I'm struggling to create a light YoloV1 (with only one bounding box) on MNIST dataset (I randomly paste 28x28 digit into a 75x75 black background).
I can't figure out how to turn relative-to-cell coordinates into absolute coordinates.
Since now, I'm using the groundtruth bounding boxes to retrieve the cell which should contain an object, then I save the i,j positions, then I use those positions to get back to absolute coordinates with my predictions.
This method works but when it's time to detect a real image, I won't have the groundtruth coordinates and so, the i,j object position, and so the absolute position of the predicted bounding box.
I provide some line of code :
Encoding absolute coordinates of shape (N,4) to (N,S,S,5)
def encode(self, box):
"""
box : torch.Tensor of shape (N,4)
Absolute coordinates [xmin, ymin, w_bbox, h_bbox]
"""
### Absolute box infos
xmin, ymin, w_bbox, h_bbox = box
### Relative box infos
rw = w_bbox / 75
rh = h_bbox / 75
rx_min = xmin / 75
ry_min = ymin / 75
### x and y box center coords
rxc = (rx_min + rw/2)
ryc = (ry_min + rh/2)
### Object grid location
i = (rxc / self.cell_size).ceil() - 1.0
j = (ryc / self.cell_size).ceil() - 1.0
i, j = int(i), int(j)
### x & y of the cell left-top corner
x0 = i * self.cell_size
y0 = j * self.cell_size
### x & y of the box on the cell, normalized from 0.0 to 1.0.
x_norm = (rxc - x0) / self.cell_size
y_norm = (ryc - y0) / self.cell_size
box_target = torch.zeros(self.S, self.S, 4+1)
box_target[j, i, :5] = torch.Tensor([x_norm, y_norm, rw, rh, 1.])
return box_target
Convert relative-to-cell coordinates into absolute ones
def relative2absolute(box_true:torch.Tensor, box_pred:torch.Tensor)->tuple:
"""
Turns bounding box relative to cell coordinates into absolute coordinates
(pixels). Used to calculate IoU and to plot boxes.
Args:
box_true : torch.Tensor of shape (N, S, S, 5)
Groundtruth bounding box coordinates to convert.
box_pred : torch.Tensor of shape (N, S, S, 5)
Predicted bounding box coordinates to convert.
Return:
box_true_absolute : torch.Tensor of shape (N, 4)
box_pred_absolute : torch.Tensor of shape (N, 4)
"""
assert len(box_true.shape)==4 and len(box_pred.shape)==4, "Bbox should be of size (N,S,S,5)."
SIZEHW = 75
S = 6
CELL_SIZE = 1/S
### Get non-zero coordinates
cells_with_obj = box_true.nonzero()[::5]
N, cells_i, cells_j, _ = cells_with_obj.permute(1,0)
### Retrieving box coordinates. TBM if nb_obj > 1
xrcell_true, yrcell_true, rw_true, rh_true = box_true[N, cells_i, cells_j, 0:4].permute(1,0)
xrcell_pred, yrcell_pred, rw_pred, rh_pred = box_pred[N, cells_i, cells_j, 0:4].permute(1,0)
### Compute relative-to-image center coordinates
xc_rimg_true = xrcell_true * CELL_SIZE + cells_j * CELL_SIZE
xc_rimg_pred = xrcell_pred * CELL_SIZE + cells_j * CELL_SIZE
yc_rimg_true = yrcell_true * CELL_SIZE + cells_i * CELL_SIZE
yc_rimg_pred = yrcell_pred * CELL_SIZE + cells_i * CELL_SIZE
### Compute absolute top left coordinates
xmin_true = (xc_rimg_true - rw_true/2) * SIZEHW
xmin_pred = (xc_rimg_pred - rw_pred/2) * SIZEHW
ymin_true = (yc_rimg_true - rh_true/2) * SIZEHW
ymin_pred = (yc_rimg_pred - rh_pred/2) * SIZEHW
### Compute absolute bottom right coordinates
xmax_true = xmin_true + rw_true*SIZEHW
xmax_pred = xmin_pred + rw_pred*SIZEHW
ymax_true = ymin_true + rh_true*SIZEHW
ymax_pred = ymin_pred + rh_pred*SIZEHW
### Stacking
box_true_absolute = torch.stack((xmin_true, ymin_true, xmax_true, ymax_true), dim=-1)
box_pred_absolute = torch.stack((xmin_pred, ymin_pred, xmax_pred, ymax_pred), dim=-1)
return box_true_absolute, box_pred_absolute
I have two points in 2D space as we can see in the figure to move from the blue point to the red points we can use the equation (1). Where b is a constant used to limit the shape of the logarithmic spiral, l is a random number in [−1,1], which is used to
control the indentation effect of the movement, D indicates the distance between blue points and the current point
I need another movement that can move from blue points to the red points like in the figure
You can use sinusoidal model.
For start point (X0, Y0) and end point (X1,Y1) we have vector end-start, determine it's length - distance between points L, and angle of vector Fi (using atan2).
Then generate sinusoidal curve for some standard situation - for example, along OX axis, with magnitude A, N periods for distance 2 * Pi * N:
Scaled sinusoid in intermediate point with parameter t, where t is in range 0..1 (t=0 corresponds to start point (X0,Y0))
X(t) = t * L
Y(t) = A * Sin(2 * N * Pi * t)
Then shift and rotate sinusoid using X and Y calculated above
X_result = X0 + X * Cos(Fi) - Y * Sin(Fi)
Y_result = Y0 + X * Sin(Fi) + Y * Cos(Fi)
Example Python code:
import math
x0 = 100
y0 = 100
x1 = 400
y1 = 200
nperiods = 4
amp = 120
nsteps = 20
leng = math.hypot(x1 - x0, y1 - y0)
an = math.atan2(y1 - y0, x1 - x0)
arg = 2 * nperiods* math.pi
points = []
for t in range(1, nsteps + 1):
r = t / nsteps
xx = r * leng
yy = amp * math.sin(arg * r)
rx = x0 + xx * math.cos(an) - yy * math.sin(an)
ry = y0 + xx * math.sin(an) + yy * math.cos(an)
points.append([rx, ry])
print(points)
Draw points:
I am creating a program which allows a user to annotate images with points.
This program allows user to zoom in an image so user can annotate more precisely.
Program zooms in an image doing the following:
Find the center of image
Find minimum and maximum coordinates of new cropped image relative to center
Crop image
Resize the image to original size
For this I have written the following Python code:
import cv2
def zoom_image(original_image, cut_off_percentage, list_of_points):
height, width = original_image.shape[:2]
center_x, center_y = int(width/2), int(height/2)
half_new_width = center_x - int(center_x * cut_off_percentage)
half_new_height = center_y - int(center_y * cut_off_percentage)
min_x, max_x = center_x - half_new_width, center_x + half_new_width
min_y, max_y = center_y - half_new_height, center_y + half_new_height
#I want to include max coordinates in new image, hence +1
cropped = original_image[min_y:max_y+1, min_x:max_x+1]
new_height, new_width = cropped.shape[:2]
resized = cv2.resize(cropped, (width, height))
translate_points(list_of_points, height, width, new_height, new_width, min_x, min_y)
I want to resize the image to original width and height so user always works on same "surface"
regardless of how zoomed image is.
The problem I encounter is how to correctly scale points (annotations) when doing this. My algorithm to do so was following:
Translate points on original image by subtracting min_x from x coordinate and min_y from y coordinate
Calculate constants for scaling x and y coordinates of points
Multiply coordinates by constants
For this I use the following Python code:
import cv2
def translate_points(list_of_points, height, width, new_height, new_width, min_x, min_y):
#Calculate constants for scaling points
scale_x, scale_y = width / new_width, height / new_height
#Translate and scale points
for point in list_of_points:
point.x = (point.x - min_x) * scale_x
point.y = (point.y - min_y) * scale_y
This code doesn't work. If I zoom in once, it is hard to detect the offset of pixels but it happens. If I keep zooming in, it will be much easier to detect the "drift" of points. Here are images to provide examples. On original image (1440x850) I places a point in the middle of blue crosshair. The more I zoom in the image it is easier to see that algorithm doesn't work with bigger cut-ofs.
Original image. Blue crosshair is middle point of an image. Red angles indicate what will be borders after image is zoomed once
Image after zooming in once.
Image after zooming in 5 times. Clearly, green point is no longer in the middle of image
The cut_off_percentage I used is 15% (meaning that I keep 85% of width and height of original image, calculated from the center).
I have also tried the following library: Augmentit python library
Library has functions for cropping images and resizing them together with points. Library also causes the points to drift. This is expected since the code I implemented and library's functions use the same algorithm.
Additionally, I have checked whether this is a rounding problem. It is not. Library rounds the points after multiplying coordinates with scales. Regardless on how they are rounded, points are still off by 4-5 px. This increases the more I zoom in the picture.
EDIT: A more detailed explanation is given here since I didn't understand a given answer.
The following is an image of right human hand.
Image of a hand in my program
Original dimension of this image is 1440 pixels in width and 850 pixels in height. As you can see in this image, I have annotated right wrist at location (756.0, 685.0). To check whether my program works correctly, I have opened this exact image in GIMP and placed a white point at location (756.0, 685.0). The result is following:
Image of a hand in GIMP
Coordinates in program work correctly. Now, if I were to calculate parameters given in first answer according to code given in first answer I get following:
vec = [756, 685]
hh = 425
hw = 720
cov = [720, 425]
These parameters make sense to me. Now I want to zoom the image to scale of 1.15. I crop the image by choosing center point and calculating low and high values which indicate what rectangle of image to keep and what to cut. On the following image you can see what is kept after cutting (everything inside red rectangle).
What is kept when cutting
Lows and highs when cutting are:
xb = [95,1349]
yb = [56,794]
Size of cropped image: 1254 x 738
This cropped image will be resized back to original image. However, when I do that my annotation gets completely wrong coordinates when using parameters described above.
After zoom
This is the code I used to crop, resize and rescale points, based on the first answer:
width, height = image.shape[:2]
center_x, center_y = int(width / 2), int(height / 2)
scale = 1.15
scaled_width = int(center_x / scale)
scaled_height = int(center_y / scale)
xlow = center_x - scaled_width
xhigh = center_x + scaled_width
ylow = center_y - scaled_height
yhigh = center_y + scaled_height
xb = [xlow, xhigh]
yb = [ylow, yhigh]
cropped = image[yb[0]:yb[1], xb[0]:xb[1]]
resized = cv2.resize(cropped, (width, height), cv2.INTER_CUBIC)
#Rescaling poitns
cov = (width / 2, height / 2)
width, height = resized.shape[:2]
hw = width / 2
hh = height / 2
for point in points:
x, y = point.scx, point.scy
x -= xlow
y -= ylow
x -= cov[0] - (hw / scale)
y -= cov[1] - (hh / scale)
x *= scale
y *= scale
x = int(x)
y = int(y)
point.set_coordinates(x, y)
So this really is an integer rounding issue. It's magnified at high zoom levels because being off by 1 pixel at 20x zoom throws you off much further. I tried out two versions of my crop-n-zoom gui. One with int rounding, another without.
You can see that the one with int rounding keeps approaching the correct position as the zoom grows, but as soon as the zoom takes another step, it rebounds back to being wrong. The non-rounded version sticks right up against the mid-lines (denoting the proper position) the whole time.
Note that the resized rectangle (the one drawn on the non-zoomed image) blurs past the midlines. This is because of the resize interpolation from OpenCV. The yellow rectangle that I'm using to check that my points are correctly scaling is redrawn on the zoomed frame so it stays crisp.
With Int Rounding
Without Int Rounding
I have the center-of-view locked to the bottom right corner of the rectangle for this demo.
import cv2
import numpy as np
# clamp value
def clamp(val, low, high):
if val < low:
return low;
if val > high:
return high;
return val;
# bound the center-of-view
def boundCenter(cov, scale, hh, hw):
# scale half res
scaled_hw = int(hw / scale);
scaled_hh = int(hh / scale);
# bound
xlow = scaled_hw;
xhigh = (2*hw) - scaled_hw;
ylow = scaled_hh;
yhigh = (2*hh) - scaled_hh;
cov[0] = clamp(cov[0], xlow, xhigh);
cov[1] = clamp(cov[1], ylow, yhigh);
# do a zoomed view
def zoomView(orig, cov, scale, hh, hw):
# calculate crop
scaled_hh = int(hh / scale);
scaled_hw = int(hw / scale);
xlow = cov[0] - scaled_hw;
xhigh = cov[0] + scaled_hw;
ylow = cov[1] - scaled_hh;
yhigh = cov[1] + scaled_hh;
xb = [xlow, xhigh];
yb = [ylow, yhigh];
# crop and resize
copy = np.copy(orig);
crop = copy[yb[0]:yb[1], xb[0]:xb[1]];
display = cv2.resize(crop, (width, height), cv2.INTER_CUBIC);
return display;
# draw vector shape
def drawVec(img, vec, pos, cov, hh, hw, scale):
con = [];
for point in vec:
# unpack point
x,y = point;
x += pos[0];
y += pos[1];
# here's the int version
# Note: this is the same as xlow and ylow from the above function
# x -= cov[0] - int(hw / scale);
# y -= cov[1] - int(hh / scale);
# rescale point
x -= cov[0] - (hw / scale);
y -= cov[1] - (hh / scale);
x *= scale;
y *= scale;
x = int(x);
y = int(y);
# add
con.append([x,y]);
con = np.array(con);
cv2.drawContours(img, [con], -1, (0,200,200), -1);
# font stuff
font = cv2.FONT_HERSHEY_SIMPLEX;
fontScale = 1;
fontColor = (255, 100, 0);
thickness = 2;
# draw blank
res = (800,1200,3);
blank = np.zeros(res, np.uint8);
print(blank.shape);
# draw a rectangle on the original
cv2.rectangle(blank, (100,100), (400,200), (200,150,0), -1);
# vectored shape
# comparison shape
bshape = [[100,100], [400,100], [400,200], [100,200]];
bpos = [0,0]; # offset
# random shape
vshape = [[148, 89], [245, 179], [299, 67], [326, 171], [385, 222], [291, 235], [291, 340], [229, 267], [89, 358], [151, 251], [57, 167], [167, 164]];
vpos = [100,100]; # offset
# get original image res
height, width = blank.shape[:2];
hh = int(height / 2);
hw = int(width / 2);
# center of view
cov = [600, 400];
camera_spd = 5;
# scale
scale = 1;
scale_step = 0.2;
# loop
done = False;
while not done:
# crop and show image
display = zoomView(blank, cov, scale, hh, hw);
# drawVec(display, vshape, vpos, cov, hh, hw, scale);
drawVec(display, bshape, bpos, cov, hh, hw, scale);
# draw a dot in the middle
cv2.circle(display, (hw, hh), 4, (0,0,255), -1);
# draw center lines
cv2.line(display, (hw,0), (hw,height), (0,0,255), 1);
cv2.line(display, (0,hh), (width,hh), (0,0,255), 1);
# draw zoom text
cv2.putText(display, "Zoom: " + str(scale), (15,40), font,
fontScale, fontColor, thickness, cv2.LINE_AA);
# show
cv2.imshow("Display", display);
key = cv2.waitKey(1);
# check keys
done = key == ord('q');
# Note: if you're actually gonna make a GUI
# use the keyboard module or something else for this
# wasd to move center-of-view
if key == ord('d'):
cov[0] += camera_spd;
if key == ord('a'):
cov[0] -= camera_spd;
if key == ord('w'):
cov[1] -= camera_spd;
if key == ord('s'):
cov[1] += camera_spd;
# z,x to decrease/increase zoom (lower bound is 1.0)
if key == ord('x'):
scale += scale_step;
if key == ord('z'):
scale -= scale_step;
scale = round(scale, 2);
# bound cov
boundCenter(cov, scale, hh, hw);
Edit: Explanation of the drawVec parameters
img: The OpenCV image to be drawn on
vec: A list of [x,y] points
pos: The offset to draw those points at
cov: Center-Of-View, where the middle of our zoomed display is pointed at
hh: Half-Height, the height of "img" divided by 2
hw: Half-Width, the width of "img" divided by 2
I have looked through my code and realized where I was making a mistake which caused points to be offset.
In my program, I have a canvas of specific size. The size of canvas is a constant and is always larger than images being drawn on canvas. When program draws an image on canvas it first resizes that image so it could fit on canvas. The size of resized image is somewhat smaller than size of canvas. Image is usually drawn starting from top left corner of canvas. Since I wanted to always draw image in the center of canvas, I shifted the location from top left corner of canvas to another point. This is what I didn't account when doing image zooming.
def zoom(image, ratio, points, canvas_off_x, canvas_off_y):
width, height = image.shape[:2]
new_width, new_height = int(ratio * width), int(ratio * height)
center_x, center_y = int(new_width / 2), int(new_height / 2)
radius_x, radius_y = int(width / 2), int(height / 2)
min_x, max_x = center_x - radius_x, center_x + radius_x
min_y, max_y = center_y - radius_y, center_y + radius_y
img_resized = cv2.resize(image, (new_width,new_height), interpolation=cv2.INTER_LINEAR)
img_cropped = img_resized[min_y:max_y+1, min_x:max_x+1]
for point in points:
x, y = point.get_original_coordinates()
x -= canvas_off_x
y -= canvas_off_y
x = int((x * ratio) - min_x + canvas_off_x)
y = int((y * ratio) - min_y + canvas_off_y)
point.set_scaled_coordinates(x, y)
In the code below canvas_off_x and canvas_off_y is the location of offset from top left corner of canvas
I'm trying to retrieve the orientation of a hand written arrows:
after removing shadows and applying binarization and dilating the lines, here are the images:
Now I'd like to get the orientation of the arrow so I have tried using HoughLines,
lines = cv2.HoughLines(edges, rho=1, theta=np.pi / 180, threshold=20)
But is seems it generates too many lines (around 54 lines), I'd like it to generate only 3 lines so I would be able to find the intersection of those lines. I can group the lines into groups of similar angle (+/-20 degrees) and then average the angle. but I'm not sure what should be rho of an average line, can somebody please give a simple example?
Is there any other approach which may be more accurate?
I'll be glad to hear, thank you all
I suggest a different approach. In summary, the approach goes as follows (made it in a hurry, might need some tuning):
Find the center of the minimum area rectangle (rotated rectangle) that encloses the whole arrow. (The circle drawn in the third image)
Find the center of gravity for all white points. It will be shifted a bit towards the actual head of the arrow. (Drawn in 4th pic as the origin of the eigenvector)
Find eigenvectors for all white points.
Find the displacement vector (the center of gravity - the center of the rotated rectangle)
Now:
Arrow angle(unoriented): is the angle of the first eigenvector
Arrow direction: is the sign of the dot product of (the first eigenvector and the centers' displacement vector)
Code:
Parts related to PCA are inspired by and mostly copied from this. I only made a minor change to the "getOrientation" method, added the following lines before it returns
angle = (angle - math.pi) * 180 / math.pi
return angle, (mean[0,0]), (mean[0,1]), p1
Code implementing the logic above:
#threshold
_, img = cv2.threshold(img, 128, 255, cv2.THRESH_OTSU)
imshow(img)
#close the image to make sure the contour is connected)
st_el = cv2.getStructuringElement(cv2.MORPH_RECT, (5, 5))
img = cv2.morphologyEx(img, cv2.MORPH_CLOSE, st_el)
imshow(img)
#get white points
pnts = cv2.findNonZero(img)
#min area rect
rect_center = cv2.minAreaRect(pnts)[0]
#draw rect center
cv2.circle(img, (int(rect_center[0]), int(rect_center[1])), 3, 128, -1)
imshow(img)
angle, pca_center, eigen_vec = getOrientation(pnts, img)
cc_vec = (rect_center[0] - pca_center[0], rect_center[1] - pca_center[1])
dot_product = cc_vec[0] * eigen_vec[0] + cc_vec[1] * eigen_vec[1]
if dot_product > 0:
angle *= -1
print ("Angle = ", angle)
imshow(img)
Edit
I suggest a simpler method. This new method does not depend on PCA for finding the unoriented angle [0 - 180]. Instead, uses the min area rectangle angle immediately. And uses the contour momentum for finding the center of gravity.
Simpler Method Code:
#get white points
pnts = cv2.findNonZero(img)
#min area rect
rect_center, size, angle = cv2.minAreaRect(pnts)
#simple fix for angle to make it in [0, 180]
angle = abs(angle)
if size[0] < size[1]:
angle += 90
#find center of gravity
M = cv2.moments(img)
gravity_center = (M["m10"] / M["m00"], M["m01"] / M["m00"])
#rot rect vec based on angle
angle_unit_vec = (math.cos(angle * 180 / math.pi), math.sin(angle * 180 / math.pi))
#cc_vec = gravity center - rect center
cc_vec = (gravity_center[0] - rect_center[0], gravity_center[1] - rect_center[1])
#if dot product is negative add 180 -> angle between [0, 360]
dot_product = cc_vec[0] * angle_unit_vec[0] + cc_vec[1] * angle_unit_vec[1]
angle += (dot_product < 0) * 180
#draw rect center
cv2.circle(img, (int(rect_center[0]), int(rect_center[1])), 3, 128, -1)
cv2.circle(img, (int(gravity_center[0]), int(gravity_center[1])), 3, 20, -1)
imshow(img)
print ("Angle = ", angle)
Edit2:
This edit includes these changes:
Use cv2.fitLine() and use the fitted line angle for orientation.
Replace angle_unit_vec with a vector that has the gravity center as the origin and goes parallel to the fitted line.
Code
#get white points
pnts = cv2.findNonZero(img)
#min area rect
rect_center, size, angle = cv2.minAreaRect(pnts)
#fit line to get angle
[vx, vy, x, y] =cv2.fitLine(pnts, cv2.DIST_L12, 0, 0.01, 0.01)
angle = (math.atan2(vy, -vx)) * 180 / math.pi
M = cv2.moments(img)
gravity_center = (M["m10"] / M["m00"], M["m01"] / M["m00"])
angle_vec = (int(gravity_center[0] + 100 * vx), int(gravity_center[1] + 100 * vy))
#cc_vec = gravity center - rect center
cc_vec = (gravity_center[0] - rect_center[0], gravity_center[1] - rect_center[1])
#if dot product is positive add 180 -> angle between [0, 360]
dot_product = cc_vec[0] * angle_vec[0] + cc_vec[1] * angle_vec[1]
angle += (dot_product > 0) * 180
angle += (angle < 0) * 360
#draw rect center
cv2.circle(img, (int(rect_center[0]), int(rect_center[1])), 3, 128, -1)
cv2.circle(img, (int(gravity_center[0]), int(gravity_center[1])), 3, 20, -1)
imshow(img)
print ("Angle = ", angle)
Output:
Using code from edit2:
First image:
Second image:
Third image:
I want to rotate an oval around it's center. Currently I can display the static object witohut rotation, and I can't seem to find what to do wit it.
EDIT: I made a rotation function based on complex number multiplication, which seemed to work on lower polygons but the ellipse kinda looks the same.
A potato-level noob C.S. student.
also, the code:
from tkinter import*
import cmath, math
import time
def poly_rot(tup, deg):
rad=deg*0.0174533
crot=cmath.exp(rad*1j)
rotpol=[]
i=0
while i < len(tup):
x=tup[i]
y=tup[i+1]
z=crot*complex(x,y)
rotpol.append(400+z.real)
rotpol.append(400+z.imag)
i=i+2
return rotpol
def poly_oval(x0,y0, x1,y1, steps=60, rotation=0):
"""return an oval as coordinates suitable for create_polygon"""
# x0,y0,x1,y1 are as create_oval
# rotation is in degrees anti-clockwise, convert to radians
rotation = rotation * math.pi / 180.0
# major and minor axes
a = (x1 - x0) / 2.0
b = (y1 - y0) / 2.0
# center
xc = x0 + a
yc = y0 + b
point_list = []
# create the oval as a list of points
for i in range(steps):
# Calculate the angle for this step
# 360 degrees == 2 pi radians
theta = (math.pi * 2) * (float(i) / steps)
x1 = a * math.cos(theta)
y1 = b * math.sin(theta)
# rotate x, y
x = (x1 * math.cos(rotation)) + (y1 * math.sin(rotation))
y = (y1 * math.cos(rotation)) - (x1 * math.sin(rotation))
point_list.append(round(x + xc))
point_list.append(round(y + yc))
return point_list
inp= input("We need an ellipse. One to fit in a 800*800 window. Give the size of it's axes separated by ','-s (ex: lx,ly)!\n")
inpu= inp.split(',')
lx=int(inpu[0])
ly=int(inpu[1])
x0=400-lx//2
x1=400+lx//2
y0=400-ly//2
y1=400+ly//2
deg= float(input("Let's rotate this ellipse! But how much, in degrees, should we?"))
pre=poly_oval(x0, y0, x1, y1)
post=poly_rot(poly_oval(x0, y0, x1, y1), deg)
root =Tk()
w = Canvas(root, width=801, height=801)
w.config(background="dark green")
w.pack()
w.create_polygon(tuple(post), fill="yellow", outline="yellow" )
root.mainloop()