Projection profile cutting, also known as ``structural analysis'', determines the structure of a formula from a number of repeated horizontal and vertical projections of a formula's image. Based on these projections the formula is subdivided, each subdivision being recursively projected and further subdivided. A tree structure is created, representing the formula's geometric structure. This structure is then further processed, taking into account the symbols in the formula, and the formula is determined.
Figure 2.7 shows how a projection profile is created. The height of the histogram is determined by the area of the bounding boxes . The histogram can also be created using the density of pixels at each x- or y-position. For example, if this formula was subdivided based on the minima in the histogram, it would be split into three parts: the integral symbol, the fraction, and the differential. The fraction could then be horizontally projected which would identify the numerator and denominator.
Blostein and Grbavec say the disadvantage of projection profile cutting is that special processing is required for square-roots, sub- and super-scripts. They report that projection profile cutting has been used on both typeset and handwritten input, although with handwritten input it has trouble with square-roots, closely-written symbols and skew.
Projection profile cutting is also used to process scanned text documents, subdividing the text into columns, paragraphs, and lines . It is also used for analysing scanned images of sheet music, to separate the staves and musical symbols.
. It is also used for analysing scanned images of sheet music, to separate the staves and musical symbols.
