BEAMS step

The purpose of the BEAMS step is to detect all beams in a sheet, both (standard) beams and small beams if any.

As a side effect, it also detects any multi-measure rest found in the sheet.

  1. Inputs
  2. Outputs
  3. Prolog: retrieval of potential beams glyphs
  4. Beams detection
  5. Multi-measure rests detection

Inputs

  • The no-staff image

Outputs

  • The beams and beam-hooks candidates
  • The multi-measure rests candidates

Prolog: retrieval of potential beams glyphs

Geometrically, a beam is a filled parallelogram, rather horizontal, long and thick.

To focus as much as possible on all relevant beam candidates and only them, the input data is carefully worked upon.

The engine cleaning actions are as follows:

  1. Remove all the staff lines, by taking the no-staff image as input
  2. Remove all stem-like items, by removing any horizontal run whose length is smaller than the maximum stem thickness
  3. Smoothen the image to get rid of noise and small holes, by applying a median filter followed by a gaussian filter, both using a 3x3 kernel
  4. Highlight the spots whose thickness is close to the beam expected thickness;
    this is the result of a morphological closing operation (a dilation followed by an erosion) using a disk-shaped mask whose diameter is the expected beam thickness – the smaller value, when the sheet exhibits two beam thickness values

The resulting cleaned image uses a gray scale.
All spots with a rather high density of black are interesting for two purposes:

  • beams recognition of course,
  • but also black heads later recognition by the HEADS step. 1

Regarding beam recognition, the prolog final actions are as follows:

  1. Binarize the resulting gray image, using a global threshold
  2. Build all glyphs (spots) from the image runs, using runs connections
  3. Dispatch all spots to their containing systems – any spot located between two systems is dispatched to both

As an example, the images below result from the processing of a score of rather poor-quality.
Notice that, in the cleaned image, the tiny black or white items have disappeared.

Legend Image
Binary image coffrets_binary
Cleaned image coffrets_gray_spots
Detected glyphs coffrets_beam_spots

The binary tab is always available via the Sheet → Display binary pull-down menu. The two other tabs require specific booleans to be set in the Tools → Constants menu, respectively displayGraySpots and displayBeamSpots.

Beams detection

Each individual spot glyph is checked for being a good beam candidate:

  • width
  • mean thickness
  • slope of the glyph center line (least squares approximation)

These very simple criterias help discarding some glyphs (displayed in gray in the image above).

At this point, a glyph may represent a beam, or a portion of a beam, or several beams stuck together, or a black note head, etc…

For each of the remaining glyphs (displayed in pale blue), the engine builds a structure, based on the glyph vertical sections:

Legend Image
Sections coffrets_beam_sections

The structure focuses on the top and bottom lines of the most significant vertical sections – the View → Switch selections menu allows the display of sections.

These lines are likely to represent the top and bottom borders of the underlying individual beams. They are checked for straightness and consistent slope.

A thick structure is likely to represent beams stuck one upon the other, it is thus split into thinner structures:

Legend Image
Double beam glyph coffrets_double_ beam

The final structures are converted to elementary beams, which can be further merged or extended horizontally to full beams and beam hooks Inters.

Legend Image
Beams inters coffrets_beams

At the end of this BEAMS step, all the created Inters are just candidates. In particular, Inters for short beams and beam hooks may still coexist for the same underlying glyph!

These beam Inters are displayed in red: they are still in an abnormal status becaused they are not yet linked to any stem!

Only the following steps, especially the REDUCTION step, will allow the engine to confirm or discard these candidates.

Multi-measure rests detection

Here is a multi-measure rest example:

It looks like a horizontal beam, vertically centered on the staff middle line, and with vertical serifs on each horizontal side.
A number (“4” in the example), located above the staff, indicates the number of measures covered by the multiple rest.

At the end of the BEAMS step, every beam candidate is checked to decide if it should be considered as a multi-measure rest rather than a plain beam.

The checks are rather obvious:

  • Minimum length
  • Maximum vertical distance from staff mid-line for the left and right extremum points
  • Presence of vertical serifs on left and right sides. At this point in time, the stem seeds have not yet been detected, therefore the engine uses a staff projection to detect peaks and thus serifs on both sides.

NOTA: The count above the staff cannot be detected during the BEAMS step. The SYMBOLS step should detect this number symbol, and the subsequent LINKS step should link the multi-measure rest and the count via a MultipleRestCountRelation.

  1. This is a forward reference to the HEADS step, since filled black heads are very likely to appear in these spots. A specially binarized version of the cleaned image is thus set aside to be used later by the HEADS step. ↩