66 lines
3.6 KiB
Python
66 lines
3.6 KiB
Python
import numpy as np
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import utils.kernels as kernels
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import utils.vector_utils as vector_utils
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def estimate_light(normals,grey_levels, treshold = (0,1)):
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"""Estimates the light directions using the given normals, grey levels, and mask.
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Args:
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normals (Array ..., n, dim): Normal vectors.
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grey_levels (Array ..., n): Grey levels corresponding to the normals.
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threshold (tuple, optional): Intensity threshold for valid grey levels. Defaults to (0, 1).
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Returns:
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Array ..., dim: Estimated light directions.
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"""
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validity_mask = np.logical_and(grey_levels>treshold[0],grey_levels<treshold[1])
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lights = kernels.weighted_least_squares(normals,grey_levels,validity_mask)
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return lights
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def geometric_shading_parameters(light_point, principal_directions, points):
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"""Computes geometric parameters for shading based on light source and points.
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Args:
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light_point (Array ..., dim): Coordinates of the light source.
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principal_directions (Array ..., dim): Principal directions of each light.
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points (Array ..., dim): Coordinates of the points on the surface.
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Returns:
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Array ..., dim: Distances from each point to the light source.
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Array ...: Computed light direction at each point.
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Array ...: Angular factors based on the principal directions and light direction.
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"""
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distance, light_direction = vector_utils.norm_vector(light_point-points)
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angular_factor = np.maximum(vector_utils.dot_product(principal_directions,-light_direction),0)
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return distance, light_direction, angular_factor
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def estimate_anisotropy(light_point, principal_directions, points,normals, grey_levels, min_grey_level = 0.1, min_dot_product = 0.2):
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"""Estimates anisotropy parameters based on geometric shading and grey levels.
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Args:
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light_point (Array ..., dim): Coordinates of the light source.
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principal_directions (Array ..., dim): Principal directions of each light.
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points (Array ..., dim): Coordinates of the points on the surface.
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normals (Array ..., dim): Normal vectors at each point.
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grey_levels (Array ...): Observed grey levels at each point.
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min_grey_level (float, optional): Minimum valid grey level. Defaults to 0.1.
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min_dot_product (float, optional): Minimum valid dot product for shading and angular factors. Defaults to 0.2.
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Returns:
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Array ..., 1: Estimated anisotropy parameter mu.
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Array ..., 1: Estimated flux parameter.
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"""
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distance, light_direction, angular_factor = geometric_shading_parameters(light_point, principal_directions, points)
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computed_shading = np.maximum(vector_utils.dot_product(normals,light_direction),0)
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validity_mask = np.logical_and(grey_levels>min_grey_level,np.logical_and(computed_shading>min_dot_product,angular_factor>min_dot_product))
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log_flux = np.log(np.maximum(grey_levels,min_grey_level)*np.square(distance)*np.reciprocal(np.maximum(computed_shading,min_dot_product)))
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log_factor = vector_utils.to_homogeneous(np.expand_dims(np.log(np.maximum(angular_factor,min_dot_product)),axis=-1))
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eta = kernels.weighted_least_squares(log_factor,log_flux,validity_mask)
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mu,log_phi = eta[...,0], eta[...,1]
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estimated_flux = np.exp(log_phi)
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return mu,estimated_flux
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def light_conditions(light_point, principal_directions, points, mu, flux):
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distance, light_direction, angular_factor = geometric_shading_parameters(light_point, principal_directions, points)
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light_conditions = light_direction*(np.reciprocal(np.square(distance))*np.power(angular_factor,mu)*flux)[...,np.newaxis]
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return light_conditions |