158 lines
4.2 KiB
Python
158 lines
4.2 KiB
Python
import cv2
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import numpy as np
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import torch
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from tqdm import tqdm
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WIN = "window"
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SPACING = 50
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GREEN = (0, 255, 0)
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RED = (0, 0, 255)
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def area_between_curves(a, b):
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polygon = torch.cat([b, torch.flip(a, dims=[0])], dim=0)
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# Calculate the area using the shoelace formula
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x = polygon[:, 0]
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y = polygon[:, 1]
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return 0.5 * torch.abs(x @ torch.roll(y, -1) - torch.roll(x, -1) @ y)
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def sample_polyline(line, t):
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deltas = seglengths(line)
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d = torch.cumsum(deltas, dim=0) / torch.sum(deltas)
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d = torch.cat([torch.zeros_like(d[0:1]), d])
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idx = torch.searchsorted(d, t)
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plus = line[idx]
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minus = line[idx - 1]
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rem = (t - d[idx - 1]) / (d[idx] - d[idx - 1] + 1e-8)
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return (1 - rem[..., None]) * minus + rem[..., None] * plus
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def per_point_manhattan_distance(a, b, t):
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points_a = sample_polyline(a, t)
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points_b = sample_polyline(b, t)
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return torch.sum(torch.abs(points_a - points_b), dim=-1)
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def per_point_euclidean_distance(a, b, t):
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points_a = sample_polyline(a, t)
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points_b = sample_polyline(b, t)
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return torch.norm(points_a - points_b, dim=-1)
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def seglengths(line):
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return torch.norm(torch.diff(line, dim=-2), dim=-1)
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def spacing_error(line):
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# Calculate the distances between consecutive points
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return torch.mean(torch.abs(SPACING - seglengths(line)))
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def fit_to_line(line, *, canvas):
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total_length = np.sum(np.linalg.norm(np.diff(line, axis=0), axis=1))
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num_points = np.ceil(total_length / SPACING).astype(int)
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# Generate evenly spaced points along the line
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if len(line) < 2:
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return None
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init = np.linspace(line[0], line[-1], num_points)
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if len(line) < 3:
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return init
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fit = torch.tensor(init, dtype=torch.float32, requires_grad=True)
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line_pt = torch.tensor(line, dtype=torch.float32)
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optimizer = torch.optim.Adam([fit], lr=1)
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while True:
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optimizer.zero_grad()
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sample_points = torch.rand((num_points // 2), dtype=torch.float32)
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sample_line = sample_polyline(line_pt, sample_points)
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sample_fit = sample_polyline(fit, sample_points)
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loss = torch.mean(torch.norm(sample_line - sample_fit, dim=-1)) + spacing_error(
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fit
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)
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loss.backward()
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optimizer.step()
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img = canvas.copy()
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img = draw_line(img, line_pt.numpy(), GREEN)
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img = draw_line(img, fit.detach().numpy(), RED, with_points=True)
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# img = draw_circles(img, sample_line.numpy(), GREEN)
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# img = draw_circles(img, sample_fit.detach().numpy(), RED)
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cv2.imshow(WIN, img)
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if cv2.waitKey(1) == ord("q"):
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break
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fit = fit.detach()
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abc = area_between_curves(line_pt, fit)
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spacing_err = spacing_error(fit)
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print("Area between curves:", abc.item())
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print("Spacing error:", spacing_err.item())
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return fit.numpy()
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def draw_circles(img, points, color):
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for point in points:
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cv2.circle(img, tuple(np.round(point).astype(np.int32)), 5, color, -1)
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return img
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def draw_line(img, line, color, *, with_points=False):
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if len(line) > 1:
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cv2.polylines(img, [np.round(line).astype(np.int32)], False, color, 2)
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if with_points:
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img = draw_circles(img, line, color)
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return img
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def main():
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line = []
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is_calculating = {}
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canvas = np.zeros((500, 500, 3), dtype=np.uint8)
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cv2.namedWindow(WIN)
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cv2.imshow(WIN, canvas)
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def on_mouse(event, x, y, flags, _):
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def lbuttondown():
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line.append((x, y))
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if len(line) == 1:
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return
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line_np = np.array(line)
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img = draw_line(canvas.copy(), line_np, GREEN)
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if (fit := fit_to_line(line_np, canvas=canvas)) is not None:
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img = draw_line(img, fit, RED)
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cv2.imshow(WIN, img)
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if is_calculating.get(event, False):
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return
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is_calculating[event] = True
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if event == cv2.EVENT_LBUTTONDOWN:
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lbuttondown()
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is_calculating[event] = False
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cv2.setMouseCallback(WIN, on_mouse)
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while True:
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if (k := cv2.waitKey(1)) == ord("c"):
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line.clear()
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cv2.imshow(WIN, canvas)
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elif k == ord("q"):
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break
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if __name__ == "__main__":
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main()
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