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cian-psandChristian Clauss
cc142b1ef5
* Add gramian algorithm * Update docstring with additional references Added references to Gram matrices and neural style transfer in the docstring. --------- Co-authored-by: Christian Clauss <cclauss@me.com>
70 lines
1.9 KiB
Python
70 lines
1.9 KiB
Python
"""
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Image style reconstruction with Gram matrices.
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https://en.wikipedia.org/wiki/Gram_matrix
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https://en.wikipedia.org/wiki/Neural_style_transfer
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https://arxiv.org/pdf/1603.08155#page=7&zoom=auto,-294,3
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"""
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import numpy as np
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def gram_matrix(mat: np.ndarray) -> np.ndarray:
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"""
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Returns the Gram (Gramian) matrix of an image.
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:param mat: matrix of shape (C, H, W); C = color channels, H = height, W = width.
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:type mat: np.ndarray
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:return: matrix of shape (C, C).
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:rtype: np.ndarray
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Examples
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--------
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>>> gram_matrix(np.ones((2,5,5)))
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array([[0.5, 0.5],
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[0.5, 0.5]])
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>>> gram_matrix(np.ones((3,5,5)))
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array([[0.33333333, 0.33333333, 0.33333333],
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[0.33333333, 0.33333333, 0.33333333],
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[0.33333333, 0.33333333, 0.33333333]])
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>>> gram_matrix(np.ones((3,5,5))).shape
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(3, 3)
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"""
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color, height, width = mat.shape
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vec = mat.reshape(color, height * width)
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gram = vec @ vec.T
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return gram / (color * height * width)
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def gram_loss(input_features: np.ndarray, reference_features: np.ndarray) -> np.float64:
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"""
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Calculates the squared Frobenius norm of the difference between
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the Gram matrices of the input and reference image.
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:param input_features: Feature map of shape (C, H, W)
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:type input_features: np.ndarray
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:param reference_features: Feature map of shape (C, H, W)
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:type reference_features: np.ndarray
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:return: Gram loss between the two feature maps.
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:rtype: float64
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Examples
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--------
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>>> a = np.random.randn(3,5,5)
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>>> gram_loss(a, a)
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np.float64(0.0)
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>>> a = np.zeros((3,5,5))
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>>> b = np.ones((3,5,5))
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>>> gram_loss(a, b)
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np.float64(1.0)
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"""
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input_gram = gram_matrix(input_features)
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reference_gram = gram_matrix(reference_features)
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return np.sum(np.square(input_gram - reference_gram)).astype(np.float64)
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if __name__ == "__main__":
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import doctest
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doctest.testmod()
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