I am trying to write a mandelbrot set to an image in python, and am having a problem with one of my functions.
The issue is: While I expect something like this. I am getting a plain white image. Here is my code:
Quick Summary of code:
Check if value is in set, if it is, mark it as true in an array of booleans. Then, draw the image based on the array of booleans, coloring the true, and leaving the false ones.
import math
import numpy as np
import scipy.misc as smp
from PIL import PILLOW_VERSION
from PIL import Image
def iterate(x, y, iterationNum):
z = 0
coord = complex(x, y)
for a in xrange(iterationNum):
#Don't use fabs. It can be negative.
z = z * z + coord
#This is a comparison between complex and int. It probably won't work.
#You want |Z| which is: z.real ** 2 + z.imag ** 2 > 4
if math.fabs(z) > 2:
return False
return True
def pixel(image,x,y,r,g,b):
"""Place pixel at pos=(x,y) on image, with color=(r,g,b)"""
image.put("#%02x%02x%02x" % (r,g,b), (y, x))
#here's some example coloring code that may help:
def draw(grid):
#Create a white image with the size of the grid as the number of pixels
img = Image.new('RGB', (len(grid), len(grid)), "white")
pixels = img.load()
for row in xrange(len(grid)):
for col in xrange(len(grid[row])):
if grid[row][col] == True:
#If that point is True (it's in the set), color it blue
pixels[row, col] = (0, 0, 255)
return img
def mandelbrot():
#you should probably use a square, it's easier to deal with
#The mandelbrot set fits completely within (-2, 2) and (2, -2)
#(-200, 200), (200, -200) is way too big!
TopLeftX = -2; BottomRightX = 2
TopLeftY = 2; BottomRightY = -2
#increment should be calculated based on the size of the bounds and the number of pixels
#For example, if you're between -2 and 2 on the X-Plane, and your image is 400 pixels wide
#Then your increment = (2 - (-2)) / 400 = 4 / 400 = .01 so that each pixel is 1/400th of the
#Total width of the bounding area
increment = 0.01
maxIt = 100
w = BottomRightX - TopLeftX
h = TopLeftY - BottomRightY
#This should be based on the size of the image, one spot in the area for one pixel
npArr = np.zeros((w / increment, h / increment), dtype=bool)
#Use the increment variable from above. It won't work with xrange because that doesn't
#Support decimals. You probably want to use a while loop or something
x = -2
y = 2
while TopLeftX <= x <= BottomRightX:
while TopLeftY <= y <= BottomRightY:
#I recommend using True or False in here (in the set or not)
#And then do your color calculations as I explained above
#Saves a lot of memory
if iterate(x, y, maxIt):
npArr[x, y] = True
y += increment
#once you've calculated the Trues and Falses, you'd call the draw() function
#using the npArr as the parameter. I haven't tested the code, so there may
#be a few bugs, but it should be helpful!
x += increment
return npArr
img = draw(mandelbrot())
img.save("mandelbrot.png")
I suspect the problem is with the "iterate" function in my code, because none of the values i put in iterate are returning true.
EDIT
I have another issue as well, The second for loop I have here isnt even running.
Your handling of the y coordinate is faulty. You begin the outer loop with
y = 2
and have the loop condition as
while TopLeftY <= y <= BottomRightY:
After substituting their values, this is
while 2 <= y <= -2:
which is a nonsense. This is followed by
y += increment
but y is already at the top end of the range. Moreover, you fail to reset y for each inner loop.
To summarise, the loop should be
x = TopLeftX # use the value you already defined!
while TopLeftX <= x <= BottomRightX:
y = TopLeftY # moved to inside x loop
while TopLeftY >= y >= BottomRightY: # change the loop condition
# ... the Mandelbrot iteration
y -= increment # reverse direction
x += increment
I am no Python expert, so there may be other problems too.
Related
I need to draw a circle in a 2D numpy array given [i,j] as indexes of the array, and r as the radius of the circle. Each time a condition is met at index [i,j], a circle should be drawn with that as the center point, increasing all values inside the circle by +1. I want to avoid the for-loops at the end where I draw the circle (where I use p,q to index) because I have to draw possibly millions of circles. Is there a way without for loops? I also don't want to import another library for just a single task.
Here is my current implementation:
for i in range(array_shape[0]):
for j in range(array_shape[1]):
if (condition): # Draw circle if condition is fulfilled
# Create a square of pixels with side lengths equal to radius of circle
x_square_min = i-r
x_square_max = i+r+1
y_square_min = j-r
y_square_max = j+r+1
# Clamp this square to the edges of the array so circles near edges don't wrap around
if x_square_min < 0:
x_square_min = 0
if y_square_min < 0:
y_square_min = 0
if x_square_max > array_shape[0]:
x_square_max = array_shape[0]
if y_square_max > array_shape[1]:
y_square_max = array_shape[1]
# Now loop over the box and draw circle inside of it
for p in range(x_square_min , x_square_max):
for q in range(y_square_min , y_square_max):
if (p - i) ** 2 + (q - j) ** 2 <= r ** 2:
new_array[p,q] += 1 # Incrementing because need to have possibility of
# overlapping circles
If you're using the same radius for every single circle, you can simplify things significantly by only calculating the circle coordinates once and then adding the center coordinates to the circle points when needed. Here's the code:
# The main array of values is called array.
shape = array.shape
row_indices = np.arange(0, shape[0], 1)
col_indices = np.arange(0, shape[1], 1)
# Returns xy coordinates for a circle with a given radius, centered at (0,0).
def points_in_circle(radius):
a = np.arange(radius + 1)
for x, y in zip(*np.where(a[:,np.newaxis]**2 + a**2 <= radius**2)):
yield from set(((x, y), (x, -y), (-x, y), (-x, -y),))
# Set the radius value before running code.
radius = RADIUS
circle_r = np.array(list(points_in_circle(radius)))
# Note that I'm using x as the row number and y as the column number.
# Center of circle is at (x_center, y_center). shape_0 and shape_1 refer to the main array
# so we can get rid of coordinates outside the bounds of array.
def add_center_to_circle(circle_points, x_center, y_center, shape_0, shape_1):
circle = np.copy(circle_points)
circle[:, 0] += x_center
circle[:, 1] += y_center
# Get rid of rows where coordinates are below 0 (can't be indexed)
bad_rows = np.array(np.where(circle < 0)).T[:, 0]
circle = np.delete(circle, bad_rows, axis=0)
# Get rid of rows that are outside the upper bounds of the array.
circle = circle[circle[:, 0] < shape_0, :]
circle = circle[circle[:, 1] < shape_1, :]
return circle
for x in row_indices:
for y in col_indices:
# You need to set CONDITION before running the code.
if CONDITION:
# Because circle_r is the same for all circles, it doesn't need to be recalculated all the time. All you need to do is add x and y to circle_r each time CONDITION is met.
circle_coords = add_center_to_circle(circle_r, x, y, shape[0], shape[1])
array[tuple(circle_coords.T)] += 1
When I set radius = 10, array = np.random.rand(1200).reshape(40, 30) and replaced if CONDITION with if (x == 20 and y == 20) or (x == 25 and y == 20), I got this, which seems to be what you want:
Let me know if you have any questions.
Adding each circle can be vectorized. This solution iterates over the coordinates where the condition is met. On a 2-core colab instance ~60k circles with radius 30 can be added per second.
import numpy as np
np.random.seed(42)
arr = np.random.rand(400,300)
r = 30
xx, yy = np.mgrid[-r:r+1, -r:r+1]
circle = xx**2 + yy**2 <= r**2
condition = np.where(arr > .999) # np.where(arr > .5) to benchmark 60k circles
for x,y in zip(*condition):
# valid indices of the array
i = slice(max(x-r,0), min(x+r+1, arr.shape[0]))
j = slice(max(y-r,0), min(y+r+1, arr.shape[1]))
# visible slice of the circle
ci = slice(abs(min(x-r, 0)), circle.shape[0] - abs(min(arr.shape[0]-(x+r+1), 0)))
cj = slice(abs(min(y-r, 0)), circle.shape[1] - abs(min(arr.shape[1]-(y+r+1), 0)))
arr[i, j] += circle[ci, cj]
Visualizing np.array arr
import matplotlib.pyplot as plt
plt.figure(figsize=(8,8))
plt.imshow(arr)
plt.show()
I am reading an image, getting objects that have a certain brightness value, and then plotting the X and Y coords to the image.
But, there is a huge group of outliers, which are all located in a rectangular part of the image, Its X and Y coords are 1110-1977 (width) and 1069-1905 (height). From here, I'm looping through this little square portion of the image, and from my pre-created x and y arrays any values that have the same coords as shown there are removed.
However, this removes a lot more coords, which, for example, have X in the range 1110-1977. So the end result is a cross pattern filtering when I only want the square in the center to be filtered. How would I do this?
Code
from PIL import Image, ImageDraw
import numpy as np
from math import sqrt
imag = Image.open("Centaurus_A-DeNoiseAI-denoise.jpg")
imag = imag.convert ('RGB')
x=[]
y=[]
imag2=Image.open("Cen_A_cropped.jpg")
imag2=imag2.convert('RGB')
r=[]
g=[]
b=[]
width2, height2=imag2.size
for count2 in range(width2):
for i2 in range(height2):
X,Y=count2,i2
(R,G,B)=imag2.getpixel((X,Y))
r.append(R)
g.append(G)
b.append(B)
average_r=sum(r)/len(r)
average_g=sum(g)/len(g)
average_b=sum(b)/len(b)
brightness_average=sqrt(0.299*(average_r**2) + 0.587*(average_g**2) + 0.114*(average_b**2))
print("Avg. brightness "+str(brightness_average))
def calculate_brightness(galaxy,ref_clus,clus_mag):
delta_b=(galaxy/ref_clus)
bright=delta_b**2
mag=np.log(bright)/np.log(2.512)
return mag+clus_mag
count=0
X,Y = 1556,1568
(R,G,B) = imag.getpixel((X,Y))
width, height=imag.size
brightness = sqrt(0.299*(R**2) + 0.587*(G**2) + 0.114*(B**2))
print("Magnitude: "+str((calculate_brightness(13050, 15.79,3.7))))
reference=brightness_average/(calculate_brightness(13050, 15.79,3.7)/6.84)
print("Reference: "+str(reference))
for count in range(width):
for i in range(height):
X,Y = count,i
(R,G,B) = imag.getpixel((X,Y))
brightness = sqrt(0.299*(R**2) + 0.587*(G**2) + 0.114*(B**2))
if(reference<=brightness<=reference+3):
x.append(X)
y.append(Y)
#post processing----------------------------------------------------------------------------------------------------
for x2 in range(1110, 1977):
for y2 in range(1069, 1905):
X,Y=x2,y2
if(X in x and Y in y):
x.remove(X)
y.remove(Y)
#-------------------------------------------------------------------------------------------------------------------
with imag as im:
delta = 19
draw = ImageDraw.Draw(im)
for i in range(len(x)):
draw.rectangle([x[i-delta],y[i-delta],x[i-delta],y[i-delta]], fill=(0,255,0))
im.save("your_image.png")
Centaurus_A-DeNoiseAI-denoise.jpg
Cen_A_cropped.jpg
Your post-processing logic is flawed. You remove a bunch of X values in the range 1110-1977, without checking whether its corresponding Y value is also in the range of the box. Remove this code section instead and add that logic the first time you loop to gather your x and y coords.
for count in range(width):
for i in range(height):
X,Y = count,i
if 1110 <= X < 1977 and 1069 <= Y < 1905: # add these
continue # two lines
(R,G,B) = imag.getpixel((X,Y))
However, there is a better way of doing the exact same thing by using numpy arrays. Instead of writing explicit loops, you can vectorise a lot of your computations.
import numpy as np
from PIL import Image, ImageDraw
image = Image.open('Centaurus_A-DeNoiseAI-denoise.jpg').convert('RGB')
img1 = np.array(image)
img2 = np.array(Image.open('Cen_A_cropped.jpg').convert('RGB'))
coeffs = np.array([.299, .587, .114])
average = img2.mean(axis=(0, 1))
brightness_average = np.sqrt(np.sum(average**2 * coeffs))
reference = brightness_average / (calculate_brightness(13050, 15.79,3.7) / 6.84)
print(f'Avg. brightness: {brightness_average}')
print(f'Reference: {reference}')
brightness = np.sqrt(np.sum(img1.astype(int)**2 * coeffs, axis=-1))
accepted_brightness = (brightness >= reference) * (brightness <= reference + 3)
pixels_used = np.ones((img1.shape[:2]), dtype=bool)
pixels_used[1069:1905,1110:1977] = False
rows, cols = np.where(accepted_brightness * pixels_used)
with image as im:
draw = ImageDraw.Draw(im)
draw.point(list(zip(cols, rows)), fill=(0, 255, 0))
image.save('out.png')
The main trick used here is in the line
rows, cols = np.where(accepted_brightness * pixels_used)
accepted_brightess is a 2d array of each pixel with a boolean value whether its brightness is within your preferred range. pixels_used is another 2d boolean array, where every pixel is True, except from the pixels in the box near the centre you want to ignore. The combination of those two gives you the pixel coordinates that have the correct brightness and are not in the square in the centre.
The output image is this:
Where you can control the angle between the drawn lines, the line of code I can´t understand is this one:
indice = ((matriz >= n*angulo) & (matriz < (n+1)*angulo))
Function:
def createImage(angulo):
#Image height and width
w ,h = (100,100)
#Image array
img = np.zeros((w, h), np.uint8)
cor = 255
x,y = np.meshgrid(range(0,w),range(0,h))
centerX = int(w/2)
centerY = int(h/2)
#Coordinates in relation to center of image
x = x-centerX
y = y-centerY
#Complex coordinates
matriz = x+1j*y
matriz =np.angle(matriz)*180/np.pi
for n in range(int(-360/angulo), int(360/angulo)):
indice = ((matriz >= n*angulo) & (matriz < (n+1)*angulo))
img[indice] = cor
cor = 0 if cor == 255 else 255
cv2.imshow("star" , img)
cv2.imwrite("star.png" , img)
Any kind of help is appreciated.
This line appears to create an index mask, that is an array that can be used to extract a part of an array or matrix where a particular condition holds.
The condition used is:
((matriz >= n*angulo) & (matriz < (n+1)*angulo))
which uses bitwise operator &. This operator returns 1 if both operands evaluate to 1 and 0 otherwise.
This means your index map will have a 1 value in locations where
values of matriz are between n * angulo and (n+1) * angulo.
Accessing matriz with this index map would give you an array containing exactly those values. Subequently, it is used to extract a part of image img. Each subsequent extracted part is colored in all black or all white (pixel values of 0 and 255 respectively).
Part of the magic happens outside the loop. Add some debug output help you visualize this. use a smaller matrix like 5x5 and large angulo value make output easier to read:
matriz = x+1j*y
# create a complex plane
print(matriz)
matriz =np.angle(matriz)*180/np.pi
# convert each point from x/y coordinate to their angle from x-axis
print(matriz)
for n in range(int(-360/angulo), int(360/angulo)):
indice = ((matriz >= n*angulo) & (matriz < (n+1)*angulo))
# select all the points that falls between n*angulo and (n+1)*angulo
print(indice)
...
I have an image with a simple circle in it.
How to detect the circle using numpy and find its radius ?
I tried learning but couldnt. I would like to learn from the program that you answer here.
Only thing I know as of now is:
from scipy import misc
f = misc.imread("/path/to/file.png")
# then dont know what to do
Here is the image - https://c2.staticflickr.com/6/5476/14135136623_3973d3f03c_b.jpg
I'm assuming for now that the image always consists of exactly one non-black circle in an otherwise black image.
I'm also assuming you don't care particularly about efficiency of the algorithm.
Loop over all of the pixels in the image, keeping a sum, count, min, and max tally of all white pixel's x- and y-coordinates (min/max needed only for x or y, not both). Something like this (just roughly -- I don't have scipy installed atm):
circle_count = 0
circle_sum_x = 0
circle_sum_y = 0
circle_min_x = 0
circle_max_x = 0
for y in range(image_height):
for x in range(image_width):
if pixel(x,y) is not black:
circle_count += 1
circle_sum_x += x
circle_sum_y += y
circle_min_x = min(circle_min_x, x)
circle_max_x = max(circle_max_y, y)
if circle_count == 0:
print "No circle found!"
else:
circle_center_x = circle_sum_x / circle_count
circle_center_y = circle_sum_y / circle_count
circle_radius = (circle_max_x - circle_min_x) / 2
I am trying to implement a program, that will increase the width of an image by one pixel. I then want to take the new maximum x ordinate and put this with a random y ordinate (that is within the range of the image) to create a new pixel.
for x in range (0,getWidth(pic)):
for y in range (0,getHeight(pic)):
X=getWidth(pic)
newX = (X+1)
colr=(255,0,0)
newPixel = getPixel (pic, newX, y)//line 25
setColor(newPixel, colr)
Y=getHeight(pic)
newY= (Y+1)
newPixel = getPixel( pic,x, newY)
setColor(newPixel, colr)
I get this error:
getPixel(picture,x,y): x (= 226) is less than 0 or bigger than the width (= 224)
The error was:
Inappropriate argument value (of correct type).
An error occurred attempting to pass an argument to a function.
Please check line 25 of D:\bla bla
I understand it is out of the range. What am I doing wrong?
Here is generalized approach to increase the size of an image keeping its current content:
Feel free to adapt.
# Increase a picture given an offset, a color and the anciant
# content must be centered or not.
# Offsets must be positive.
def increaseAndCopy(pic, offsetX, offsetY, bg_color=black, center=True):
# Offsets must be positive
if (offsetX < 0.0) or (offsetY < 0.0):
printNow("Error: Offsets must be positive !")
return None
new_w = pic.getWidth() + int(2*offsetX)
new_h = pic.getHeight() + int(2*offsetY)
startX = 0
startY = 0
if (center) and (offsetX > 1.0):
startX = int(offsetX)
if (center) and (offsetY > 1.0):
startY = int(offsetY)
new_pic = makeEmptyPicture(new_w, new_h)
# Fill with background color
setAllPixelsToAColor(new_pic, bg_color)
# Process copy
for x in xrange(pic.getWidth()):
for y in xrange(pic.getHeight()):
px = getPixel(pic, x, y)
new_px = getPixel(new_pic, x + startX, y + startY)
setColor(new_px, getColor(px))
return new_pic
file = pickAFile()
picture = makePicture(file)
# Pass an offset of 0.5 to increase by 1 pixel
#new_picture = increaseAndCopy(picture, 0.5, 0, blue)
new_picture = increaseAndCopy(picture, 10, 20, gray, True)
if (new_picture):
writePictureTo(new_picture, "/home/biggerPic.png")
show(new_picture)
Output (Painting by Jean-Michel Basquiat):
...........................................................
How can you get something that an object does not have?
newPixel = getPixel (pic, newX, y)//line 25
The original image remains sized at getWidth(pic) but you are asking for a pixel at getWidth(pic) + 1 which does not exist.
You can enlarge the image by copying it to a new picture similar to this answer.
...
newPic=makeEmptyPicture(newX,newY)
xstart=0
ystart=0
for y in range(ystart,newY):
for x in range(xstart, newX):
if x == newX or y == newY:
colour=(255,0,0)
else:
oldPixel=getPixel(oldPic,x,y)
colour=getColor(oldPixel)
newPixel=getPixel(newPic,x,y)
setColor(newPixel,colour)
explore(newPic)