the phenomenon of diffraction is important in order to understand even qualitatively the optics associated with image projection. 

Fig. 9. Cylindrical imaging system prototype (top) and 24-40 GHz laboratory cylindrical imaging results. Lower left image is a single 90° arc segment reconstruction of a mannequin with no concealed weapons. Lower right image is a combined 360° cylindrical reconstruction projected into an individual image showing...

The earliest MRI method, projection imaging, relied on the acquisition of a series of frequency-encoded projections of the subject at successive angles followed by reconstruction of the set of projections into an image. 

Figure 14.4. Schematic diagram to illustrate the principle of 3D reconstruction. Each 2D projected image, as recorded on the micrograph and after CTF correction, represents a section through the 3D Fourier transform. This is called the projection theorem. After accumulation of enough information from enough different views, a 3D map of the structure can be calculated by Fourier inversion.

Reconstruction of images from tomographic methods are performed using the reverse Radon transform (Herman, 1980) which uses the series of angular projections to reconstruct images. The resulting data set can be displayed as a rotating three-dimensional movie or resliced in any direction to display a series of tw o-dimensional slices. 

From a set of projections acquired under different angles (p in polar coordinates, a spin density map is reconstructed in back-projection imaging (cf. Section 6.1). For a 2D spin density Mq(jc, y) the projection onto an axis r which is at an angle (p with respect to the j -axis follows by integration over the space variable s orthogonal to r (Fig. 5.4.1),... 

Finally, the inverse Fourier transformation is performed to obtain filtered projection data in the spatial domain, which are then backprojected in the same manner as in the simple backprojection. With the use of faster computers, the Fourier technique of filtered backprojection has gained wide acceptance in reconstruction of images in nuclear medicine. 

One novel aspect of CADe development for tomosynthesis is that the CADe algorithm can be applied to either the reconstructed slices or the projection images (the images that are used to reconstruct the slices). When operating on the projection images, a CADe algorithm analyzes each projection independently, and the detections from projection are back-projected in to a virtual breast volume. Actual lesions are more likely to be detected in many slices, while false detections due to superposition of normal breast tissue may not. This knowledge can be used to reduce the false detection rate. 

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