#?-*-?coding:?utf-8?-*-

“““
morphsnakes
===========

This?is?a?Python?implementation?of?the?algorithms?introduced?in?the?paper

??Márquez-Neila?P.?Baumela?L.?álvarez?L.?“A?morphological?approach
??to?curvature-based?evolution?of?curves?and?surfaces“.?IEEE?Transactions
??on?Pattern?Analysis?and?Machine?Intelligence?（PAMI）?2013.

This?implementation?is?intended?to?be?as?brief?understandable?and?self-contained
as?possible.?It?does?not?include?any?enhancement?to?make?it?fast?or?efficient.

Any?practical?implementation?of?this?algorithm?should?work?only?over?the
neighbor?pixels?of?the?0.5-levelset?not?over?all?the?embedding?function
and?perhaps?should?feature?multi-threading?or?GPU?capabilities.

The?classes?MorphGAC?and?MorphACWE?provide?most?of?the?functionality?of?this
module.?They?implement?the?Morphological?Geodesic?Active?Contours?and?the
Morphological?Active?Contours?without?Edges?respectively.?See?the
aforementioned?paper?for?full?details.

See?test.py?for?examples?of?usage.
“““

__author__?=?“P.?Márquez?Neila?“

from?itertools?import?cycle

import?numpy?as?np
from?scipy?import?ndimage
from?scipy.ndimage?import?binary_dilation?binary_erosion?\
????????????????????????gaussian_filter?gaussian_gradient_magnitude

class?fcycle（object）:
????
????def?__init__（self?iterable）:
????????“““Call?functions?from?the?iterable?each?time?it?is?called.“““
????????self.funcs?=?cycle（iterable）
????
????def?__call__（self?*args?**kwargs）:
????????f?=?next（self.funcs）
????????return?f（*args?**kwargs）
????

#?SI?and?IS?operators?for?2D?and?3D.
_P2?=?[np.eye（3）?np.array（[[010]]*3）?np.flipud（np.eye（3））?np.rot90（[[010]]*3）]
_P3?=?[np.zeros（（333））?for?i?in?range（9）]

_P3[0][::1]?=?1
_P3[1][:1:]?=?1
_P3[2][1::]?=?1
_P3[3][:[012][012]]?=?1
_P3[4][:[012][210]]?=?1
_P3[5][[012]:[012]]?=?1
_P3[6][[012]:[210]]?=?1
_P3[7][[012][012]:]?=?1
_P3[8][[012][210]:]?=?1

_aux?=?np.zeros（（0））
def?SI（u）:
????“““SI?operator.“““
????global?_aux
????if?np.ndim（u）?==?2:
????????P?=?_P2
????elif?np.ndim（u）?==?3:
????????P?=?_P3
????else:
????????raise?ValueError（“u?has?an?invalid?number?of?dimensions?（should?be?2?or?3）“）
????
????if?u.shape?!=?_aux.shape[1:]:
????????_aux?=?np.zeros（（len（P））?+?u.shape）
????
????for?_aux_i?P_i?in?zip（_aux?P）:
????????_aux_i[:]?=?binary_erosion（u?P_i）
????
????return?_aux.max（0）

def?IS（u）:
????“““IS?operator.“““
????global?_aux
????if?np.ndim（u）?==?2:
????????P?=?_P2
????elif?np.ndim（u）?==?3:
????????P?=?_P3
????else:
????????raise?ValueError（“u?has?an?invalid?number?of?dimensions?（should?be?2?or?3）“）
????
????if?u.shape?!=?_aux.shape[1:]:
????????_aux?=?np.zeros（（len（P））?+?u.shape）
????
????for?_aux_i?P_i?in?zip（_aux?P）:
????????_aux_i[:]?=?binary_dilation（u?P_i）
????
????return?_aux.min（0）

#?SIoIS?operator.
SIoIS?=?lambda?u:?SI（IS（u））
ISoSI?=?lambda?u:?IS（SI（u））
curvop?=?fcycle（[SIoIS?ISoSI]）

#?Stopping?factors?（function?g（I）?in?the?paper）.
def?gborders（img?a