Implemention of an algorithm for image style reconstruction (#14233)

* 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>

Author: pablocian

computer_vision/gramian.py

@@ -0,0 +1,69 @@
+"""
+Image style reconstruction with Gram matrices.
+
+https://en.wikipedia.org/wiki/Gram_matrix
+https://en.wikipedia.org/wiki/Neural_style_transfer
+https://arxiv.org/pdf/1603.08155#page=7&zoom=auto,-294,3
+"""
+
+import numpy as np
+
+
+def gram_matrix(mat: np.ndarray) -> np.ndarray:
+    """
+    Returns the Gram (Gramian) matrix of an image.
+
+    :param mat: matrix of shape (C, H, W); C = color channels, H = height, W = width.
+    :type mat: np.ndarray
+    :return: matrix of shape (C, C).
+    :rtype: np.ndarray
+
+    Examples
+    --------
+    >>> gram_matrix(np.ones((2,5,5)))
+    array([[0.5, 0.5],
+           [0.5, 0.5]])
+    >>> gram_matrix(np.ones((3,5,5)))
+    array([[0.33333333, 0.33333333, 0.33333333],
+           [0.33333333, 0.33333333, 0.33333333],
+           [0.33333333, 0.33333333, 0.33333333]])
+    >>> gram_matrix(np.ones((3,5,5))).shape
+    (3, 3)
+    """
+    color, height, width = mat.shape
+    vec = mat.reshape(color, height * width)
+    gram = vec @ vec.T
+    return gram / (color * height * width)
+
+
+def gram_loss(input_features: np.ndarray, reference_features: np.ndarray) -> np.float64:
+    """
+    Calculates the squared Frobenius norm of the difference between
+    the Gram matrices of the input and reference image.
+
+    :param input_features: Feature map of shape (C, H, W)
+    :type input_features: np.ndarray
+    :param reference_features: Feature map of shape (C, H, W)
+    :type reference_features: np.ndarray
+    :return: Gram loss between the two feature maps.
+    :rtype: float64
+
+    Examples
+    --------
+    >>> a = np.random.randn(3,5,5)
+    >>> gram_loss(a, a)
+    np.float64(0.0)
+    >>> a = np.zeros((3,5,5))
+    >>> b = np.ones((3,5,5))
+    >>> gram_loss(a, b)
+    np.float64(1.0)
+    """
+    input_gram = gram_matrix(input_features)
+    reference_gram = gram_matrix(reference_features)
+    return np.sum(np.square(input_gram - reference_gram)).astype(np.float64)
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()