From 394e19b012cb9264feaec582948fa7ac8bff901c Mon Sep 17 00:00:00 2001 From: Chuyan Zhang Date: Mon, 15 Jan 2024 15:49:41 -0800 Subject: init commit --- similarity.py | 69 +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ 1 file changed, 69 insertions(+) create mode 100644 similarity.py (limited to 'similarity.py') diff --git a/similarity.py b/similarity.py new file mode 100644 index 0000000..fec83d6 --- /dev/null +++ b/similarity.py @@ -0,0 +1,69 @@ +from gaussian import Gaussian +from utils import quat2rot +from aabb import process_aabb, intersect, min_interval +import numpy as np + +def similarity(gaussian: Gaussian, id1: int, id2: int): + geometry_sim = geometry_similarity(gaussian, id1, id2) + color_sim = color_similarity(gaussian.sh[id1], gaussian.sh[id2]) + color_max = np.max(np.abs(gaussian.sh)) + # return geometry_sim * geometry_coeff + color_sim * color_coeff + return geometry_sim, color_sim / (color_max * color_max * 48) + +def color_similarity(c1: np.ndarray, c2: np.ndarray): + return np.sum(c1 * c2) + +def geometry_similarity(gaussian: Gaussian, id1: int, id2: int): + def geometry_similarity_using_overlap(gaussian: Gaussian, id1: int, id2: int): + aabb1 = process_aabb(gaussian.positions[id1], gaussian.scales[id1], gaussian.rotations[id1], scale_factor=2) + aabb2 = process_aabb(gaussian.positions[id2], gaussian.scales[id2], gaussian.rotations[id2], scale_factor=2) + # 在两个 aabb 里 stratified sample 点，对两个 Gaussian 的乘积做积分 + # 然后除以总sample数作为重叠程度的 metric + + intersected_aabb = intersect(aabb1, aabb2) + + if intersected_aabb is None: + return 0 + + x_stride = (intersected_aabb[1] - intersected_aabb[0]) / (4. + 1e-3) + y_stride = (intersected_aabb[3] - intersected_aabb[2]) / (4. + 1e-3) + z_stride = (intersected_aabb[5] - intersected_aabb[4]) / (4. + 1e-3) + + score = 0 + for i in range(int(np.floor((intersected_aabb[1] - intersected_aabb[0]) / x_stride))): + x = intersected_aabb[0] + i * x_stride + for j in range(int(np.floor((intersected_aabb[3] - intersected_aabb[2]) / y_stride))): + y = intersected_aabb[2] + j * y_stride + for k in range(int(np.floor((intersected_aabb[5] - intersected_aabb[4]) / z_stride))): + z = intersected_aabb[4] + k * z_stride + pos = np.array([x, y, z]) + score += gaussian.calc(pos, id1, 10) * gaussian.calc(pos, id2, 10) * gaussian.opacity[id1] * gaussian.opacity[id2] + + scale1 = gaussian.scales[id1][0] * gaussian.scales[id1][1] * gaussian.scales[id1][2] + scale2 = gaussian.scales[id2][0] * gaussian.scales[id2][1] * gaussian.scales[id2][2] + + # print(f"calculating pair ({id1},{id2}), used {64} samples.") + return score / (scale1 * scale2) + + def geometry_similarity_using_position(gaussian: Gaussian, id1: int, id2: int): + def position_similarity(p1: np.ndarray, p2: np.ndarray): + return np.linalg.norm(p1 - p2) + + def scale_similarity(s1: np.ndarray, s2: np.ndarray): + return np.linalg.norm(s1 - s2) + + def rotation_similarity(q1: np.ndarray, q2: np.ndarray): + return 1 - np.dot(q1, q2) + # r1 = quat2rot(q1) + # r2 = quat2rot(q2) + # eigenvalues, eigenvectors = np.linalg.eig(r1 @ r2.T) + # return np.linalg.norm(eigenvectors @ np.diag(np.log(eigenvalues)) @ np.linalg.inv(eigenvectors)) + position_coeff = 1. + scale_coeff = 1. + rotation_coeff = 1. + return position_similarity(gaussian.positions[id1], gaussian.positions[id2]) * position_coeff + \ + scale_similarity(gaussian.scales[id1], gaussian.scales[id2]) * scale_coeff + \ + rotation_similarity(gaussian.rotations[id1], gaussian.rotations[id2]) * rotation_coeff + + return geometry_similarity_using_overlap(gaussian, id1, id2) + -- cgit v1.2.3-70-g09d2