mirror of https://github.com/GNOME/gimp.git
Flood op: improve descriptions
Add more user friendly description to the PDB op. Partially keep the technical description for the PDB op and add a reference to the developer wiki. Use the new "reference" key for the GEGL op.
This commit is contained in:
Sven Claussner
parent
f4adb9a078
commit
9272da1a21
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@ -19,371 +19,8 @@
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*/
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/* Flood
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* =====
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*
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* The flood operation eliminates "holes" -- darker areas surrounded by lighter
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* areas -- in single-component (grayscale) images. It is particularly useful
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* for eliminating such holes from selections; see GIMP bug #761060 for more
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* details.
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*
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* The conceptual model considers the input image as the height-map of a hilly
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* terrain. After heavy rain completely floods the terrain, the remaining
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* water form lakes in its depressions.
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*
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* _______
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* /.\ /\_____________
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* ____________/...\ /..\ Water /..\
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* /....\ /.....\/....\__ /....\____
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* /......\____/....Ground.....\___/......\ /\
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* __/........................................\/..\_
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*
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* A depiction of a one-dimensional flood.
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* Valleys correspond to "holes" in the input
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* image, filled with "water" according to
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* their surrounding.
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*
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* The result of the flood operation is the height-map of the terrain after the
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* flood, taking both ground- and water-level into account.
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*
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* More formally, the flood operation assigns to each pixel the minimum of the
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* maximal input-image values along all paths from the pixel to the "outside".
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* That is, the output value at pixel `x`, `o(x)`, is given by
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*
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* o(x) = min max i(y),
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* p in P(x) y in p
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*
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* where `P(x)` is the set of all paths from `x` to the outside, and `i(y)` is
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* the value of the input image at pixel `y`.
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*
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* Algorithm
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* ---------
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*
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* In accord with the conceptual flood model, we refer to the values of the
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* input image as the "ground level", and to the values of the output image as
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* the "water level"; these values range from 0 to 1, and are considered to
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* be 0 outside the bounds of the image. Note not to confuse "water level"
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* with "water depth"; we use the term "water level" simply to refer to the
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* elevation of either the ground or the water at a certain point.
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*
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* Our starting point is modeling the problem as a cellular automaton. The
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* state of each cell (pixel) is its current water level, which is initially 1
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* everywhere inside the image. The water level at each cell is updated
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* according to the rule
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*
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* w (x) = max { g(x), min w (y) },
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* n+1 y in N(x) n
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*
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* where `w_n(x)` is the water level at pixel `x` on generation `n`, `g(x)` is
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* the ground level at `x`, and `N(x)` is the set of (orthogonal) neighbors of
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* `x`, including itself. In other words, the new water level at each pixel is
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* the maximum of its ground level, and the minimum of its own water level, and
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* that of its neighbors. This automaton converges to the output of the
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* operation.
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*
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* The automaton converges after, at most, `n` generations, where `n` is the
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* number of pixels in the image. Therefore, a naive implementation, where
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* at most `O(n)` cells are processed on each generation, has a worst-case
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* time complexity of `O(n^2)`. By making a few observations, we can do
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* better, at least in the most common cases.
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*
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* First, note that the final state doesn't depend on the order of the
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* individual steps. That is, we don't actually have to update the water level
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* an entire generation at a time, but rather we can apply the transformation
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* rule to any pixel, at any time, arbitrarily, until convergence.
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* Furthermore, we don't even have to consider all the neighbors of a pixel
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* each time we apply the rule: as long as we make sure to never increase the
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* water level of a pixel, i.e., as long as we consider the pixel's own water
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* level as part of the minimum term, we can take a different subset of the
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* neighbors into account each time.
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*
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* Second, using the above observation, note that we can solve a one-
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* dimensional automaton (i.e., compute its final state) in linear time, using
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* two passes: On the first pass, we iterate over the pixels left-to-right,
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* applying the transformation rule while considering only the left neighbor of
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* each pixel (using the water level assigned to the neighbor on the previous
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* iteration; recall that the water level of the left neighbor of the leftmost
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* pixel of the image is considered to be 0.) On the second pass, we work in
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* reverse -- we iterate over the pixels right-to-left, applying the rule while
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* considering only the right neighbors.
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*
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* _________________________________________________
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* /.\ /\ __
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* ____ /...\ /..\ /..\
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* (a) /....\ /.....\/....\__ /....\
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* /......\____/...............\___/......\ /\
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* __/........................................\/..\_
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* ______________________________
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* /.\ /\ __
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* ____________/...\ /..\ /..\
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* (b) /....\ /.....\/....\__ /....\
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* /......\____/...............\___/......\ /\
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* __/........................................\/..\_
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* _______
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* /.\ /\_____________
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* ____________/...\ /..\ /..\
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* (c) /....\ /.....\/....\__ /....\____
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* /......\____/...............\___/......\ /\
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* __/........................................\/..\_
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*
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* Water level of a one-dimensional automaton
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* (a) initially; (b) after the first pass;
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* (c) after the second pass.
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*
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* While this technique doesn't extend directly to two dimensions, we can
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* leverage it by processing one-dimensional strips of pixels in batch, as
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* described above, instead of transforming pixels individually.
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*
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* Finally, another obvious way to speed things up is to minimize the amount of
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* unnecessary work we're doing. In particular, we only need to process pixels
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* whose neighbors' state changed.
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*
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* Taking all of the above into consideration, this is what we do:
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*
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* We maintain a queue of "segments" -- one-dimensional, contiguous, strips of
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* pixels -- whose water level needs to be updated, as a result of a change in
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* the water level of the pixels of a neighboring segment, referred to as the
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* "source segment". Although, for efficiency reasons, we allow segments to be
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* either horizontal or vertical, for simplicity, we treat all segments as
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* though they're horizontal, and perform the necessary coordinate-system
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* transformation when dealing with vertical segments, as explained later.
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*
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* Each segment is processed using the following steps:
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*
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* 1. Vertical propagation: The segment's pixels are updated, using the
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* above transformation rule, considering only the corresponding
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* neighboring pixels of the source segment. During the process, we
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* inspect which of the segment's pixels actually changed, and create a
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* list of "dirty ranges" of modified pixels. We construct the ranges
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* such that all pixels of each range have the same water level; this
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* becomes important in the next step.
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*
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* - - -+-----+-----+-----+-----+-----+-----+-----+- - -
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* Source | | | | | | | |
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* Segment | | | | | | | | | | | | | | |
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* - - -+--|--+--|--+--|--+--|--+--|--+--|--+--|--+- - -
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* Current | V | V | V | V | V | V | V |
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* Segment | | x | x | | y | z | |
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* - - -+-----+-----+-----+-----+-----+-----+-----+- - -
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* Dirty
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* Ranges |-----------| |-----|-----|
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*
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* The current segment's pixels are updated
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* according to the neighboring pixels of the
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* source segment, and contiguous runs of
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* modified, equivalent pixels form a list of
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* dirty ranges.
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*
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* 2. Horizontal propagation: The segment's pixels are updated, considering
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* only their left and right neighbors, using the two-pass process
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* described above. Though semantically equivalent, this process is
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* slightly more intricate than the one described above, since we use the
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* dirty ranges from the previous step to take a few shortcuts.
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*
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* Recall that all pixels of a single dirty range are equal, and
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* therefore, unless modified as part of the current pass, don't affect
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* each other's state. On the other hand, all pixels outside any dirty
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* range didn't change, and therefore, unless modified as part of the
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* current pass, don't affect each other's state either. As a result,
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* initially, only the pixels that directly neighbor a dirty range, in the
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* direction of the pass, need to be updated. If the water level of such
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* pixel changes, we need to update the following pixel, and so on. Once
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* the water level of a pixel remains the same, we don't have to update
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* the next pixel, but can rather jump directly to the pixel at the edge
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* of the next dirty range, and so on.
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*
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* For example, when scanning left-to-right, we start at the pixel
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* directly to the right of the first (leftmost) dirty range. We apply
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* the transformation rule to this pixel, and to the pixels to its right,
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* until the water level of one of them is unaffected. At this point, we
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* jump directly to the pixel to the right of the next dirty range.
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*
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* - -+---+---+---+---+---+---+---+---+---+---+---+- -
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* | | | | 1 | 2 |(3)| | | 4 |(5)| |
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* - -+---+---+---+---+---+---+---+---+---+---+---+- -
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*
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* |-------| |---|
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*
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* Pixel traversal order on a left-to-right
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* pass. Traversal starts to the right of
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* the first dirty range, at pixel `1`.
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* Pixel `(3)` is unaffected, and so we jump
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* directly to the right of the second dirty
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* range.
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*
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* Of course, when scanning right-to-left, it all reverses, and we start
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* to the left of the last (rightmost) dirty range, etc.
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*
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* During each pass, we extend the dirty ranges, in the direction of the
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* scan, to include the newly modified pixels. Note that, while scanning
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* a sequence of pixels next to one of the dirty ranges, we may reach the
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* edge of the next range. In such case, we keep scanning the pixels of
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* the second range, but we don't extend the previous range any further,
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* so that the two ranges meet, but don't overlap.
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*
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* - -+---+---+---+---+---+---+---+---+---+---+---+- -
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* | | | | 1 | 2 |(3)| | | 4 | 5 | 6 |
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* - -+---+---+---+---+---+---+---+---+---+---+---+- -
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*
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* Original |-------| |---| |---|
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* Extended |---------------| |-------|-------|
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*
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* The dirty ranges are extended, in the
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* direction of the scan, to include the
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* newly modified pixels. The scan can
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* "leak" into existing ranges (notice the
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* third range in the illustration), in which
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* case the previous range is only extended
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* as far as the leaked-into range.
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*
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* Note that the rightmost and leftmost ranges may be extended past the
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* bounds of the segment, during the left-to-right and right-to-left
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* passes, respectively (recall that a segment doesn't necessarily span an
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* entire row.)
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*
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* Also note that, if a dirty range is extended, or if its existing pixels
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* are modified, during the first, left-to-right, pass, then it's possible
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* that its water level will not be uniform come the second, right-to-
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* left, pass; this seems to break our assumption about the state of the
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* dirty ranges, which allowed us to take the shortcut described above.
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* This shortcut is still valid on the second pass, though. It turns out
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* that we only need the ranges to meet a weaker condition -- it's enough
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* for the water level of the pixels of each dirty range to be
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* monotonically decreasing in the direction of the scan (right-to-left,
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* in our case). This condition is still met at the end of the first
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* pass.
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*
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* One final detail: each dirty range has an associated `modified` flag,
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* which is initially cleared. If, during the above process, the range is
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* extended, or its existing pixels are modified, then its `modified` flag
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* is set. This flag is used by the next step.
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*
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* 3. Distribution: The changes to the current segment's water level may
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* affect the two neighboring rows. For each dirty range, we push two new
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* segments into the queue -- one for each neighboring row -- using the
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* current row as their source segment.
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*
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* There's one exception to this, however: if a dirty range hasn't been
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* modified during the horizontal propagation step, i.e., if its
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* `modified` flag is clear, then it necessarily doesn't affect the
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* neighboring pixels of the source segment. Hence, in this case, we can
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* avoid pushing a corresponding segment for the row of the source
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* segment.
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*
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*
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* +---+---+---+---+ . . . +---+---+ . .
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* Source | | | | | | | |
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* +---+---+---+---+---+---+---+---+---+---+ . .
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* Current | | | | | | | | |
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* +---+---+---+---+---+---+---+---+---+---+ . .
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* | | | | | | | | | |
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* +---+---+---+---+ . +---+ +---+---+ . .
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*
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* |---------------| |---| |-------|
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* Modified Modified
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*
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* New segments, corresponding to the dirty
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* ranges, are pushed into the queue for each
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* of the current segment's neighboring rows.
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* No segments are pushed for the row of the
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* source segment for non-modified dirty
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* ranges.
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*
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* To amortize the cost of maintaining and processing multiple separate
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* segments, dirty ranges that are separated by a small-enough gap are
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* coalesced into a single range prior to this step; the gap between the
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* ranges, if exists, becomes part of the coalesced range; the `modified`
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* flag of the coalesced range is the logical-OR of the `modified` flags
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* of the individual ranges.
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*
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* Start and Termination
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* ---------------------
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*
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* Recall that segments are pushed into the queue as a result of a change in
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* the water level of a neighboring segment. To kick this process off, we
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* pretend that the water level outside the image instantaneously dropped from
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* 1 to 0, and push four segments, referred to as the "seed segments",
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* corresponding to the four edges of the image (there may, in fact, be less
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* than four seed segments, if the image is 1- or 2-pixel wide or high.) The
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* source segment of the seed segments, hypothetically, lies outside the image;
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* in particular, the water level of the neighboring pixels in the vertical
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* propagation step is taken to be 0 for the seed segments.
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*
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* +-----------------------------------+
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* | |
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* +---+---------------------------+---+
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* | | | |
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* | | | |
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* | | | |
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* | | | |
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* | | | |
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* | | | |
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* | | | |
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* +---+---------------------------+---+
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* | |
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* +-----------------------------------+
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*
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* The four seed segments -- one for each
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* edge of the image.
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*
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* The process terminates when there are no more segments left in the queue.
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* At this point, the automaton has converged, and the water level corresponds
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* to the output of the flood operation.
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*
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* Coordinate Systems
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* ------------------
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*
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* As mentioned above, segments can be either horizontal or vertical, but are
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* treated internally as horizontal. Additionally, the region-of-interest
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* (ROI) of the operation might not span the entire image; in this case, the
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* operation is performed on the ROI in isolation, and what we've been calling
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* the "image" up until now is in fact the ROI (in particular, the ground level
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* outside the ROI is considered to be 0, even if the input image isn't
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* completely black outside the ROI.)
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*
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* To deal with this, we employ three coordinate systems:
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*
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* - Image-physical: This is the "real" coordinate system of the operation,
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* used when talking to the outside world (i.e., GEGL). Its origin is at
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* the top-left corner of the image, its x-axis points right, and its y-
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* axis points down.
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*
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* - Image-virtual: This is the same as the image-physical coordinate
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* system, except that the x- and y-coordinates are swapped when dealing
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* with vertical segments. In other words, when processing a vertical
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* segment, we pretend that image is transposed (i.e., reflected along the
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* south-east diagonal). We transform to/from this coordinate system on
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* the boundary between GEGL and the rest of the algorithm.
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*
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* - ROI-virtual: This is the same as the image-virtual coordinate system,
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* except that its origin is translated to the top-left corner of the ROI.
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* Internal coordinates, that aren't communicated to GEGL, are given in
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* this coordinate system.
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*
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* x y
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* +----> - - - - - - -+ +----> - - - - - - -+ +- - - - - - - - - -+
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* y | | x | | | y |
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* | +- - - - -+ | +- - - - -+ +----> - -+
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* v | | | v | | | | x | | |
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* ROI ROI | ROI
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* | | | | | | | | | v | |
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* +- - - - -+ +- - - - -+ +- - - - -+
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* | | | | | |
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* +- - - - - - - - - -+ +- - - - - - - - - -+ +- - - - - - - - - -+
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*
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* (a) (b) (c)
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*
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* The three coordinate systems: (a) image-
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* physical, (b) image-virtual (here shown
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* transposed), and (c) ROI-virtual.
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*
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* To sum it up, internal coordinates (e.g., the y-coordinate of the current
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* segment, or the x-coordinates of the dirty ranges) are given in the ROI-
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* virtual coordinate system. Coordinates of `GeglRectangle`s (such as the ROI
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* rectangle, or the rectangles used when reading and writing to the GEGL
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* buffers) are given in the image-virtual coordinate system, but are
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* transformed to/from the image-physical coordinate system before being
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* passed-to/received-from GEGL.
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/* Implementation of the Flood algorithm.
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* See http://wiki.gimp.org/wiki/Algorithms:Flood for details.
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*/
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@ -601,6 +238,7 @@ gimp_operation_flood_class_init (GimpOperationFloodClass *klass)
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"name", "gimp:flood",
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"categories", "gimp",
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"description", "GIMP Flood operation",
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"reference", "http://wiki.gimp.org/wiki/Algorithms:Flood",
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"reference-image", "flood-output.png",
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"reference-composition", reference_xml,
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NULL);
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@ -978,8 +978,9 @@ register_selection_procs (GimpPDB *pdb)
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"gimp-selection-flood");
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gimp_procedure_set_static_strings (procedure,
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"gimp-selection-flood",
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"Flood the image's selection",
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"This procedure floods the selection. Flooding assigns to each pixel of the selection mask the minimum of the maxima of all paths from that pixel to the outside, as if the selection mask were a height map of a terrain flooded with water.",
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"Remove holes from the image's selection",
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"This procedure removes holes from the selection, that can come from selecting a patchy area with the Fuzzy Select Tool. "
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"In technical terms this procedure floods the selection. See the Algorithms page in the developer wiki for details.",
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"Ell",
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"Ell",
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"2016",
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