Uniform 1d kernels

[mathpluscode]

Subject of the feature

Once we merged #719, we will have two nearly identical gaussian kernels

def gaussian_kernel1d_size(kernel_size: int) -> tf.Tensor:
    """
    Return a the 1D Gaussian kernel for LocalNormalizedCrossCorrelation.

    Sum of the weights is 1.

    :param kernel_size: scalar, size of the 1-D kernel
    :return: filters, of shape (kernel_size, )
    """
    mean = (kernel_size - 1) / 2.0
    sigma = kernel_size / 3

    grid = tf.range(0, kernel_size, dtype=tf.float32)
    filters = tf.exp(-tf.square(grid - mean) / (2 * sigma ** 2))
    filters = filters / tf.reduce_sum(filters)

    return filters


def gaussian_kernel1d_sigma(sigma: int) -> tf.Tensor:
    """
    Calculate a gaussian kernel.

    :param sigma: number defining standard deviation for
                  gaussian kernel.
    :return: shape = (dim, )
    """
    assert sigma > 0
    tail = int(sigma * 3)
    kernel = tf.exp([-0.5 * x ** 2 / sigma ** 2 for x in range(-tail, tail + 1)])
    kernel = kernel / tf.reduce_sum(kernel)
    return kernel

Therefore it's better to merge them, so that kernel accepts uniformly the size as an argument.

The Cauchy kernel needs to be updated to

[mathpluscode]

Now we no longer normalize the kernel, but it's still worth uniforming the kernels.

[stale]

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