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|
# coding: utf-8
# /*##########################################################################
# Copyright (C) 2018-2020 European Synchrotron Radiation Facility
#
# Permission is hereby granted, free of charge, to any person obtaining a copy
# of this software and associated documentation files (the "Software"), to deal
# in the Software without restriction, including without limitation the rights
# to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
# copies of the Software, and to permit persons to whom the Software is
# furnished to do so, subject to the following conditions:
#
# The above copyright notice and this permission notice shall be included in
# all copies or substantial portions of the Software.
#
# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
# IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
# AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
# LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
# OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
# THE SOFTWARE.
#
# ############################################################################*/
"""
Marching squares implementation based on a merge of segements and polygons.
"""
__authors__ = ["Almar Klein", "Jerome Kieffer", "Valentin Valls"]
__license__ = "MIT"
__date__ = "23/04/2018"
import numpy
cimport numpy as cnumpy
from libcpp.vector cimport vector
from libcpp.list cimport list as clist
from libcpp.set cimport set as cset
from libcpp.map cimport map
from libcpp cimport bool
from libc.math cimport fabs
from libc.math cimport floor
from cython.parallel import prange
from cython.operator cimport dereference
from cython.operator cimport preincrement
cimport libc.stdlib
cimport libc.string
cimport cython
from ...utils._have_openmp cimport COMPILED_WITH_OPENMP
"""Store in the module if it was compiled with OpenMP"""
cdef double EPSILON = numpy.finfo(numpy.float64).eps
# Windows compatibility: Cross-platform INFINITY
from libc.float cimport DBL_MAX
cdef double INFINITY = DBL_MAX + DBL_MAX
# from libc.math cimport INFINITY
cdef extern from "include/patterns.h":
cdef unsigned char EDGE_TO_POINT[][2]
cdef unsigned char CELL_TO_EDGE[][5]
cdef struct coord_t:
short x
short y
ctypedef cnumpy.uint32_t point_index_t
"""Type of the unique index identifying a connection for the polygons."""
"""Define a point of a polygon."""
cdef struct point_t:
cnumpy.float32_t x
cnumpy.float32_t y
"""Description of a non-final polygon."""
cdef cppclass PolygonDescription:
point_index_t begin
point_index_t end
clist[point_t] points
PolygonDescription() nogil:
pass
"""Description of a tile context.
It contains structure to store intermediate and final data of a thread.
Pixels and contours structures are merged together as it looks to have
mostly no cost.
"""
cdef cppclass TileContext:
int pos_x
int pos_y
int dim_x
int dim_y
# Only used to find contours
clist[PolygonDescription*] final_polygons
map[point_index_t, PolygonDescription*] polygons
# Only used to find pixels
clist[coord_t] final_pixels
cset[coord_t] pixels
TileContext() nogil:
pass
cdef class _MarchingSquaresAlgorithm(object):
"""Abstract class managing a marching squares algorithm.
It provides common methods to execute the process, with the support of
OpenMP, plus some hooks. Mostly created to be able to reuse part of the
logic between `_MarchingSquaresContours` and `_MarchingSquaresPixels`.
"""
cdef cnumpy.float32_t *_image_ptr
cdef cnumpy.int8_t *_mask_ptr
cdef int _dim_x
cdef int _dim_y
cdef int _group_size
cdef bool _use_minmax_cache
cdef bool _force_sequencial_reduction
cdef TileContext* _final_context
cdef cnumpy.float32_t *_min_cache
cdef cnumpy.float32_t *_max_cache
def __cinit__(self):
self._use_minmax_cache = False
self._force_sequencial_reduction = False
@cython.boundscheck(False)
@cython.wraparound(False)
@cython.cdivision(True)
cdef void marching_squares(self, cnumpy.float64_t level) nogil:
"""
Main method to execute the marching squares.
:param level: The level expected.
"""
cdef:
TileContext** contexts
TileContext** valid_contexts
int nb_contexts, nb_valid_contexts
int i, j
TileContext* context
int dim_x, dim_y
contexts = self.create_contexts(level, &dim_x, &dim_y, &nb_valid_contexts)
nb_contexts = dim_x * dim_y
if nb_valid_contexts == 0:
# shortcut
self._final_context = new TileContext()
libc.stdlib.free(contexts)
return
j = 0
valid_contexts = <TileContext **>libc.stdlib.malloc(nb_valid_contexts * sizeof(TileContext*))
for i in xrange(nb_contexts):
if contexts[i] != NULL:
valid_contexts[j] = contexts[i]
j += 1
# openmp
for i in prange(nb_valid_contexts, nogil=True):
self.marching_squares_mp(valid_contexts[i], level)
if nb_valid_contexts == 1:
# shortcut
self._final_context = valid_contexts[0]
libc.stdlib.free(valid_contexts)
libc.stdlib.free(contexts)
return
if self._force_sequencial_reduction:
self.sequencial_reduction(nb_valid_contexts, valid_contexts)
# FIXME can only be used if compiled with openmp
# elif copenmp.omp_get_num_threads() <= 1:
# self._sequencial_reduction(nb_valid_contexts, valid_contexts)
else:
self.reduction_2d(dim_x, dim_y, contexts)
libc.stdlib.free(valid_contexts)
libc.stdlib.free(contexts)
@cython.boundscheck(False)
@cython.wraparound(False)
@cython.cdivision(True)
cdef void reduction_2d(self, int dim_x, int dim_y, TileContext **contexts) nogil:
"""
Reduce the problem merging first neighbours together in a recursive
process. Optimized with OpenMP.
:param dim_x: Number of contexts in the x dimension
:param dim_y: Number of contexts in the y dimension
:param contexts: Array of contexts
"""
cdef:
int x1, y1, x2, y2, i1, i2
int delta = 1
while True:
if delta >= dim_x and delta >= dim_y:
break
# NOTE: Cython 0.21.1 is buggy with prange + steps
# It is needed to add a delta and the 'to'
# Here is what we can use with Cython 0.28:
# for i in prange(0, dim_x, (delta + delta)):
for i1 in prange(0, dim_x + (delta + delta - 1), delta + delta, nogil=True):
x1 = i1
if x1 + delta < dim_x:
y1 = 0
while y1 < dim_y:
self.merge_array_contexts(contexts, y1 * dim_x + x1, y1 * dim_x + x1 + delta)
y1 = y1 + delta
# NOTE: Cython 0.21.1 is buggy with prange + steps
# It is needed to add a delta and the 'to'
# Here is what we can use with Cython 0.28:
# for i in prange(0, dim_y, (delta + delta)):
for i2 in prange(0, dim_y + (delta + delta - 1), delta + delta, nogil=True):
y2 = i2
if y2 + delta < dim_y:
x2 = 0
while x2 < dim_x:
self.merge_array_contexts(contexts, y2 * dim_x + x2, (y2 + delta) * dim_x + x2)
x2 = x2 + delta + delta
delta <<= 1
self._final_context = contexts[0]
@cython.boundscheck(False)
@cython.wraparound(False)
@cython.cdivision(True)
cdef inline void merge_array_contexts(self,
TileContext **contexts,
int index1,
int index2) nogil:
"""
Merge contexts from `index2` to `index1` and delete the one from index2.
If the one from index1 was NULL, the one from index2 is moved to index1
and is not deleted.
This intermediate function was needed to avoid compilation problem of
Cython + OpenMP.
"""
cdef:
TileContext *context1
TileContext *context2
context1 = contexts[index1]
context2 = contexts[index2]
if context1 != NULL and context2 != NULL:
self.merge_context(context1, context2)
del context2
elif context2 != NULL:
contexts[index1] = context2
# for sanity
# contexts[index2] = NULL
@cython.boundscheck(False)
@cython.wraparound(False)
@cython.cdivision(True)
cdef void sequencial_reduction(self,
int nb_contexts,
TileContext **contexts) nogil:
"""
Reduce the problem sequencially without taking care of the topology
:param nb_contexts: Number of contexts
:param contexts: Array of contexts
"""
cdef:
int i
# merge
self._final_context = new TileContext()
for i in xrange(nb_contexts):
if contexts[i] != NULL:
self.merge_context(self._final_context, contexts[i])
del contexts[i]
@cython.boundscheck(False)
@cython.wraparound(False)
@cython.cdivision(True)
cdef void marching_squares_mp(self,
TileContext *context,
cnumpy.float64_t level) nogil:
"""
Main entry of the marching squares algorithm for each threads.
:param context: Context used by the thread to store data
:param level: The requested level
"""
cdef:
int x, y, pattern
cnumpy.float64_t tmpf
cnumpy.float32_t *image_ptr
cnumpy.int8_t *mask_ptr
image_ptr = self._image_ptr + (context.pos_y * self._dim_x + context.pos_x)
if self._mask_ptr != NULL:
mask_ptr = self._mask_ptr + (context.pos_y * self._dim_x + context.pos_x)
else:
mask_ptr = NULL
for y in range(context.pos_y, context.pos_y + context.dim_y):
for x in range(context.pos_x, context.pos_x + context.dim_x):
# Calculate index.
pattern = 0
if image_ptr[0] > level:
pattern += 1
if image_ptr[1] > level:
pattern += 2
if image_ptr[self._dim_x] > level:
pattern += 8
if image_ptr[self._dim_x + 1] > level:
pattern += 4
# Resolve ambiguity
if pattern == 5 or pattern == 10:
# Calculate value of cell center (i.e. average of corners)
tmpf = 0.25 * (image_ptr[0] +
image_ptr[1] +
image_ptr[self._dim_x] +
image_ptr[self._dim_x + 1])
# If below level, swap
if tmpf <= level:
if pattern == 5:
pattern = 10
else:
pattern = 5
# Cache mask information
if mask_ptr != NULL:
# Note: Store the mask in the index. It could be usefull to
# generate accurate segments in some cases, but yet it
# is not used
if mask_ptr[0] > 0:
pattern += 16
if mask_ptr[1] > 0:
pattern += 32
if mask_ptr[self._dim_x] > 0:
pattern += 128
if mask_ptr[self._dim_x + 1] > 0:
pattern += 64
mask_ptr += 1
if pattern < 16 and pattern != 0 and pattern != 15:
self.insert_pattern(context, x, y, pattern, level)
image_ptr += 1
# There is a missing pixel at the end of each rows
image_ptr += self._dim_x - context.dim_x
if mask_ptr != NULL:
mask_ptr += self._dim_x - context.dim_x
self.after_marching_squares(context)
@cython.boundscheck(False)
@cython.wraparound(False)
@cython.cdivision(True)
cdef void after_marching_squares(self, TileContext *context) nogil:
"""
Called by each threads after execution of the marching squares
algorithm. Called before merging together the contextes.
:param context: Context used by the thread to store data
"""
pass
@cython.boundscheck(False)
@cython.wraparound(False)
@cython.cdivision(True)
cdef void insert_pattern(self,
TileContext *context,
int x,
int y,
int pattern,
cnumpy.float64_t level) nogil:
"""
Called by the marching squares algorithm each time a pattern is found.
:param context: Context used by the thread to store data
:param x: X location of the pattern
:param y: Y location of the pattern
:param pattern: Binary-field identifying lower and higher pixel levels
:param level: The requested level
"""
pass
@cython.boundscheck(False)
@cython.wraparound(False)
@cython.cdivision(True)
cdef void merge_context(self,
TileContext *context,
TileContext *other) nogil:
"""
Merge into a context another context.
:param context: Context which will contains the merge result
:param other: Context to merge into the other one. The merging process
is destructive. The context may returns empty.
"""
pass
@cython.boundscheck(False)
@cython.wraparound(False)
@cython.cdivision(True)
cdef TileContext** create_contexts(self,
cnumpy.float64_t level,
int* dim_x,
int* dim_y,
int* nb_valid_contexts) nogil:
"""
Create and initialize a 2d-array of contexts.
If the minmax cache is used, only useful context will be created.
Thous with the minmax range excluding the level will not be created and
will have a `NULL` reference in the context array.
:param level: The requested level
:param dim_x: Resulting X dimension of context array
:param dim_x: Resulting Y dimension of context array
:param nb_valid_contexts: Resulting number of created contexts
:return: The context array
"""
cdef:
int context_dim_x, context_dim_y
int context_size, valid_contexts
int x, y
int icontext
TileContext* context
TileContext** contexts
context_dim_x = self._dim_x // self._group_size + (self._dim_x % self._group_size > 0)
context_dim_y = self._dim_y // self._group_size + (self._dim_y % self._group_size > 0)
context_size = context_dim_x * context_dim_y
contexts = <TileContext **>libc.stdlib.malloc(context_size * sizeof(TileContext*))
libc.string.memset(contexts, 0, context_size * sizeof(TileContext*))
valid_contexts = 0
icontext = 0
y = 0
while y < self._dim_y - 1:
x = 0
while x < self._dim_x - 1:
if self._use_minmax_cache:
if level < self._min_cache[icontext] or level > self._max_cache[icontext]:
icontext += 1
x += self._group_size
continue
context = self.create_context(x, y, self._group_size, self._group_size)
contexts[icontext] = context
icontext += 1
valid_contexts += 1
x += self._group_size
y += self._group_size
# dereference is not working here... then we uses array index but
# it is not the proper way
dim_x[0] = context_dim_x
dim_y[0] = context_dim_y
nb_valid_contexts[0] = valid_contexts
return contexts
@cython.boundscheck(False)
@cython.wraparound(False)
@cython.cdivision(True)
cdef TileContext *create_context(self,
int x,
int y,
int dim_x,
int dim_y) nogil:
"""
Allocate and initialize a context.
:param x: Left location of the context into the image
:param y: Top location of the context into the image
:param dim_x: Size of the context in the X dimension of the image
:param dim_y: Size of the context in the Y dimension of the image
:return: The context
"""
cdef:
TileContext *context
context = new TileContext()
context.pos_x = x
context.pos_y = y
context.dim_x = dim_x
context.dim_y = dim_y
if x + context.dim_x > self._dim_x - 1:
context.dim_x = self._dim_x - 1 - x
if y + context.dim_y > self._dim_y - 1:
context.dim_y = self._dim_y - 1 - y
if context.dim_x <= 0 or context.dim_y <= 0:
del context
return NULL
return context
@cython.boundscheck(False)
@cython.wraparound(False)
@cython.cdivision(True)
cdef void compute_point(self,
cnumpy.uint32_t x,
cnumpy.uint32_t y,
cnumpy.uint8_t edge,
cnumpy.float64_t level,
point_t *result_point) nogil:
"""
Compute the location of a point of the polygons according to the level
and the neighbours.
:param x: X location of the 4-pixels
:param y: Y location of the 4-pixels
:param edge: Enumeration identifying the 2-pixels to process
:param level: The requested level
:param result_point: Resulting value of the point
"""
cdef:
int dx1, dy1, index1
int dx2, dy2, index2
cnumpy.float64_t fx, fy, ff, weight1, weight2
# Use these to look up the relative positions of the pixels to interpolate
dx1, dy1 = EDGE_TO_POINT[edge][0], EDGE_TO_POINT[edge][1]
dx2, dy2 = EDGE_TO_POINT[edge + 1][0], EDGE_TO_POINT[edge + 1][1]
# Define "strength" of each corner of the cube that we need
index1 = (y + dy1) * self._dim_x + x + dx1
index2 = (y + dy2) * self._dim_x + x + dx2
weight1 = 1.0 / (EPSILON + fabs(self._image_ptr[index1] - level))
weight2 = 1.0 / (EPSILON + fabs(self._image_ptr[index2] - level))
# Apply a kind of center-of-mass method
fx, fy, ff = 0.0, 0.0, 0.0
fx += dx1 * weight1
fy += dy1 * weight1
ff += weight1
fx += dx2 * weight2
fy += dy2 * weight2
ff += weight2
fx /= ff
fy /= ff
result_point.x = x + fx
result_point.y = y + fy
@cython.boundscheck(False)
@cython.wraparound(False)
@cython.cdivision(True)
cdef void compute_ipoint(self,
cnumpy.uint32_t x,
cnumpy.uint32_t y,
cnumpy.uint8_t edge,
cnumpy.float64_t level,
coord_t *result_coord) nogil:
"""
Compute the location of pixel which contains the point of the polygons
according to the level and the neighbours.
This implementation is supposed to be faster than `compute_point` when
we only request the location of the pixel.
:param x: X location of the 4-pixels
:param y: Y location of the 4-pixels
:param edge: Enumeration identifying the 2-pixels to process
:param level: The requested level
:param result_coord: Resulting location of the pixel
"""
cdef:
int dx1, dy1, index1
int dx2, dy2, index2
cnumpy.float64_t fx, fy, ff, weight1, weight2
# Use these to look up the relative positions of the pixels to interpolate
dx1, dy1 = EDGE_TO_POINT[edge][0], EDGE_TO_POINT[edge][1]
dx2, dy2 = EDGE_TO_POINT[edge + 1][0], EDGE_TO_POINT[edge + 1][1]
# Define "strength" of each corner of the cube that we need
index1 = (y + dy1) * self._dim_x + x + dx1
index2 = (y + dy2) * self._dim_x + x + dx2
weight1 = EPSILON + fabs(self._image_ptr[index1] - level)
weight2 = EPSILON + fabs(self._image_ptr[index2] - level)
# Apply a kind of center-of-mass method
if edge == 0:
result_coord.x = x + (weight1 > weight2)
result_coord.y = y
elif edge == 1:
result_coord.x = x + 1
result_coord.y = y + (weight1 > weight2)
elif edge == 2:
result_coord.x = x + (weight1 < weight2)
result_coord.y = y + 1
elif edge == 3:
result_coord.x = x
result_coord.y = y + (weight1 < weight2)
@cython.boundscheck(False)
@cython.wraparound(False)
@cython.cdivision(True)
cdef point_index_t create_point_index(self, int yx, cnumpy.uint8_t edge) nogil:
"""
Create a unique identifier for a point of a polygon based on the
pattern location and the edge.
A index can be shared by different pixel coordinates. For example,
the index of the tuple (x=0, y=0, edge=2) is equal to the one of
(x=1, y=0, edge=0).
:param yx: Index of the location of the pattern in the image
:param edge: Enumeration identifying the edge of the pixel
:return: An index
"""
if edge == 2:
yx += self._dim_x
edge = 0
elif edge == 1:
yx += 1
elif edge == 3:
edge = 1
# Reserve the zero value
yx += 1
return edge + (yx << 1)
cdef class _MarchingSquaresContours(_MarchingSquaresAlgorithm):
"""Implementation of the marching squares algorithm to find iso contours.
"""
@cython.boundscheck(False)
@cython.wraparound(False)
@cython.cdivision(True)
cdef void insert_pattern(self,
TileContext *context,
int x,
int y,
int pattern,
cnumpy.float64_t level) nogil:
cdef:
int segment
for segment in range(CELL_TO_EDGE[pattern][0]):
begin_edge = CELL_TO_EDGE[pattern][1 + segment * 2 + 0]
end_edge = CELL_TO_EDGE[pattern][1 + segment * 2 + 1]
self.insert_segment(context, x, y, begin_edge, end_edge, level)
@cython.boundscheck(False)
@cython.wraparound(False)
@cython.cdivision(True)
cdef void insert_segment(self, TileContext *context,
int x, int y,
cnumpy.uint8_t begin_edge,
cnumpy.uint8_t end_edge,
cnumpy.float64_t level) nogil:
cdef:
int i, yx
point_t point
point_index_t begin, end
PolygonDescription *description
PolygonDescription *description_begin
PolygonDescription *description_end
map[point_index_t, PolygonDescription*].iterator it_begin
map[point_index_t, PolygonDescription*].iterator it_end
yx = self._dim_x * y + x
begin = self.create_point_index(yx, begin_edge)
end = self.create_point_index(yx, end_edge)
it_begin = context.polygons.find(begin)
it_end = context.polygons.find(end)
if it_begin == context.polygons.end() and it_end == context.polygons.end():
# insert a new polygon
description = new PolygonDescription()
description.begin = begin
description.end = end
self.compute_point(x, y, begin_edge, level, &point)
description.points.push_back(point)
self.compute_point(x, y, end_edge, level, &point)
description.points.push_back(point)
context.polygons[begin] = description
context.polygons[end] = description
elif it_begin == context.polygons.end():
# insert the beginning point to an existing polygon
self.compute_point(x, y, begin_edge, level, &point)
description = dereference(it_end).second
context.polygons.erase(it_end)
if end == description.begin:
# insert at start
description.points.push_front(point)
description.begin = begin
context.polygons[begin] = description
else:
# insert on tail
description.points.push_back(point)
description.end = begin
context.polygons[begin] = description
elif it_end == context.polygons.end():
# insert the ending point to an existing polygon
self.compute_point(x, y, end_edge, level, &point)
description = dereference(it_begin).second
context.polygons.erase(it_begin)
if begin == description.begin:
# insert at start
description.points.push_front(point)
description.begin = end
context.polygons[end] = description
else:
# insert on tail
description.points.push_back(point)
description.end = end
context.polygons[end] = description
else:
# merge 2 polygons using this segment
description_begin = dereference(it_begin).second
description_end = dereference(it_end).second
if description_begin == description_end:
# The segment closes a polygon
# FIXME: this intermediate assign is not needed
point = description_begin.points.front()
description_begin.points.push_back(point)
context.polygons.erase(begin)
context.polygons.erase(end)
context.final_polygons.push_back(description_begin)
else:
if ((begin == description_begin.begin or end == description_begin.begin) and
(begin == description_end.end or end == description_end.end)):
# worst case, let's make it faster
description = description_end
description_end = description_begin
description_begin = description
# FIXME: We can recycle a description instead of creating a new one
description = new PolygonDescription()
# Make sure the last element of the list is the one to connect
if description_begin.begin == begin or description_begin.begin == end:
# O(n)
description_begin.points.reverse()
description.begin = description_begin.end
else:
description.begin = description_begin.begin
# O(1)
description.points.splice(description.points.end(), description_begin.points)
# Make sure the first element of the list is the one to connect
if description_end.end == begin or description_end.end == end:
description_end.points.reverse()
description.end = description_end.begin
else:
description.end = description_end.end
description.points.splice(description.points.end(), description_end.points)
context.polygons.erase(it_begin)
context.polygons.erase(it_end)
context.polygons[description.begin] = description
context.polygons[description.end] = description
@cython.boundscheck(False)
@cython.wraparound(False)
@cython.cdivision(True)
cdef void merge_context(self, TileContext *context, TileContext *other) nogil:
cdef:
map[point_index_t, PolygonDescription*].iterator it_begin
map[point_index_t, PolygonDescription*].iterator it_end
map[point_index_t, PolygonDescription*].iterator it
PolygonDescription *description_other
PolygonDescription *description
PolygonDescription *description2
point_index_t point_index
vector[PolygonDescription*] mergeable_polygons
size_t i
# merge final polygons
context.final_polygons.splice(context.final_polygons.end(), other.final_polygons)
# mergeable_polygons.reserve(other.polygons.size() / 2)
it = other.polygons.begin()
while it != other.polygons.end():
point_index = dereference(it).first
description_other = dereference(it).second
if description_other.begin == point_index:
mergeable_polygons.push_back(description_other)
preincrement(it)
for i in range(mergeable_polygons.size()):
description_other = mergeable_polygons[i]
it_begin = context.polygons.find(description_other.begin)
it_end = context.polygons.find(description_other.end)
if it_begin == context.polygons.end() and it_end == context.polygons.end():
# It's a new polygon
context.polygons[description_other.begin] = description_other
context.polygons[description_other.end] = description_other
elif it_end == context.polygons.end():
# The head of the polygon have to be merged
description = dereference(it_begin).second
context.polygons.erase(description.begin)
context.polygons.erase(description.end)
if description.begin == description_other.begin:
description.begin = description.end
description.points.reverse()
description.end = description_other.end
# remove the dup element
description_other.points.pop_front()
description.points.splice(description.points.end(), description_other.points)
context.polygons[description.begin] = description
context.polygons[description.end] = description
del description_other
elif it_begin == context.polygons.end():
# The tail of the polygon have to be merged
description = dereference(it_end).second
context.polygons.erase(description.begin)
context.polygons.erase(description.end)
if description.begin == description_other.end:
description.begin = description.end
description.points.reverse()
description.end = description_other.begin
description_other.points.reverse()
# remove the dup element
description_other.points.pop_front()
description.points.splice(description.points.end(), description_other.points)
context.polygons[description.begin] = description
context.polygons[description.end] = description
del description_other
else:
# Both sides have to be merged
description = dereference(it_begin).second
description2 = dereference(it_end).second
if description == description2:
# It became a closed polygon
context.polygons.erase(description.begin)
context.polygons.erase(description.end)
if description.begin == description_other.begin:
description.begin = description.end
description.points.reverse()
description.end = description_other.end
# remove the dup element
description_other.points.pop_front()
description.points.splice(description.points.end(), description_other.points)
context.final_polygons.push_back(description)
del description_other
else:
context.polygons.erase(description.begin)
context.polygons.erase(description.end)
context.polygons.erase(description2.begin)
context.polygons.erase(description2.end)
if description.begin == description_other.begin:
description.begin = description.end
description.points.reverse()
if description2.end == description_other.end:
description.end = description2.begin
description2.points.reverse()
else:
description.end = description2.end
description_other.points.pop_front()
description2.points.pop_front()
description.points.splice(description.points.end(), description_other.points)
description.points.splice(description.points.end(), description2.points)
context.polygons[description.begin] = description
context.polygons[description.end] = description
del description_other
del description2
@cython.boundscheck(False)
@cython.wraparound(False)
@cython.cdivision(True)
cdef extract_polygons(self):
cdef:
size_t i
int i_pixel
cnumpy.uint8_t index
map[point_index_t, PolygonDescription*].iterator it
vector[PolygonDescription*] descriptions
clist[point_t].iterator it_points
PolygonDescription *description
cnumpy.float32_t[:, ::1] polygon
if self._final_context == NULL:
return []
# move all the polygons in a final structure
with nogil:
it = self._final_context.polygons.begin()
while it != self._final_context.polygons.end():
description = dereference(it).second
if dereference(it).first == description.begin:
# polygones are stored 2 times
# only use one
descriptions.push_back(description)
preincrement(it)
self._final_context.polygons.clear()
descriptions.insert(descriptions.end(),
self._final_context.final_polygons.begin(),
self._final_context.final_polygons.end())
self._final_context.final_polygons.clear()
del self._final_context
self._final_context = NULL
# create result and clean up allocated memory
polygons = []
for i in range(descriptions.size()):
description = descriptions[i]
polygon = numpy.empty((description.points.size(), 2), dtype=numpy.float32)
it_points = description.points.begin()
i_pixel = 0
while it_points != description.points.end():
polygon[i_pixel, 0] = dereference(it_points).y
polygon[i_pixel, 1] = dereference(it_points).x
i_pixel += 1
preincrement(it_points)
polygons.append(numpy.asarray(polygon))
del description
return polygons
cdef class _MarchingSquaresPixels(_MarchingSquaresAlgorithm):
"""Implementation of the marching squares algorithm to find pixels of the
image containing points of the polygons of the iso contours.
"""
@cython.boundscheck(False)
@cython.wraparound(False)
@cython.cdivision(True)
cdef void insert_pattern(self,
TileContext *context,
int x,
int y,
int pattern,
cnumpy.float64_t level) nogil:
cdef:
int segment
for segment in range(CELL_TO_EDGE[pattern][0]):
begin_edge = CELL_TO_EDGE[pattern][1 + segment * 2 + 0]
end_edge = CELL_TO_EDGE[pattern][1 + segment * 2 + 1]
self.insert_segment(context, x, y, begin_edge, end_edge, level)
@cython.boundscheck(False)
@cython.wraparound(False)
@cython.cdivision(True)
cdef void insert_segment(self, TileContext *context,
int x, int y,
cnumpy.uint8_t begin_edge,
cnumpy.uint8_t end_edge,
cnumpy.float64_t level) nogil:
cdef:
coord_t coord
self.compute_ipoint(x, y, begin_edge, level, &coord)
context.pixels.insert(coord)
self.compute_ipoint(x, y, end_edge, level, &coord)
context.pixels.insert(coord)
@cython.boundscheck(False)
@cython.wraparound(False)
@cython.cdivision(True)
cdef void after_marching_squares(self, TileContext *context) nogil:
cdef:
coord_t coord
cset[coord_t].iterator it_coord
cset[coord_t].iterator it_coord_erase
pass
it_coord = context.pixels.begin()
while it_coord != context.pixels.end():
coord = dereference(it_coord)
if (coord.x > context.pos_x and coord.x < context.pos_x + context.dim_x - 1 and
coord.y > context.pos_y and coord.y < context.pos_y + context.dim_y - 1):
it_coord_erase = it_coord
preincrement(it_coord)
context.pixels.erase(it_coord_erase)
context.final_pixels.push_back(coord)
else:
preincrement(it_coord)
@cython.boundscheck(False)
@cython.wraparound(False)
@cython.cdivision(True)
cdef void merge_context(self, TileContext *context, TileContext *other) nogil:
cdef:
cset[coord_t].iterator it_coord
# merge final pixels
context.final_pixels.splice(context.final_pixels.end(), other.final_pixels)
# merge final pixels
# NOTE: This is not declared in Cython
# context.final_pixels.insert(other.final_pixels.begin(), other.final_pixels.end())
it_coord = other.pixels.begin()
while it_coord != other.pixels.end():
context.pixels.insert(dereference(it_coord))
preincrement(it_coord)
@cython.boundscheck(False)
@cython.wraparound(False)
@cython.cdivision(True)
cdef extract_pixels(self):
cdef:
int i, x, y
point_index_t index
cset[coord_t].iterator it
clist[coord_t].iterator it_coord
coord_t coord
cnumpy.int32_t[:, ::1] pixels
if self._final_context == NULL:
return numpy.empty((0, 2), dtype=numpy.int32)
# create result
it = self._final_context.pixels.begin()
while it != self._final_context.pixels.end():
coord = dereference(it)
self._final_context.final_pixels.push_back(coord)
preincrement(it)
pixels = numpy.empty((self._final_context.final_pixels.size(), 2), dtype=numpy.int32)
i = 0
it_coord = self._final_context.final_pixels.begin()
while it_coord != self._final_context.final_pixels.end():
coord = dereference(it_coord)
pixels[i, 0] = coord.y
pixels[i, 1] = coord.x
i += 1
preincrement(it_coord)
del self._final_context
self._final_context = NULL
return numpy.asarray(pixels)
cdef class MarchingSquaresMergeImpl(object):
"""
Marching squares implementation based on a merge of segements and polygons.
The main logic is based on the common marching squares algorithms.
Segments of the iso-valued contours are identified using a pattern based
on blocks of 2*2 pixels. The image is read sequencially and when a segment
is identified it is inserted at a right place is a set of valid polygons.
This process can grow up polygons on bounds, or merge polygons together.
The algorithm can take care of a mask. If a pixel is invalidated by a
non-zero value of the mask at it's location, the computation of the pattern
cancelled and no segements are generated.
This implementation based on merge allow to use divide and conquer
implementation in multi process using OpenMP.The image is subdivised into
many tiles, each one is processed independantly. The result is finally
reduced by consecutives polygon merges.
The OpenMP group size can also by used to skip part of the image using
pre-computed informations. `use_minmax_cache` can enable the computation of
minimum and maximum pixel levels available on each tile groups. It was
designed to improve the efficiency of the extraction of many contour levels
from the same gradient image.
Finally the implementation provides an implementation to reach polygons
(:meth:`find_contours`) or pixels (:meth:`find_pixels`) from the iso-valued
data.
.. code-block:: python
# Example using a mask
shape = 100, 100
image = numpy.random.random(shape)
mask = numpy.random.random(shape) < 0.01
ms = MarchingSquaresMergeImpl(image, mask)
polygons = ms.find_contours(level=0.5)
for polygon in polygons:
print(polygon)
.. code-block:: python
# Example using multi requests
shape = 1000, 1000
image = numpy.random.random(shape)
ms = MarchingSquaresMergeImpl(image)
levels = numpy.arange(0, 1, 0.05)
for level in levels:
polygons = ms.find_contours(level=level)
.. code-block:: python
# Efficient cache using multi requests
shape = 1000, 1000
image = numpy.arange(shape[0] * shape[1]) / (shape[0] * shape[1])
image.shape = shape
ms = MarchingSquaresMergeImpl(image, use_minmax_cache=True)
levels = numpy.arange(0, 1, 0.05)
for level in levels:
polygons = ms.find_contours(level=level)
:param numpy.ndarray image: Image to process.
If the image is not a continuous array of native float 32bits, the data
will be first normalized. This can reduce efficiency.
:param numpy.ndarray mask: An optional mask (a non-zero value invalidate
the pixels of the image)
If the image is not a continuous array of signed integer 8bits, the
data will be first normalized. This can reduce efficiency.
:param int group_size: Specify the size of the tile to split the
computation with OpenMP. It is also used as tile size to compute the
min/max cache
:param bool use_minmax_cache: If true the min/max cache is enabled.
"""
cdef cnumpy.float32_t[:, ::1] _image
cdef cnumpy.int8_t[:, ::1] _mask
cdef cnumpy.float32_t *_image_ptr
cdef cnumpy.int8_t *_mask_ptr
cdef int _dim_x
cdef int _dim_y
cdef int _group_size
cdef bool _use_minmax_cache
cdef cnumpy.float32_t *_min_cache
cdef cnumpy.float32_t *_max_cache
cdef _MarchingSquaresContours _contours_algo
cdef _MarchingSquaresPixels _pixels_algo
def __init__(self,
image, mask=None,
group_size=256,
use_minmax_cache=False):
if not isinstance(image, numpy.ndarray) or len(image.shape) != 2:
raise ValueError("Only 2D arrays are supported.")
if image.shape[0] < 2 or image.shape[1] < 2:
raise ValueError("Input array must be at least 2x2.")
# Force contiguous native array
self._image = numpy.ascontiguousarray(image, dtype='=f4')
self._image_ptr = &self._image[0][0]
if mask is not None:
if not isinstance(mask, numpy.ndarray):
raise ValueError("Only 2D arrays are supported.")
if image.shape != mask.shape:
raise ValueError("Mask size and image size must be the same.")
# Force contiguous native array
self._mask = numpy.ascontiguousarray(mask, dtype='=i1')
self._mask_ptr = &self._mask[0][0]
else:
self._mask = None
self._mask_ptr = NULL
self._group_size = group_size
self._use_minmax_cache = use_minmax_cache
self._min_cache = NULL
self._max_cache = NULL
with nogil:
self._dim_y = self._image.shape[0]
self._dim_x = self._image.shape[1]
self._contours_algo = None
self._pixels_algo = None
def __dealloc__(self):
if self._min_cache != NULL:
libc.stdlib.free(self._min_cache)
if self._max_cache != NULL:
libc.stdlib.free(self._max_cache)
@cython.boundscheck(False)
@cython.wraparound(False)
@cython.cdivision(True)
cdef void _compute_minmax_on_block(self, int block_x, int block_y, int block_index) nogil:
"""
Initialize the minmax cache.
The cache is computed for each tiles of the image. It reuses the OpenMP
group size for the size of the tile, which allow to skip a full OpenMP
context in case the requested level do not match the cache.
The minmax is compuded with an overlap of 1 pixel, in order to match
the marching squares algorithm.
The mask is taking into accound. As result if a tile is fully masked,
the minmax cache result for this tile will have infinit values.
:param block_x: X location of tile in block unit
:param block_y: Y location of tile in block unit
:param block_index: Index of the tile in the minmax cache structure
"""
cdef:
int x, y
int pos_x, end_x, pos_y, end_y
cnumpy.float32_t minimum, maximum, value
cnumpy.float32_t *image_ptr
cnumpy.int8_t *mask_ptr
pos_x = block_x * self._group_size
end_x = pos_x + self._group_size + 1
if end_x > self._dim_x:
end_x = self._dim_x
pos_y = block_y * self._group_size
end_y = pos_y + self._group_size + 1
if end_y > self._dim_y:
end_y = self._dim_y
image_ptr = self._image_ptr + (pos_y * self._dim_x + pos_x)
if self._mask_ptr != NULL:
mask_ptr = self._mask_ptr + (pos_y * self._dim_x + pos_x)
else:
mask_ptr = NULL
minimum = INFINITY
maximum = -INFINITY
for y in range(pos_y, end_y):
for x in range(pos_x, end_x):
if mask_ptr != NULL:
if mask_ptr[0] != 0:
image_ptr += 1
mask_ptr += 1
continue
value = image_ptr[0]
if value < minimum:
minimum = value
if value > maximum:
maximum = value
image_ptr += 1
if mask_ptr != NULL:
mask_ptr += 1
image_ptr += self._dim_x + pos_x - end_x
if mask_ptr != NULL:
mask_ptr += self._dim_x + pos_x - end_x
self._min_cache[block_index] = minimum
self._max_cache[block_index] = maximum
@cython.boundscheck(False)
@cython.wraparound(False)
@cython.cdivision(True)
cdef void _create_minmax_cache(self) nogil:
"""
Create and initialize minmax cache.
"""
cdef:
int icontext, context_x, context_y
int context_dim_x, context_dim_y, context_size
context_dim_x = self._dim_x // self._group_size + (self._dim_x % self._group_size > 0)
context_dim_y = self._dim_y // self._group_size + (self._dim_y % self._group_size > 0)
context_size = context_dim_x * context_dim_y
self._min_cache = <cnumpy.float32_t *>libc.stdlib.malloc(context_size * sizeof(cnumpy.float32_t))
self._max_cache = <cnumpy.float32_t *>libc.stdlib.malloc(context_size * sizeof(cnumpy.float32_t))
for icontext in prange(context_size, nogil=True):
context_x = icontext % context_dim_x
context_y = icontext // context_dim_x
self._compute_minmax_on_block(context_x, context_y, icontext)
@cython.boundscheck(False)
@cython.wraparound(False)
@cython.cdivision(True)
def find_pixels(self, level):
"""
Compute the pixels from the image over the requested iso contours
at this `level`. Pixels are those over the bound of the segments.
:param float level: Level of the requested iso contours.
:returns: An array of y-x coordinates.
:rtype: numpy.ndarray
"""
if self._use_minmax_cache and self._min_cache == NULL:
self._create_minmax_cache()
if self._pixels_algo is None:
algo = _MarchingSquaresPixels()
algo._image_ptr = self._image_ptr
algo._mask_ptr = self._mask_ptr
algo._dim_x = self._dim_x
algo._dim_y = self._dim_y
algo._group_size = self._group_size
algo._use_minmax_cache = self._use_minmax_cache
algo._force_sequencial_reduction = COMPILED_WITH_OPENMP == 0
if self._use_minmax_cache:
algo._min_cache = self._min_cache
algo._max_cache = self._max_cache
self._pixels_algo = algo
else:
algo = self._pixels_algo
algo.marching_squares(level)
pixels = algo.extract_pixels()
return pixels
@cython.boundscheck(False)
@cython.wraparound(False)
@cython.cdivision(True)
def find_contours(self, level=None):
"""
Compute the list of polygons of the iso contours at this `level`.
:param float level: Level of the requested iso contours.
:returns: A list of array containg y-x coordinates of points
:rtype: List[numpy.ndarray]
"""
if self._use_minmax_cache and self._min_cache == NULL:
self._create_minmax_cache()
if self._contours_algo is None:
algo = _MarchingSquaresContours()
algo._image_ptr = self._image_ptr
algo._mask_ptr = self._mask_ptr
algo._dim_x = self._dim_x
algo._dim_y = self._dim_y
algo._group_size = self._group_size
algo._use_minmax_cache = self._use_minmax_cache
algo._force_sequencial_reduction = COMPILED_WITH_OPENMP == 0
if self._use_minmax_cache:
algo._min_cache = self._min_cache
algo._max_cache = self._max_cache
self._contours_algo = algo
else:
algo = self._contours_algo
algo.marching_squares(level)
polygons = algo.extract_polygons()
return polygons
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