fmix.py

# Copyright (c) 2021 PaddlePaddle Authors. All Rights Reserved.
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
#     http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.

import math
import random

import numpy as np
from scipy.stats import beta


def fftfreqnd(h, w=None, z=None):
    """ Get bin values for discrete fourier transform of size (h, w, z)

    :param h: Required, first dimension size
    :param w: Optional, second dimension size
    :param z: Optional, third dimension size
    """
    fz = fx = 0
    fy = np.fft.fftfreq(h)

    if w is not None:
        fy = np.expand_dims(fy, -1)

        if w % 2 == 1:
            fx = np.fft.fftfreq(w)[:w // 2 + 2]
        else:
            fx = np.fft.fftfreq(w)[:w // 2 + 1]

    if z is not None:
        fy = np.expand_dims(fy, -1)
        if z % 2 == 1:
            fz = np.fft.fftfreq(z)[:, None]
        else:
            fz = np.fft.fftfreq(z)[:, None]

    return np.sqrt(fx * fx + fy * fy + fz * fz)


def get_spectrum(freqs, decay_power, ch, h, w=0, z=0):
    """ Samples a fourier image with given size and frequencies decayed by decay power

    :param freqs: Bin values for the discrete fourier transform
    :param decay_power: Decay power for frequency decay prop 1/f**d
    :param ch: Number of channels for the resulting mask
    :param h: Required, first dimension size
    :param w: Optional, second dimension size
    :param z: Optional, third dimension size
    """
    scale = np.ones(1) / (np.maximum(freqs, np.array([1. / max(w, h, z)]))
                          **decay_power)

    param_size = [ch] + list(freqs.shape) + [2]
    param = np.random.randn(*param_size)

    scale = np.expand_dims(scale, -1)[None, :]

    return scale * param


def make_low_freq_image(decay, shape, ch=1):
    """ Sample a low frequency image from fourier space

    :param decay_power: Decay power for frequency decay prop 1/f**d
    :param shape: Shape of desired mask, list up to 3 dims
    :param ch: Number of channels for desired mask
    """
    freqs = fftfreqnd(*shape)
    spectrum = get_spectrum(freqs, decay, ch,
                            *shape)  #.reshape((1, *shape[:-1], -1))
    spectrum = spectrum[:, 0] + 1j * spectrum[:, 1]
    mask = np.real(np.fft.irfftn(spectrum, shape))

    if len(shape) == 1:
        mask = mask[:1, :shape[0]]
    if len(shape) == 2:
        mask = mask[:1, :shape[0], :shape[1]]
    if len(shape) == 3:
        mask = mask[:1, :shape[0], :shape[1], :shape[2]]

    mask = mask
    mask = (mask - mask.min())
    mask = mask / mask.max()
    return mask


def sample_lam(alpha, reformulate=False):
    """ Sample a lambda from symmetric beta distribution with given alpha

    :param alpha: Alpha value for beta distribution
    :param reformulate: If True, uses the reformulation of [1].
    """
    if reformulate:
        lam = beta.rvs(alpha + 1, alpha)
    else:
        lam = beta.rvs(alpha, alpha)

    return lam


def binarise_mask(mask, lam, in_shape, max_soft=0.0):
    """ Binarises a given low frequency image such that it has mean lambda.

    :param mask: Low frequency image, usually the result of `make_low_freq_image`
    :param lam: Mean value of final mask
    :param in_shape: Shape of inputs
    :param max_soft: Softening value between 0 and 0.5 which smooths hard edges in the mask.
    :return:
    """
    idx = mask.reshape(-1).argsort()[::-1]
    mask = mask.reshape(-1)
    num = math.ceil(lam * mask.size) if random.random() > 0.5 else math.floor(
        lam * mask.size)

    eff_soft = max_soft
    if max_soft > lam or max_soft > (1 - lam):
        eff_soft = min(lam, 1 - lam)

    soft = int(mask.size * eff_soft)
    num_low = int(num - soft)
    num_high = int(num + soft)

    mask[idx[:num_high]] = 1
    mask[idx[num_low:]] = 0
    mask[idx[num_low:num_high]] = np.linspace(1, 0, (num_high - num_low))

    mask = mask.reshape((1, 1, in_shape[0], in_shape[1]))
    return mask


def sample_mask(alpha, decay_power, shape, max_soft=0.0, reformulate=False):
    """ Samples a mean lambda from beta distribution parametrised by alpha, creates a low frequency image and binarises
    it based on this lambda

    :param alpha: Alpha value for beta distribution from which to sample mean of mask
    :param decay_power: Decay power for frequency decay prop 1/f**d
    :param shape: Shape of desired mask, list up to 3 dims
    :param max_soft: Softening value between 0 and 0.5 which smooths hard edges in the mask.
    :param reformulate: If True, uses the reformulation of [1].
    """
    if isinstance(shape, int):
        shape = (shape, )

    # Choose lambda
    lam = sample_lam(alpha, reformulate)

    # Make mask, get mean / std
    mask = make_low_freq_image(decay_power, shape)
    mask = binarise_mask(mask, lam, shape, max_soft)

    return float(lam), mask


def sample_and_apply(x,
                     alpha,
                     decay_power,
                     shape,
                     max_soft=0.0,
                     reformulate=False):
    """

    :param x: Image batch on which to apply fmix of shape [b, c, shape*]
    :param alpha: Alpha value for beta distribution from which to sample mean of mask
    :param decay_power: Decay power for frequency decay prop 1/f**d
    :param shape: Shape of desired mask, list up to 3 dims
    :param max_soft: Softening value between 0 and 0.5 which smooths hard edges in the mask.
    :param reformulate: If True, uses the reformulation of [1].
    :return: mixed input, permutation indices, lambda value of mix,
    """
    lam, mask = sample_mask(alpha, decay_power, shape, max_soft, reformulate)
    index = np.random.permutation(x.shape[0])

    x1, x2 = x * mask, x[index] * (1 - mask)
    return x1 + x2, index, lam


class FMixBase:
    """ FMix augmentation

        Args:
            decay_power (float): Decay power for frequency decay prop 1/f**d
            alpha (float): Alpha value for beta distribution from which to sample mean of mask
            size ([int] | [int, int] | [int, int, int]): Shape of desired mask, list up to 3 dims
            max_soft (float): Softening value between 0 and 0.5 which smooths hard edges in the mask.
            reformulate (bool): If True, uses the reformulation of [1].
    """

    def __init__(self,
                 decay_power=3,
                 alpha=1,
                 size=(32, 32),
                 max_soft=0.0,
                 reformulate=False):
        super().__init__()
        self.decay_power = decay_power
        self.reformulate = reformulate
        self.size = size
        self.alpha = alpha
        self.max_soft = max_soft
        self.index = None
        self.lam = None

    def __call__(self, x):
        raise NotImplementedError

    def loss(self, *args, **kwargs):
        raise NotImplementedError