Get points coordinates in correspondance to ellipse axes

I have a couple of objects that have points inside of them. I fitted an ellipse around them and want to get the coordinates of the points in a normalized way since the ellipses have different shapes and rotations

The original images are as such:

I got to this point but don’t know how to make the axes of the ellipse as my axes:

I first fitted the ellipse:

# find largest contour
mask_gray = cv2.cvtColor(img, cv2.COLOR_BGR2GRAY)
ret, thresh = cv2.threshold(mask_gray, 0, 255, cv2.THRESH_BINARY)

contours, hierarchy = cv2.findContours(thresh, cv2.RETR_TREE,
cnt=[item for sublist in contours for item in sublist]
ellipse = cv2.fitEllipse(cnt)
(xc,yc),(d1,d2),angle = ellipse

I then detected the points and drew them with the function then drew the ellipse
I also drew the axis this way:

rmajor = max(d1,d2)/2
if angle > 90:
     angle = angle - 90
      angle = angle + 90
xtop = xc + math.cos(math.radians(angle))*rmajor
ytop = yc + math.sin(math.radians(angle))*rmajor
xbot = xc + math.cos(math.radians(angle+180))*rmajor
ybot = yc + math.sin(math.radians(angle+180))*rmajor
cv2.line(result, (int(xtop),int(ytop)), (int(xbot),int(ybot)), (0, 0, 255), 1)

I then rotated the image with:

result = ndimage.rotate(result,angle) 

with the angle being the angle of the ellipse so that the axes are kind of the same for all ellipses since I want the coordinates to be normalized for all images