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math.py
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"""Mathematical operations and structures.
This module provides classes and utilities to perform common mathematical
operations and transformations on images, including clipping, normalization,
blurring, and pooling. These are implemented as subclasses of `Feature` for
seamless integration with the feature-based design of the library. Each
`Feature` supports lazy evaluation and can be composed using operators (e.g.,
`>>` for chaining), enabling efficient and readable construction of image
processing pipelines.
Key Features
------------
- **Clipping**
Restrict image values to a specified range.
- **Normalization**
Adjust image values to a common scale.
- **Blurring**
Smooth images using various filters.
- **Pooling**
Downsample images by applying a function to local regions.
- **Resizing**
Change the dimensions of images.
Module Structure
-----------------
Classes:
- `Clip`: Clip the input values within a specified minimum and maximum range.
- `NormalizeMinMax`: Perform min-max normalization on images.
- `NormalizeStandard`: Normalize images to have mean 0 and standard
deviation 1.
- `NormalizeQuantile`: Normalize images based on specified quantiles.
- `Blur`: Apply a blurring filter to the image.
- `AverageBlur`: Apply average blurring to the image.
- `GaussianBlur`: Apply Gaussian blurring to the image.
- `MedianBlur`: Apply median blurring to the image.
- `Pool`: Apply a pooling function to downsample the image.
- `AveragePooling`: Apply average pooling to the image.
- `MaxPooling`: Apply max pooling to the image.
- `MinPooling`: Apply min pooling to the image.
- `MedianPooling`: Apply median pooling to the image.
- `Resize`: Resize the image to a specified size.
- `BlurCV2`: Apply a blurring filter using OpenCV2.
- `BilateralBlur`: Apply bilateral blurring to preserve edges while smoothing.
Examples
--------
Define a simple pipeline with mathematical operations:
>>> import deeptrack as dt
>>> import numpy as np
Create features for clipping and normalization:
>>> clip = dt.Clip(min=0, max=200)
>>> normalize = dt.NormalizeMinMax()
Chain features together:
>>> pipeline = clip >> normalize
Process an input image:
>>> input_image = np.array([0, 100, 200, 400])
>>> output_image = pipeline(input_image)
>>> print(output_image)
[0., 0.5, 1., 1.]
"""
from __future__ import annotations
from typing import Callable, Any
import numpy as np
import scipy.ndimage as ndimage
import skimage
import skimage.measure
from deeptrack import utils
from deeptrack.features import Feature
from deeptrack.image import Image, strip
from deeptrack.types import PropertyLike
class Average(Feature):
"""Average of input images.
This class computes the average of input images along the specified axis.
If `features` is not None, it instead resolves all features in the list and
averages the result.
Parameters
----------
axis: int or tuple of ints
Axis along which to average
features: list of features, optional
Attributes
----------
__distributed__: bool
Determines whether `.get(image, **kwargs)` is applied to each element
of the input list independently (`__distributed__ = True`) or to the
list as a whole (`__distributed__ = False`).
Methods
-------
`get(images: np.ndarray | Image | list[Image], axis: int, **kwargs: Any) --> np.ndarray`
Computes the average of the input images along the specified axis.
Examples
--------
>>> import deeptrack as dt
>>> import numpy as np
Create two input images:
>>> input_image1 = np.random.rand(10, 30, 20)
>>> input_image2 = np.random.rand(10, 30, 20)
Define a simple pipeline with the average feature:
>>> average = dt.Average(axis=1)
>>> output_image = average([input_image1, input_image2])
>>> print(output_image)
(2, 30, 20)
Notes
-----
Calling this feature returns a `np.ndarray` by default. If
`store_properties` is set to `True`, the returned array will be
automatically wrapped in an `Image` object. This behavior is handled
internally and does not affect the return type of the `get()` method.
"""
__distributed__ = False
def __init__(
self: Average,
features: PropertyLike[list[Feature] | None] = None,
axis: PropertyLike[int] = 0,
**kwargs: Any
):
"""Initialize the parameters for averaging input features.
This constructor initializes the parameters for averaging input
features.
Parameters
----------
features: list of Feature or None, optional
List of features to be resolved and averaged. Defaults to None.
axis: int or tuple[int]
Axis along which to compute the average. Defaults to 0.
**kwargs: Any
Additional keyword arguments.
"""
super().__init__(axis=axis, **kwargs)
if features is None:
self.features = None
else:
self.features = [self.add_feature(f) for f in features]
def get(
self: Average,
images: np.ndarray | Image | list[Image],
axis: int,
**kwargs: Any,
) -> np.ndarray:
"""Computes the average of input images along the specified axis.
This method computes the average of the input images along the
specified axis.
Parameters
----------
images: np.ndarray
The input images to average.
axis: int
The axis along which to average.
Returns
-------
np.ndarray
The average of the input images along the specified axis.
"""
if self.features is not None:
images = [feature.resolve() for feature in self.features]
result = Image(np.mean(images, axis=axis))
for image in images:
result.merge_properties_from(image)
return result
class Clip(Feature):
"""Clip the input within a minimum and a maximum value.
This class clips the input values within a specified minimum and maximum
range.
Parameters
----------
min: float
Clip the input to be larger than this value.
max: float
Clip the input to be smaller than this value.
Methods
-------
`get(image: np.ndarray | Image, min: float, max: float, **kwargs: Any) --> np.ndarray`
Clips the input image within the specified minimum and maximum values.
Examples
--------
>>> import deeptrack as dt
>>> import numpy as np
Create an input image:
>>> input_image = np.array([[10, 4], [4, -10]])
Define a clipper feature:
>>> clipper = dt.Clip(min=0, max=5)
>>> output_image = clipper(input_image)
>>> print(output_image)
[[5 4]
[4 0]]
Notes
-----
Calling this feature returns a `np.ndarray` by default. If
`store_properties` is set to `True`, the returned array will be
automatically wrapped in an `Image` object. This behavior is handled
internally and does not affect the return type of the `get()` method.
"""
def __init__(
self: Clip,
min: PropertyLike[float] = -np.inf,
max: PropertyLike[float] = +np.inf,
**kwargs: Any,
):
"""Initialize the parameters for clipping input features.
This constructor initializes the parameters for clipping input features.
Parameters
----------
min: float
Clip the input to be larger than this value.
max: float
Clip the input to be smaller than this value.
**kwargs: Any
Additional keyword arguments.
"""
super().__init__(min=min, max=max, **kwargs)
def get(
self: Clip,
image: np.ndarray | Image,
min: float = None,
max: float = None,
**kwargs: Any,
) -> np.ndarray:
"""Clips the input image within the specified values.
This method clips the input image within the specified minimum and
maximum values.
Parameters
----------
image: np.ndarray
The input image to clip.
min: float
Clip the input to be larger than this value.
max: float
Clip the input to be smaller than this value.
Returns
-------
np.ndarray
The clipped image.
"""
return np.clip(image, min, max)
class NormalizeMinMax(Feature):
"""Image normalization.
Transforms the input to be between a minimum and a maximum value using
a linear transformation.
Parameters
----------
min: float
The minimum of the transformation.
max: float
The maximum of the transformation.
featurewise: bool
Whether to normalize each feature independently.
Methods
-------
`get(image: np.ndarray | Image, min: float, max: float, **kwargs: Any) --> np.ndarray`
Normalizes the input image to be between the specified minimum and
maximum values.
Examples
--------
>>> import deeptrack as dt
>>> import numpy as np
Create an input image:
>>> input_image = np.array([[10, 4], [4, -10]])
Define a min-max normalizer:
>>> normalizer = dt.NormalizeMinMax(min=-5, max=5)
>>> output_image = normalizer(input_image)
>>> print(output_image)
[[ 5. 2.]
[ 2. -5.]]
Notes
-----
Calling this feature returns a `np.ndarray` by default. If
`store_properties` is set to `True`, the returned array will be
automatically wrapped in an `Image` object. This behavior is handled
internally and does not affect the return type of the `get()` method.
"""
def __init__(
self: NormalizeMinMax,
min: PropertyLike[float] = 0,
max: PropertyLike[float] = 1,
featurewise: bool = True,
**kwargs: Any,
):
"""Initialize the parameters for min-max normalization.
This constructor initializes the parameters for min-max normalization.
Parameters
----------
min: float
The minimum of the transformation.
max: float
The maximum of the transformation.
featurewise: bool
Whether to normalize each feature independently.
**kwargs: Any
Additional keyword arguments.
"""
super().__init__(min=min, max=max, featurewise=featurewise, **kwargs)
def get(
self: NormalizeMinMax,
image: np.ndarray | Image,
min: float = None,
max: float = None,
**kwargs: Any,
) -> np.ndarray:
"""Normalizes the input image to be between the specified minimum and
maximum values.
This method normalizes the input image to be between the specified
minimum and maximum values.
Parameters
----------
image: np.ndarray
The input image to normalize.
min: float
The minimum of the transformation.
max: float
The maximum of the transformation.
Returns
-------
np.ndarray
The normalized image.
"""
image = image / np.ptp(image) * (max - min)
image = image - np.min(image) + min
try:
image[np.isnan(image)] = 0
except TypeError:
pass
return image
class NormalizeStandard(Feature):
"""Image normalization (standardization).
Normalize (standardize) the image to have sigma 1 and mean 0.
Parameters
----------
featurewise: bool
Whether to normalize each feature independently
Methods
-------
`get(image: np.ndarray | Image, **kwargs: Any) --> np.ndarray`
Normalizes (standardizes) the input image to have mean 0 and standard
deviation 1.
Examples
--------
>>> import deeptrack as dt
>>> import numpy as np
Create an input image:
>>> input_image = np.array([[1, 2], [3, 4]], dtype=float)
>>> standardizer = dt.NormalizeStandard()
>>> output_image = standardizer(input_image)
>>> print(output_image)
[[-1.34164079 -0.4472136]
[ 0.4472136 1.34164079]]
Notes
-----
Calling this feature returns a `np.ndarray` by default. If
`store_properties` is set to `True`, the returned array will be
automatically wrapped in an `Image` object. This behavior is handled
internally and does not affect the return type of the `get()` method.
"""
def __init__(
self:NormalizeStandard,
featurewise: bool = True,
**kwargs: Any,
):
"""Initialize the parameters for standardization.
This constructor initializes the parameters for standardization.
Parameters
----------
featurewise: bool
Whether to normalize each feature independently.
**kwargs: Any
Additional keyword arguments.
"""
super().__init__(featurewise=featurewise, **kwargs)
def get(
self: NormalizeStandard,
image: np.ndarray | Image,
**kwargs: Any,
) -> np.ndarray:
"""Normalizes the input image to have mean 0 and standard deviation 1.
This method normalizes the input image to have mean 0 and standard
deviation 1.
Parameters
----------
image: np.ndarray
The input image to normalize.
Returns
-------
np.ndarray
The normalized image.
"""
return (image - np.mean(image)) / np.std(image)
class NormalizeQuantile(Feature):
"""Image normalization.
Center the image to the median, and divide by the difference between the
quantiles defined by `q_max` and `q_min`.
Parameters
----------
quantiles: tuple (q_min, q_max), 0.0 < q_min < q_max < 1.0
Quantile range to calculate scaling factor
featurewise: bool
Whether to normalize each feature independently
Methods
-------
`get(image: np.ndarray | Image, quantiles: tuple[float, float], **kwargs: Any) --> np.ndarray`
Normalizes the input image based on the specified quantiles.
Examples
--------
>>> import deeptrack as dt
>>> import numpy as np
Create an input image:
>>> input_image = np.array([[10, 4], [4, -10]])
Define a quantile normalizer:
>>> normalizer = dt.NormalizeQuantile(quantiles=(0.25, 0.75))
>>> output_image = normalizer(input_image)
>>> print(output_image)
[[ 1.2 0. ]
[ 0. -2.8]]
Notes
-----
Calling this feature returns a `np.ndarray` by default. If
`store_properties` is set to `True`, the returned array will be
automatically wrapped in an `Image` object. This behavior is handled
internally and does not affect the return type of the `get()` method.
"""
def __init__(
self: NormalizeQuantile,
quantiles: tuple[float, float] = (0.25, 0.75),
featurewise: bool = True,
**kwargs: Any,
):
"""Initialize the parameters for quantile normalization.
This constructor initializes the parameters for quantile normalization.
Parameters
----------
quantiles: tuple[float, float]
Quantile range to calculate scaling factor.
featurewise: bool
Whether to normalize each feature independently.
**kwargs: Any
Additional keyword arguments.
"""
super().__init__(
quantiles=quantiles,
featurewise=featurewise,
**kwargs)
def get(
self: NormalizeQuantile,
image: np.ndarray | Image,
quantiles: tuple[float, float] = None,
**kwargs: Any,
) -> np.ndarray:
"""Normalizes the input image based on the specified quantiles.
This method normalizes the input image based on the specified
quantiles.
Parameters
----------
image: np.ndarray
The input image to normalize.
quantiles: tuple[float, float]
Quantile range to calculate scaling factor.
Returns
-------
np.ndarray
The normalized image.
"""
if quantiles is None:
quantiles = self.quantiles
q_low, q_high, median = np.quantile(image, (*quantiles, 0.5))
return (image - median) / (q_high - q_low)
class Blur(Feature):
"""Apply a blurring filter to an image.
This class applies a blurring filter to an image. The filter function
must be a function that takes an input image and returns a blurred
image.
Parameters
----------
filter_function: Callable
The blurring function to apply. This function must accept the input
image as a keyword argument named `input`. If using OpenCV functions
(e.g., `cv2.GaussianBlur`), use `BlurCV2` instead.
mode: str
Border mode for handling boundaries (e.g., 'reflect').
Methods
-------
`get(image: np.ndarray | Image, **kwargs: Any) --> np.ndarray`
Applies the blurring filter to the input image.
Examples
--------
>>> import deeptrack as dt
>>> import numpy as np
>>> from scipy.ndimage import convolve
Create an input image:
>>> input_image = np.random.rand(32, 32)
Define a Gaussian kernel for blurring:
>>> gaussian_kernel = np.array([
... [1, 4, 6, 4, 1],
... [4, 16, 24, 16, 4],
... [6, 24, 36, 24, 6],
... [4, 16, 24, 16, 4],
... [1, 4, 6, 4, 1]
... ], dtype=float)
>>> gaussian_kernel /= np.sum(gaussian_kernel)
Define a blur function using the Gaussian kernel:
>>> def gaussian_blur(input, **kwargs):
... return convolve(input, gaussian_kernel, mode='reflect')
Define a blur feature using the Gaussian blur function:
>>> blur = dt.Blur(filter_function=gaussian_blur)
>>> output_image = blur(input_image)
>>> print(output_image.shape)
(32, 32)
Notes
-----
Calling this feature returns a `np.ndarray` by default. If
`store_properties` is set to `True`, the returned array will be
automatically wrapped in an `Image` object. This behavior is handled
internally and does not affect the return type of the `get()` method.
The filter_function must accept the input image as a keyword argument named
input. This is required because it is called via utils.safe_call. If you
are using functions that do not support input=... (such as OpenCV filters
like cv2.GaussianBlur), consider using BlurCV2 instead.
"""
def __init__(
self: Blur,
filter_function: Callable,
mode: PropertyLike[str] = "reflect",
**kwargs: Any,
):
"""Initialize the parameters for blurring input features.
This constructor initializes the parameters for blurring input
features.
Parameters
----------
filter_function: Callable
The blurring function to apply.
mode: str
Border mode for handling boundaries (e.g., 'reflect').
**kwargs: Any
Additional keyword arguments.
"""
self.filter = filter_function
super().__init__(borderType=mode, **kwargs)
def get(
self: Blur,
image: np.ndarray | Image,
**kwargs: Any
) -> np.ndarray:
"""Applies the blurring filter to the input image.
This method applies the blurring filter to the input image.
Parameters
----------
image: np.ndarray
The input image to blur.
**kwargs: dict[str, Any]
Additional keyword arguments.
Returns
-------
np.ndarray
The blurred image.
"""
kwargs.pop("input", False)
return utils.safe_call(self.filter, input=image, **kwargs)
class AverageBlur(Blur):
"""Blur an image by computing simple means over neighbourhoods.
Performs a (N-1)D convolution if the last dimension is smaller than
the kernel size.
Parameters
----------
ksize: int
Kernel size for the pooling operation.
Methods
-------
`get(image: np.ndarray | Image, ksize: int, **kwargs: Any) --> np.ndarray`
Applies the average blurring filter to the input image.
Examples
--------
>>> import deeptrack as dt
>>> import numpy as np
Create an input image:
>>> input_image = np.random.rand(32, 32)
Define an average blur feature:
>>> average_blur = dt.AverageBlur(ksize=3)
>>> output_image = average_blur(input_image)
>>> print(output_image.shape)
(32, 32)
Notes
-----
Calling this feature returns a `np.ndarray` by default. If
`store_properties` is set to `True`, the returned array will be
automatically wrapped in an `Image` object. This behavior is handled
internally and does not affect the return type of the `get()` method.
"""
def __init__(
self: AverageBlur,
ksize: PropertyLike[int] = 3,
**kwargs: Any,
):
"""Initialize the parameters for averaging input features.
This constructor initializes the parameters for averaging input
features.
Parameters
----------
ksize: int
Kernel size for the pooling operation.
**kwargs: Any
Additional keyword arguments.
"""
super().__init__(None, ksize=ksize, **kwargs)
def get(
self: AverageBlur,
input: np.ndarray | Image,
ksize: int,
**kwargs: Any,
) -> np.ndarray:
"""Applies the average blurring filter to the input image.
This method applies the average blurring filter to the input image.
Parameters
----------
input: np.ndarray
The input image to blur.
ksize: int
Kernel size for the pooling operation.
**kwargs: dict[str, Any]
Additional keyword arguments.
Returns
-------
np.ndarray
The blurred image.
"""
if input.shape[-1] < ksize:
ksize = (ksize,) * (input.ndim - 1) + (1,)
else:
ksize = ((ksize,) * input.ndim,)
weights = np.ones(ksize) / np.prod(ksize)
return utils.safe_call(
ndimage.convolve,
input=input,
weights=weights,
**kwargs,
)
class GaussianBlur(Blur):
"""Applies a Gaussian blur to images using Gaussian kernels.
This class blurs images by convolving them with a Gaussian filter, which
smooths the image and reduces high-frequency details. The level of blurring
is controlled by the standard deviation (`sigma`) of the Gaussian kernel.
Parameters
----------
sigma: float
Standard deviation of the Gaussian kernel.
Examples
--------
>>> import deeptrack as dt
>>> import numpy as np
>>> import matplotlib.pyplot as plt
Create an input image:
>>> input_image = np.random.rand(32, 32)
Define a Gaussian blur feature:
>>> gaussian_blur = dt.GaussianBlur(sigma=2)
>>> output_image = gaussian_blur(input_image)
>>> print(output_image.shape)
(32, 32)
Visualize the input and output images:
>>> plt.figure(figsize=(8, 4))
>>> plt.subplot(1, 2, 1)
>>> plt.imshow(input_image, cmap='gray')
>>> plt.subplot(1, 2, 2)
>>> plt.imshow(output_image, cmap='gray')
>>> plt.show()
Notes
-----
Calling this feature returns a `np.ndarray` by default. If
`store_properties` is set to `True`, the returned array will be
automatically wrapped in an `Image` object. This behavior is handled
internally and does not affect the return type of the `get()` method.
"""
def __init__(
self: GaussianBlur,
sigma: PropertyLike[float] = 2,
**kwargs: Any
):
"""Initialize the parameters for Gaussian blurring.
This constructor initializes the parameters for Gaussian blurring.
Parameters
----------
sigma: float
Standard deviation of the Gaussian kernel.
**kwargs: Any
Additional keyword arguments.
"""
super().__init__(ndimage.gaussian_filter, sigma=sigma, **kwargs)
class MedianBlur(Blur):
"""Applies a median blur.
This class replaces each pixel of the input image with the median value of
its neighborhood. The `ksize` parameter determines the size of the
neighborhood used to calculate the median filter. The median filter is
useful for reducing noise while preserving edges. It is particularly
effective for removing salt-and-pepper noise from images.
Parameters
----------
ksize: int
Kernel size.
**kwargs: dict
Additional parameters sent to the blurring function.
Examples
--------
>>> import deeptrack as dt
>>> import numpy as np
>>> import matplotlib.pyplot as plt
Create an input image:
>>> input_image = np.random.rand(32, 32)
Define a median blur feature:
>>> median_blur = dt.MedianBlur(ksize=3)
>>> output_image = median_blur(input_image)
>>> print(output_image.shape)
(32, 32)
Visualize the input and output images:
>>> plt.figure(figsize=(8, 4))
>>> plt.subplot(1, 2, 1)
>>> plt.imshow(input_image, cmap='gray')
>>> plt.subplot(1, 2, 2)
>>> plt.imshow(output_image, cmap='gray')
>>> plt.show()
Notes
-----
Calling this feature returns a `np.ndarray` by default. If
`store_properties` is set to `True`, the returned array will be
automatically wrapped in an `Image` object. This behavior is handled
internally and does not affect the return type of the `get()` method.
"""
def __init__(
self: MedianBlur,
ksize: PropertyLike[int] = 3,
**kwargs: Any,
):
"""Initialize the parameters for median blurring.
This constructor initializes the parameters for median blurring.
Parameters
----------
ksize: int
Kernel size.
**kwargs: Any
Additional keyword arguments.
"""
super().__init__(ndimage.median_filter, size=ksize, **kwargs)
class Pool(Feature):
"""Downsamples the image by applying a function to local regions of the
image.
This class reduces the resolution of an image by dividing it into
non-overlapping blocks of size `ksize` and applying the specified pooling
function to each block. The result is a downsampled image where each pixel
value represents the result of the pooling function applied to the
corresponding block.
Parameters
----------
pooling_function: function
A function that is applied to each local region of the image.
DOES NOT NEED TO BE WRAPPED IN ANOTHER FUNCTION.
The `pooling_function` must accept the input image as a keyword argument
named `input`, as it is called via `utils.safe_call`.
Examples include `np.mean`, `np.max`, `np.min`, etc.
ksize: int
Size of the pooling kernel.
**kwargs: Any
Additional parameters sent to the pooling function.
Methods
-------
`get(image: np.ndarray | Image, ksize: int, **kwargs: Any) --> np.ndarray`
Applies the pooling function to the input image.
Examples
--------
>>> import deeptrack as dt
>>> import numpy as np
Create an input image:
>>> input_image = np.random.rand(32, 32)
Define a pooling feature:
>>> pooling_feature = dt.Pool(pooling_function=np.mean, ksize=4)
>>> output_image = pooling_feature.get(input_image, ksize=4)
>>> print(output_image.shape)
(8, 8)
Notes
-----
Calling this feature returns a `np.ndarray` by default. If