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OC is a projection direction (φi, θi) near OB.
Note that this simple expression avoids estimating a projection direction as required by the general multi-dimensional expression of Fisher's discriminant.
The intersection of a projection direction with the sphere defines a point on its surface that denotes the projection orientation.
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Next, we compute for each such volume slab the projection extent on the detector, combined for the full range of projection angles; this is the region of the detector that is affected by an FP of the slab (in any projection direction), or, equivalently, the region of the detector that affects a BP to the slab.
From a geometrical perspective, the projection direction is determined by the angle it makes with the connection of each point pair of the various classes: x T S uv x = ∑ i ≠ j, u ∈ A i, v ∈ A j x cos θ xuv λ uv cos θ xuv x (15) = ∑ i ≠ j, u ∈ A i, v ∈ A j x 2 cos θ xuv 2 λ uv.
In total, 50,000 density maps were generated in this way and each map was projected once with the projection direction randomly selected.
Hence, a more reasonable classification plane and projection direction were achieved.
The digital projection P l α at angle α of a two-dimensional function is the sum of densities along one pixel wide parallel rays: where i and j are the object pixel indices, k is the projection pixel index, and δ(1 k – L⃗· r⃗ i, j ) is a line (or plane) over which the summation is performed, L⃗ is a unit vector that defines the projection direction at angle α, and l k is the projection coordinate.
For instance, a bright region in a photoacoustic projection image (few of them are indicated by arrows in Fig. 5) can either mean an enhanced local light absorption or that an absorbing structure is oriented along the projection direction.
In order to design a ULSA with the optimal number of PEs we then perform an accommodation of the index space to the projection direction vector.
Unlike conventional tomography, DTS is not limited to reconstruction of a single plane, but can generate an arbitrary number of slice planes orthogonal to the projection direction.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com