378 lines
14 KiB
Python
378 lines
14 KiB
Python
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# Copyright 2015 The TensorFlow Authors. All Rights Reserved.
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#
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# Licensed under the Apache License, Version 2.0 (the "License");
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# you may not use this file except in compliance with the License.
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# You may obtain a copy of the License at
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#
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# http://www.apache.org/licenses/LICENSE-2.0
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#
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# Unless required by applicable law or agreed to in writing, software
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# distributed under the License is distributed on an "AS IS" BASIS,
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# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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# See the License for the specific language governing permissions and
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# limitations under the License.
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# ==============================================================================
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"""Contains Gradient functions for image ops."""
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from tensorflow.python.framework import dtypes
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from tensorflow.python.framework import ops
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from tensorflow.python.ops import array_ops
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from tensorflow.python.ops import gen_image_ops
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from tensorflow.python.ops import math_ops
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@ops.RegisterGradient("ResizeNearestNeighbor")
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def _ResizeNearestNeighborGrad(op, grad):
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"""The derivatives for nearest neighbor resizing.
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Args:
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op: The ResizeNearestNeighbor op.
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grad: The tensor representing the gradient w.r.t. the output.
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Returns:
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The gradients w.r.t. the input and the output.
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"""
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image = op.inputs[0]
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if image.get_shape()[1:3].is_fully_defined():
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image_shape = image.get_shape()[1:3]
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else:
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image_shape = array_ops.shape(image)[1:3]
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grads = gen_image_ops.resize_nearest_neighbor_grad(
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grad,
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image_shape,
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align_corners=op.get_attr("align_corners"),
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half_pixel_centers=op.get_attr("half_pixel_centers"))
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return [grads, None]
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@ops.RegisterGradient("ResizeBilinear")
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def _ResizeBilinearGrad(op, grad):
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"""The derivatives for bilinear resizing.
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Args:
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op: The ResizeBilinear op.
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grad: The tensor representing the gradient w.r.t. the output.
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Returns:
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The gradients w.r.t. the input.
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"""
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grad0 = gen_image_ops.resize_bilinear_grad(
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grad,
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op.inputs[0],
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align_corners=op.get_attr("align_corners"),
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half_pixel_centers=op.get_attr("half_pixel_centers"))
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return [grad0, None]
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@ops.RegisterGradient("ScaleAndTranslate")
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def _ScaleAndTranslateGrad(op, grad):
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"""The derivatives for ScaleAndTranslate transformation op.
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Args:
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op: The ScaleAndTranslate op.
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grad: The tensor representing the gradient w.r.t. the output.
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Returns:
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The gradients w.r.t. the input.
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"""
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grad0 = gen_image_ops.scale_and_translate_grad(
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grad,
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op.inputs[0],
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op.inputs[2],
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op.inputs[3],
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kernel_type=op.get_attr("kernel_type"),
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antialias=op.get_attr("antialias"))
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return [grad0, None, None, None]
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@ops.RegisterGradient("ResizeBicubic")
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def _ResizeBicubicGrad(op, grad):
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"""The derivatives for bicubic resizing.
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Args:
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op: The ResizeBicubic op.
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grad: The tensor representing the gradient w.r.t. the output.
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Returns:
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The gradients w.r.t. the input.
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"""
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allowed_types = [dtypes.float32, dtypes.float64]
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grad0 = None
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if op.inputs[0].dtype in allowed_types:
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grad0 = gen_image_ops.resize_bicubic_grad(
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grad,
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op.inputs[0],
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align_corners=op.get_attr("align_corners"),
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half_pixel_centers=op.get_attr("half_pixel_centers"))
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return [grad0, None]
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@ops.RegisterGradient("CropAndResize")
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def _CropAndResizeGrad(op, grad):
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"""The derivatives for crop_and_resize.
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We back-propagate to the image only when the input image tensor has floating
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point dtype but we always back-propagate to the input boxes tensor.
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Args:
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op: The CropAndResize op.
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grad: The tensor representing the gradient w.r.t. the output.
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Returns:
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The gradients w.r.t. the input image, boxes, as well as the always-None
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gradients w.r.t. box_ind and crop_size.
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"""
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image = op.inputs[0]
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if image.get_shape().is_fully_defined():
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image_shape = image.get_shape().as_list()
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else:
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image_shape = array_ops.shape(image)
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allowed_types = [dtypes.float16, dtypes.float32, dtypes.float64]
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if op.inputs[0].dtype in allowed_types:
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# pylint: disable=protected-access
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grad0 = gen_image_ops.crop_and_resize_grad_image(
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grad, op.inputs[1], op.inputs[2], image_shape, T=op.get_attr("T"),
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method=op.get_attr("method"))
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# pylint: enable=protected-access
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else:
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grad0 = None
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# `grad0` is the gradient to the input image pixels and it
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# has been implemented for nearest neighbor and bilinear sampling
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# respectively. `grad1` is the gradient to the input crop boxes' coordinates.
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# When using nearest neighbor sampling, the gradient to crop boxes'
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# coordinates are not well defined. In practice, we still approximate
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# grad1 using the gradient derived from bilinear sampling.
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grad1 = gen_image_ops.crop_and_resize_grad_boxes(
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grad, op.inputs[0], op.inputs[1], op.inputs[2])
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return [grad0, grad1, None, None]
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def _CustomReciprocal(x):
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"""Wrapper function around `math_ops.div_no_nan()` to perform a "safe" reciprocal incase the input is zero. Avoids divide by zero and NaNs.
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Input:
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x -> input tensor to be reciprocat-ed.
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Returns:
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x_reciprocal -> reciprocal of x without NaNs.
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"""
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return math_ops.div_no_nan(math_ops.cast(1.0, x.dtype), x)
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@ops.RegisterGradient("RGBToHSV")
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def _RGBToHSVGrad(op, grad):
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"""The gradients for `rgb_to_hsv` operation.
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This function is a piecewise continuous function as defined here:
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https://en.wikipedia.org/wiki/HSL_and_HSV#From_RGB
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We perform the multivariate derivative and compute all partial derivatives
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separately before adding them in the end. Formulas are given before each
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partial derivative calculation.
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Args:
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op: The `rgb_to_hsv` `Operation` that we are differentiating.
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grad: Gradient with respect to the output of the `rgb_to_hsv` op.
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Returns:
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Gradients with respect to the input of `rgb_to_hsv`.
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"""
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# Input Channels
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reds = op.inputs[0][..., 0]
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greens = op.inputs[0][..., 1]
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blues = op.inputs[0][..., 2]
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# Output Channels
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saturation = op.outputs[0][..., 1]
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value = op.outputs[0][..., 2]
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dtype = op.inputs[0].dtype
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# Mask/Indicator for max and min values of each pixel.
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# Arbitrary assignment in case of tie breakers with R>G>B.
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# Max values
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red_biggest = math_ops.cast((reds >= blues) & \
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(reds >= greens), dtype)
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green_biggest = math_ops.cast((greens > reds) & \
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(greens >= blues), dtype)
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blue_biggest = math_ops.cast((blues > reds) & \
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(blues > greens), dtype)
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# Min values
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red_smallest = math_ops.cast((reds < blues) & \
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(reds < greens), dtype)
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green_smallest = math_ops.cast((greens <= reds) & \
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(greens < blues), dtype)
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blue_smallest = math_ops.cast((blues <= reds) & \
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(blues <= greens), dtype)
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# Derivatives of R, G, B wrt Value slice
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dv_dr = red_biggest
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dv_dg = green_biggest
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dv_db = blue_biggest
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# Derivatives of R, G, B wrt Saturation slice
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# The first term in the addition is the case when the corresponding color
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# from (r,g,b) was "MAX"
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# -> derivative = MIN/square(MAX), MIN could be one of the other two colors
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# The second term is the case when the corresponding color from
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# (r,g,b) was "MIN"
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# -> derivative = -1/MAX, MAX could be one of the other two colours.
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ds_dr = math_ops.cast(reds > 0, dtype) * math_ops.add(
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red_biggest * math_ops.add(green_smallest * greens, blue_smallest * blues)
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* _CustomReciprocal(math_ops.square(reds)), red_smallest * -1 *
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_CustomReciprocal((green_biggest * greens) + (blue_biggest * blues)))
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ds_dg = math_ops.cast(greens > 0, dtype) * math_ops.add(
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green_biggest * math_ops.add(red_smallest * reds, blue_smallest * blues) *
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_CustomReciprocal(math_ops.square(greens)), green_smallest * -1 *
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_CustomReciprocal((red_biggest * reds) + (blue_biggest * blues)))
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ds_db = math_ops.cast(blues > 0, dtype) * math_ops.add(
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blue_biggest * math_ops.add(green_smallest * greens, red_smallest * reds)
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* _CustomReciprocal(math_ops.square(blues)), blue_smallest * -1 *
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_CustomReciprocal((green_biggest * greens) + (red_biggest * reds)))
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# Derivatives of R, G, B wrt Hue slice
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# Need to go case by case for each color.
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# for red, dh_dr -> dh_dr_1 + dh_dr_2 + dh_dr_3 + dh_dr_4 + dh_dr_5
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# dh_dr_1 ->
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# if red was MAX, then derivative = 60 * -1 * (G-B)/square(MAX-MIN) == 60 *\
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# -1 * (greens-blues) * reciprocal(square(saturation)) * \
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# reciprocal(square(value))
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# elif green was MAX, there are two subcases
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# ie when red was MIN and when red was NOT MIN
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# dh_dr_2 ->
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# if red was MIN (use UV rule) -> 60 * ((1 * -1/(MAX-MIN)) +\
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# (B-R)*(-1/square(MAX-MIN) * -1)) == 60 * (blues - greens) *\
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# reciprocal(square(reds - greens))
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# dh_dr_3 ->
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# if red was NOT MIN -> 60 * -1/MAX-MIN == -60 * reciprocal(greens-blues)
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# elif blue was MAX, there are two subcases
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# dh_dr_4 ->
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# if red was MIN (similarly use the UV rule) -> 60 * (blues - greens) *\
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# reciprocal(square(blues - reds))
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# dh_dr_5 ->
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# if red was NOT MIN -> 60 * 1/MAX-MIN == 60 * reciprocal(blues-greens)
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dh_dr_1 = 60 * (
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math_ops.cast(reds > 0, dtype) * red_biggest * -1 *
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(greens - blues) * _CustomReciprocal(math_ops.square(saturation)) *
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_CustomReciprocal(math_ops.square(value)))
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dh_dr_2 = 60 * (
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math_ops.cast(greens > 0, dtype) * green_biggest * red_smallest *
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(blues - greens) * _CustomReciprocal(math_ops.square(reds - greens)))
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dh_dr_3 = 60 * (
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math_ops.cast(greens > 0, dtype) * green_biggest * blue_smallest * -1 *
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_CustomReciprocal(greens - blues))
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dh_dr_4 = 60 * (
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math_ops.cast(blues > 0, dtype) * blue_biggest * red_smallest *
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(blues - greens) * _CustomReciprocal(math_ops.square(blues - reds)))
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dh_dr_5 = 60 * (
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math_ops.cast(blues > 0, dtype) * blue_biggest * green_smallest *
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_CustomReciprocal(blues - greens))
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dh_dr = dh_dr_1 + dh_dr_2 + dh_dr_3 + dh_dr_4 + dh_dr_5
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# Converting from degrees to [0,1] scale as specified in
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# https://www.tensorflow.org/api_docs/python/tf/image/rgb_to_hsv
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dh_dr = dh_dr / 360
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# for green, dh_dg -> dh_dg_1 + dh_dg_2 + dh_dg_3 + dh_dg_4 + dh_dg_5
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# dh_dg_1 ->
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# if green was MAX, then derivative = 60 * -1 * (B-R)/square(MAX-MIN) == 60 *\
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# -1 * (blues - reds) * reciprocal(square(saturation)) * \
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# reciprocal(square(value))
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# elif red was MAX, there are two subcases ie
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# when green was MIN and when green was NOT MIN
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# dh_dg_2 ->
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# if green was MIN (use UV rule) -> 60 * ((1 * 1/(MAX-MIN)) + \
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# (greens-blues) * (-1/square(MAX-MIN) * -1)) == 60 * \
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# ((reciprocal(reds-greens) + (greens-blues) * \
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# reciprocal(square(reds-greens))))
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# dh_dg_3 ->
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# if green was NOT MIN -> 60 * 1/MAX-MIN == 60 * reciprocal(reds - blues)
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# elif blue was MAX, there are two subcases
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# dh_dg_4 ->
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# if green was MIN (similarly use the UV rule) -> 60 * -1 * \
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# (reciprocal(blues - greens) + (reds-greens)* -1 * \
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# reciprocal(square(blues-greens)))
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# dh_dr_5 ->
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# if green was NOT MIN -> 60 * -1/MAX-MIN == -60 * reciprocal(blues - reds)
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dh_dg_1 = 60 * (
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math_ops.cast(greens > 0, dtype) * green_biggest * -1 *
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(blues - reds) * _CustomReciprocal(math_ops.square(saturation)) *
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_CustomReciprocal(math_ops.square(value)))
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dh_dg_2 = 60 * (
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math_ops.cast(reds > 0, dtype) * red_biggest * green_smallest *
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(reds - blues) * _CustomReciprocal(math_ops.square(reds - greens)))
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dh_dg_3 = 60 * (
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math_ops.cast(reds > 0, dtype) * red_biggest * blue_smallest *
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_CustomReciprocal(reds - blues))
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dh_dg_4 = 60 * (
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math_ops.cast(blues > 0, dtype) * blue_biggest * green_smallest *
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(reds - blues) * _CustomReciprocal(math_ops.square(blues - greens)))
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dh_dg_5 = 60 * (
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math_ops.cast(blues > 0, dtype) * blue_biggest * red_smallest * -1 *
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_CustomReciprocal(blues - reds))
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dh_dg = dh_dg_1 + dh_dg_2 + dh_dg_3 + dh_dg_4 + dh_dg_5
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# Converting from degrees to [0,1] scale as specified in
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# https://www.tensorflow.org/api_docs/python/tf/image/rgb_to_hsv
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dh_dg = dh_dg / 360
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# for blue, dh_db -> dh_db_1 + dh_db_2 + dh_db_3 + dh_db_4 + dh_db_5
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# dh_db_1 ->
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# if blue was MAX, then derivative = 60 * -1 * (R-G)/square(MAX-MIN) == 60 *\
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# -1 * reciprocal(square(saturation)) * reciprocal(square(value))
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# elif red was MAX, there are two subcases
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# ie when blue was MIN and when blue was NOT MIN
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# dh_dg_2 ->
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# if blue was MIN (use UV rule) -> 60 * ((1 * -1/(MAX-MIN)) + \
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# (greens-blues) * (-1/square(MAX-MIN) * -1)) == 60 * (greens - reds) *\
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# reciprocal(square(reds - blues))
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# dh_dg_3 ->
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# if blue was NOT MIN -> 60 * -1/MAX-MIN == 60 * -1 * \
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# reciprocal(reds - greens)
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# elif green was MAX, there are two subcases
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# dh_dg_4 ->
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# if blue was MIN (similarly use the UV rule) -> 60 * -1 * \
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# (reciprocal(greens - blues) + (blues - reds) * -1 * \
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# reciprocal(square(greens - blues)))
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# dh_dr_5 ->
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# if blue was NOT MIN -> 60 * 1/MAX-MIN == 60 * reciprocal(greens - reds)
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dh_db_1 = 60 * (
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math_ops.cast(blues > 0, dtype) * blue_biggest * -1 *
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(reds - greens) * _CustomReciprocal(math_ops.square(saturation)) *
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_CustomReciprocal(math_ops.square(value)))
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dh_db_2 = 60 * (
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math_ops.cast(reds > 0, dtype) * red_biggest * blue_smallest *
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(greens - reds) * _CustomReciprocal(math_ops.square(reds - blues)))
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dh_db_3 = 60 * (
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math_ops.cast(reds > 0, dtype) * red_biggest * green_smallest * -1 *
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_CustomReciprocal(reds - greens))
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dh_db_4 = 60 * (
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math_ops.cast(greens > 0, dtype) * green_biggest * blue_smallest *
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(greens - reds) * _CustomReciprocal(math_ops.square(greens - blues)))
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dh_db_5 = 60 * (
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math_ops.cast(greens > 0, dtype) * green_biggest * red_smallest *
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_CustomReciprocal(greens - reds))
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dh_db = dh_db_1 + dh_db_2 + dh_db_3 + dh_db_4 + dh_db_5
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|
# Converting from degrees to [0,1] scale as specified in
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|
# https://www.tensorflow.org/api_docs/python/tf/image/rgb_to_hsv
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|
dh_db = dh_db / 360
|
||
|
|
||
|
# Gradients wrt to inputs
|
||
|
dv_drgb = array_ops.stack(
|
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|
[grad[..., 2] * dv_dr, grad[..., 2] * dv_dg, grad[..., 2] * dv_db],
|
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|
axis=-1)
|
||
|
ds_drgb = array_ops.stack(
|
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|
[grad[..., 1] * ds_dr, grad[..., 1] * ds_dg, grad[..., 1] * ds_db],
|
||
|
axis=-1)
|
||
|
dh_drgb = array_ops.stack(
|
||
|
[grad[..., 0] * dh_dr, grad[..., 0] * dh_dg, grad[..., 0] * dh_db],
|
||
|
axis=-1)
|
||
|
|
||
|
gradient_input = math_ops.add(math_ops.add(dv_drgb, ds_drgb), dh_drgb)
|
||
|
return gradient_input
|