实施"基本法"的问题；波坍缩函数“；Python中的算法
简而言之： 我在Python2.7中的实现存在缺陷，但我无法确定问题所在。我需要帮助来找出我可能遗漏了什么或做错了什么 什么是波折叠函数算法？ 它是Maxim Gumin于2016年编写的一种算法，可以从样本图像生成程序模式。您可以在动作（二维重叠模型）和（三维平铺模型）中看到它 此实施的目标： 将算法（2D重叠模型）归结为其本质，并避免算法的重复性和笨拙性（令人惊讶的长且难以阅读）。这是一个尝试，使一个更短，更清晰和python版本的算法实施"基本法"的问题；波坍缩函数“；Python中的算法,python,algorithm,markov-chains,procedural-generation,Python,Algorithm,Markov Chains,Procedural Generation,简而言之： 我在Python2.7中的实现存在缺陷，但我无法确定问题所在。我需要帮助来找出我可能遗漏了什么或做错了什么 什么是波折叠函数算法？ 它是Maxim Gumin于2016年编写的一种算法，可以从样本图像生成程序模式。您可以在动作（二维重叠模型）和（三维平铺模型）中看到它 此实施的目标： 将算法（2D重叠模型）归结为其本质，并避免算法的重复性和笨拙性（令人惊讶的长且难以阅读）。这是一个尝试，使一个更短，更清晰和python版本的算法 if not inte
if not intersection:
print 'contradiction'
noLoop()
- 不是面向对象的（处于当前状态），因此更容易理解/更接近伪代码
- 正在使用一维阵列而不是二维阵列
- 正在使用数组切片进行矩阵操作
WTrueFalseTrueW = [[True for pattern in xrange(len(patterns))] for cell in xrange(20*20)]
HTrueW[22]TrueH[22]HTrueH = [entropyValue for cell in xrange(20*20)]
HH[22]W[22]TrueFalseW[22]246TrueFalse22246from collections import Counter
from itertools import chain, izip
import math
d = 20 # dimensions of output (array of dxd cells)
N = 3 # dimensions of a pattern (NxN matrix)
Output = [120 for i in xrange(d*d)] # array holding the color value for each cell in the output (at start each cell is grey = 120)
def setup():
size(800, 800, P2D)
textSize(11)
global W, H, A, freqs, patterns, directions, xs, ys, npat
img = loadImage('Flowers.png') # path to the input image
iw, ih = img.width, img.height # dimensions of input image
xs, ys = width//d, height//d # dimensions of cells (squares) in output
kernel = [[i + n*iw for i in xrange(N)] for n in xrange(N)] # NxN matrix to read every patterns contained in input image
directions = [(-1, 0), (1, 0), (0, -1), (0, 1)] # (x, y) tuples to access the 4 neighboring cells of a collapsed cell
all = [] # array list to store all the patterns found in input
# Stores the different patterns found in input
for y in xrange(ih):
for x in xrange(iw):
''' The one-liner below (cmat) creates a NxN matrix with (x, y) being its top left corner.
This matrix will wrap around the edges of the input image.
The whole snippet reads every NxN part of the input image and store the associated colors.
Each NxN part is called a 'pattern' (of colors). Each pattern can be rotated or flipped (not mandatory). '''
cmat = [[img.pixels[((x+n)%iw)+(((a[0]+iw*y)/iw)%ih)*iw] for n in a] for a in kernel]
# Storing rotated patterns (90°, 180°, 270°, 360°)
for r in xrange(4):
cmat = zip(*cmat[::-1]) # +90° rotation
all.append(cmat)
# Storing reflected patterns (vertical/horizontal flip)
all.append(cmat[::-1])
all.append([a[::-1] for a in cmat])
# Flatten pattern matrices + count occurences
''' Once every pattern has been stored,
- we flatten them (convert to 1D) for convenience
- count the number of occurences for each one of them (one pattern can be found multiple times in input)
- select unique patterns only
- store them from less common to most common (needed for weighted choice)'''
all = [tuple(chain.from_iterable(p)) for p in all] # flattern pattern matrices (NxN --> [])
c = Counter(all)
freqs = sorted(c.values()) # number of occurences for each unique pattern, in sorted order
npat = len(freqs) # number of unique patterns
total = sum(freqs) # sum of frequencies of unique patterns
patterns = [p[0] for p in c.most_common()[:-npat-1:-1]] # list of unique patterns sorted from less common to most common
# Computes entropy
''' The entropy of a cell is correlated to the number of possible patterns that cell holds.
The more a cell has valid patterns (set to 'True'), the higher its entropy is.
At start, every pattern is set to 'True' for each cell. So each cell holds the same high entropy value'''
ent = math.log(total) - sum(map(lambda x: x * math.log(x), freqs)) / total
# Initializes the 'wave' (W), entropy (H) and adjacencies (A) array lists
W = [[True for _ in xrange(npat)] for i in xrange(d*d)] # every pattern is set to 'True' at start, for each cell
H = [ent for i in xrange(d*d)] # same entropy for each cell at start (every pattern is valid)
A = [[set() for dir in xrange(len(directions))] for i in xrange(npat)] #see below for explanation
# Compute patterns compatibilities (check if some patterns are adjacent, if so -> store them based on their location)
''' EXAMPLE:
If pattern index 42 can placed to the right of pattern index 120,
we will store this adjacency rule as follow:
A[120][1].add(42)
Here '1' stands for 'right' or 'East'/'E'
0 = left or West/W
1 = right or East/E
2 = up or North/N
3 = down or South/S '''
# Comparing patterns to each other
for i1 in xrange(npat):
for i2 in xrange(npat):
for dir in (0, 2):
if compatible(patterns[i1], patterns[i2], dir):
A[i1][dir].add(i2)
A[i2][dir+1].add(i1)
def compatible(p1, p2, dir):
'''NOTE:
what is refered as 'columns' and 'rows' here below is not really columns and rows
since we are dealing with 1D patterns. Remember here N = 3'''
# If the first two columns of pattern 1 == the last two columns of pattern 2
# --> pattern 2 can be placed to the left (0) of pattern 1
if dir == 0:
return [n for i, n in enumerate(p1) if i%N!=2] == [n for i, n in enumerate(p2) if i%N!=0]
# If the first two rows of pattern 1 == the last two rows of pattern 2
# --> pattern 2 can be placed on top (2) of pattern 1
if dir == 2:
return p1[:6] == p2[-6:]
def draw(): # Equivalent of a 'while' loop in Processing (all the code below will be looped over and over until all cells are collapsed)
global H, W, grid
### OBSERVATION
# Find cell with minimum non-zero entropy (not collapsed yet)
'''Randomly select 1 cell at the first iteration (when all entropies are equal),
otherwise select cell with minimum non-zero entropy'''
emin = int(random(d*d)) if frameCount <= 1 else H.index(min(H))
# Stoping mechanism
''' When 'H' array is full of 'collapsed' cells --> stop iteration '''
if H[emin] == 'CONT' or H[emin] == 'collapsed':
print 'stopped'
noLoop()
return
### COLLAPSE
# Weighted choice of a pattern
''' Among the patterns available in the selected cell (the one with min entropy),
select one pattern randomly, weighted by the frequency that pattern appears in the input image.
With Python 2.7 no possibility to use random.choice(x, weight) so we have to hard code the weighted choice '''
lfreqs = [b * freqs[i] for i, b in enumerate(W[emin])] # frequencies of the patterns available in the selected cell
weights = [float(f) / sum(lfreqs) for f in lfreqs] # normalizing these frequencies
cumsum = [sum(weights[:i]) for i in xrange(1, len(weights)+1)] # cumulative sums of normalized frequencies
r = random(1)
idP = sum([cs < r for cs in cumsum]) # index of selected pattern
# Set all patterns to False except for the one that has been chosen
W[emin] = [0 if i != idP else 1 for i, b in enumerate(W[emin])]
# Marking selected cell as 'collapsed' in H (array of entropies)
H[emin] = 'collapsed'
# Storing first color (top left corner) of the selected pattern at the location of the collapsed cell
Output[emin] = patterns[idP][0]
### PROPAGATION
# For each neighbor (left, right, up, down) of the recently collapsed cell
for dir, t in enumerate(directions):
x = (emin%d + t[0])%d
y = (emin/d + t[1])%d
idN = x + y * d #index of neighbor
# If that neighbor hasn't been collapsed yet
if H[idN] != 'collapsed':
# Check indices of all available patterns in that neighboring cell
available = [i for i, b in enumerate(W[idN]) if b]
# Among these indices, select indices of patterns that can be adjacent to the collapsed cell at this location
intersection = A[idP][dir] & set(available)
# If the neighboring cell contains indices of patterns that can be adjacent to the collapsed cell
if intersection:
# Remove indices of all other patterns that cannot be adjacent to the collapsed cell
W[idN] = [True if i in list(intersection) else False for i in xrange(npat)]
### Update entropy of that neighboring cell accordingly (less patterns = lower entropy)
# If only 1 pattern available left, no need to compute entropy because entropy is necessarily 0
if len(intersection) == 1:
H[idN] = '0' # Putting a str at this location in 'H' (array of entropies) so that it doesn't return 0 (float) when looking for minimum entropy (min(H)) at next iteration
# If more than 1 pattern available left --> compute/update entropy + add noise (to prevent cells to share the same minimum entropy value)
else:
lfreqs = [b * f for b, f in izip(W[idN], freqs) if b]
ent = math.log(sum(lfreqs)) - sum(map(lambda x: x * math.log(x), lfreqs)) / sum(lfreqs)
H[idN] = ent + random(.001)
# If no index of adjacent pattern in the list of pattern indices of the neighboring cell
# --> mark cell as a 'contradiction'
else:
H[idN] = 'CONT'
# Draw output
''' dxd grid of cells (squares) filled with their corresponding color.
That color is the first (top-left) color of the pattern assigned to that cell '''
for i, c in enumerate(Output):
x, y = i%d, i/d
fill(c)
rect(x * xs, y * ys, xs, ys)
# Displaying corresponding entropy value
fill(0)
text(H[i], x * xs + xs/2 - 12, y * ys + ys/2)
22246W[21]W[23]W[2]W[42]246W[23]22while stack:
while stack:
idC = stack.pop() # index of current cell
for dir, t in enumerate(mat):
x = (idC%w + t[0])%w
y = (idC/w + t[1])%h
idN = x + y * w # index of neighboring cell
if H[idN] != 'c':
possible = set([n for idP in W[idC] for n in A[idP][dir]])
available = W[idN]
if not available.issubset(possible):
intersection = possible & available
if not intersection:
print 'contradiction'
noLoop()
W[idN] = intersection
lfreqs = [freqs[i] for i in W[idN]]
H[idN] = (log(sum(lfreqs)) - sum(map(lambda x: x * log(x), lfreqs)) / sum(lfreqs)) - random(.001)
stack.add(idN)
from collections import Counter
from itertools import chain
from random import choice
w, h = 40, 25
N = 3
def setup():
size(w*20, h*20, P2D)
background('#FFFFFF')
frameRate(1000)
noStroke()
global W, A, H, patterns, freqs, npat, mat, xs, ys
img = loadImage('Flowers.png')
iw, ih = img.width, img.height
xs, ys = width//w, height//h
kernel = [[i + n*iw for i in xrange(N)] for n in xrange(N)]
mat = ((-1, 0), (1, 0), (0, -1), (0, 1))
all = []
for y in xrange(ih):
for x in xrange(iw):
cmat = [[img.pixels[((x+n)%iw)+(((a[0]+iw*y)/iw)%ih)*iw] for n in a] for a in kernel]
for r in xrange(4):
cmat = zip(*cmat[::-1])
all.append(cmat)
all.append(cmat[::-1])
all.append([a[::-1] for a in cmat])
all = [tuple(chain.from_iterable(p)) for p in all]
c = Counter(all)
patterns = c.keys()
freqs = c.values()
npat = len(freqs)
W = [set(range(npat)) for i in xrange(w*h)]
A = [[set() for dir in xrange(len(mat))] for i in xrange(npat)]
H = [100 for i in xrange(w*h)]
for i1 in xrange(npat):
for i2 in xrange(npat):
if [n for i, n in enumerate(patterns[i1]) if i%N!=(N-1)] == [n for i, n in enumerate(patterns[i2]) if i%N!=0]:
A[i1][0].add(i2)
A[i2][1].add(i1)
if patterns[i1][:(N*N)-N] == patterns[i2][N:]:
A[i1][2].add(i2)
A[i2][3].add(i1)
def draw():
global H, W
emin = int(random(w*h)) if frameCount <= 1 else H.index(min(H))
if H[emin] == 'c':
print 'finished'
noLoop()
id = choice([idP for idP in W[emin] for i in xrange(freqs[idP])])
W[emin] = [id]
H[emin] = 'c'
stack = set([emin])
while stack:
idC = stack.pop()
for dir, t in enumerate(mat):
x = (idC%w + t[0])%w
y = (idC/w + t[1])%h
idN = x + y * w
if H[idN] != 'c':
possible = set([n for idP in W[idC] for n in A[idP][dir]])
if not W[idN].issubset(possible):
intersection = possible & W[idN]
if not intersection:
print 'contradiction'
noLoop()
return
W[idN] = intersection
lfreqs = [freqs[i] for i in W[idN]]
H[idN] = (log(sum(lfreqs)) - sum(map(lambda x: x * log(x), lfreqs)) / sum(lfreqs)) - random(.001)
stack.add(idN)
fill(patterns[id][0])
rect((emin%w) * xs, (emin/w) * ys, xs, ys)