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import random
import torch
import numpy as np
class Plane:
"""
Implementation of planar RANSAC.
Class for Plane object, which finds the equation of a infinite plane using RANSAC algorithim.
Call `fit(.)` to randomly take 3 points of pointcloud to verify inliers based on a threshold.
---
"""
def __init__(self):
self.inliers = []
self.equation = []
def fit(self, pts, thresh=0.05, minPoints=100, maxIteration=1000):
"""
Find the best equation for a plane.
:param pts: 3D point cloud as a `torch.Tensor (N,3)`.
:param thresh: Threshold distance from the plane which is considered inlier.
:param maxIteration: Number of maximum iteration which RANSAC will loop over.
:returns:
- `self.equation`: Parameters of the plane using Ax+By+Cy+D `torch.Tensor(4)`
- `self.inliers`: points from the dataset considered inliers
---
"""
n_points = pts.shape[0]
best_eq = []
best_inliers = []
for it in range(maxIteration):
# Samples 3 random points
id_samples = torch.randperm(n_points)[:3]
pt_samples = pts[id_samples]
# We have to find the plane equation described by those 3 points
# We find first 2 vectors that are part of this plane
# A = pt2 - pt1
# B = pt3 - pt1
vecA = pt_samples[1, :] - pt_samples[0, :]
vecB = pt_samples[2, :] - pt_samples[0, :]
# Now we compute the cross product of vecA and vecB to get vecC which is normal to the plane
vecC = torch.cross(vecA, vecB)
# The plane equation will be vecC[0]*x + vecC[1]*y + vecC[0]*z = -k
# We have to use a point to find k
vecC = vecC / torch.norm(vecC, p=2)
k = -torch.sum(torch.mul(vecC, pt_samples[1, :]))
plane_eq = torch.tensor([vecC[0], vecC[1], vecC[2], k])
# Distance from a point to a plane
# https://mathworld.wolfram.com/Point-PlaneDistance.html
pt_id_inliers = [] # list of inliers ids
dist_pt = (
plane_eq[0] * pts[:, 0] + plane_eq[1] * pts[:, 1] + plane_eq[2] * pts[:, 2] + plane_eq[3]
) / torch.sqrt(plane_eq[0] ** 2 + plane_eq[1] ** 2 + plane_eq[2] ** 2)
# Select indexes where distance is smaller than the threshold
pt_id_inliers = torch.where(torch.abs(dist_pt) <= thresh)[0]
if len(pt_id_inliers) > len(best_inliers):
best_eq = plane_eq
best_inliers = pt_id_inliers
self.inliers = best_inliers
self.equation = best_eq
return -self.equation, self.inliers
def fit_parallel(self, pts:torch.Tensor, thresh=0.05, minPoints=100, maxIteration=1000):
"""
Find the best equation for a plane.
:param pts: 3D point cloud as a `torch.Tensor (N,3)`.
:param thresh: Threshold distance from the plane which is considered inlier.
:param maxIteration: Number of maximum iteration which RANSAC will loop over.
:returns:
- `self.equation`: Parameters of the plane using Ax+By+Cy+D `torch.Tensor(4)`
- `self.inliers`: points from the dataset considered inliers
---
"""
n_points = pts.shape[0]
# Samples shape (maxIteration, 3) random points
id_samples = torch.tensor([random.sample(range(0, n_points), 3) for _ in range(maxIteration)],device=pts.device)
pt_samples = pts[id_samples]
# We have to find the plane equation described by those 3 points
# We find first 2 vectors that are part of this plane
# A = pt2 - pt1
# B = pt3 - pt1
vecA = pt_samples[:, 1, :] - pt_samples[:, 0, :]
vecB = pt_samples[:, 2, :] - pt_samples[:, 0, :]
# Now we compute the cross product of vecA and vecB to get vecC which is normal to the plane
vecC = torch.cross(vecA, vecB, dim=-1)
# The plane equation will be vecC[0]*x + vecC[1]*y + vecC[0]*z = -k
# We have to use a point to find k
vecC = vecC / torch.norm(vecC, p=2, dim=1, keepdim=True)
k = -torch.sum(torch.mul(vecC, pt_samples[:, 1, :]), dim=1)
plane_eqs = torch.column_stack([vecC[:, 0], vecC[:, 1], vecC[:, 2], k])
# Distance from a point to a plane
# https://mathworld.wolfram.com/Point-PlaneDistance.html
dist_pt = (
plane_eqs[:,0].unsqueeze(1) * pts[:, 0] + plane_eqs[:,1].unsqueeze(1) * pts[:, 1] + plane_eqs[:,2].unsqueeze(1) * pts[:, 2] + plane_eqs[:,3].unsqueeze(1)
) / torch.sqrt(plane_eqs[:,0] ** 2 + plane_eqs[:,1] ** 2 + plane_eqs[:,2] ** 2).unsqueeze(1)
# Select indexes where distance is smaller than the threshold
# maxIteration x n_points
# row with most inliers
pt_id_inliers = torch.abs(dist_pt) <= thresh
counts = torch.sum(pt_id_inliers, dim=1)
best_eq = plane_eqs[torch.argmax(counts)]
best_inliers_id = pt_id_inliers[torch.argmax(counts)]
# convert boolean tensor to indices
best_inliers = torch.where(best_inliers_id)[0]
self.inliers = best_inliers
self.equation = best_eq
return -self.equation, self.inliers
class Plane_np:
"""
Implementation of planar RANSAC.
Class for Plane object, which finds the equation of a infinite plane using RANSAC algorithim.
Call `fit(.)` to randomly take 3 points of pointcloud to verify inliers based on a threshold.
---
"""
def __init__(self):
self.inliers = []
self.equation = []
def fit(self, pts, thresh=0.05, minPoints=100, maxIteration=1000):
"""
Find the best equation for a plane.
:param pts: 3D point cloud as a `np.array (N,3)`.
:param thresh: Threshold distance from the plane which is considered inlier.
:param maxIteration: Number of maximum iteration which RANSAC will loop over.
:returns:
- `self.equation`: Parameters of the plane using Ax+By+Cy+D `np.array (1, 4)`
- `self.inliers`: points from the dataset considered inliers
---
"""
n_points = pts.shape[0]
best_eq = []
best_inliers = []
for it in range(maxIteration):
# Samples 3 random points
id_samples = random.sample(range(0, n_points), 3)
pt_samples = pts[id_samples]
# We have to find the plane equation described by those 3 points
# We find first 2 vectors that are part of this plane
# A = pt2 - pt1
# B = pt3 - pt1
vecA = pt_samples[1, :] - pt_samples[0, :]
vecB = pt_samples[2, :] - pt_samples[0, :]
# Now we compute the cross product of vecA and vecB to get vecC which is normal to the plane
vecC = np.cross(vecA, vecB)
# The plane equation will be vecC[0]*x + vecC[1]*y + vecC[0]*z = -k
# We have to use a point to find k
vecC = vecC / np.linalg.norm(vecC)
k = -np.sum(np.multiply(vecC, pt_samples[1, :]))
plane_eq = [vecC[0], vecC[1], vecC[2], k]
# Distance from a point to a plane
# https://mathworld.wolfram.com/Point-PlaneDistance.html
pt_id_inliers = [] # list of inliers ids
dist_pt = (
plane_eq[0] * pts[:, 0] + plane_eq[1] * pts[:, 1] + plane_eq[2] * pts[:, 2] + plane_eq[3]
) / np.sqrt(plane_eq[0] ** 2 + plane_eq[1] ** 2 + plane_eq[2] ** 2)
# Select indexes where distance is biggers than the threshold
pt_id_inliers = np.where(np.abs(dist_pt) <= thresh)[0]
if len(pt_id_inliers) > len(best_inliers):
best_eq = plane_eq
best_inliers = pt_id_inliers
self.inliers = best_inliers
self.equation = best_eq
return self.equation, self.inliers
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