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Geometry

Provides functions for manipulating ndarrays of device geometries.

binarize(device_array, eta=0.5, beta=np.inf)

Binarize the input ndarray based on a threshold and a scaling factor.

Parameters:

Name Type Description Default
device_array ndarray

The input array to be binarized.

 required
eta float

The threshold value for binarization. Defaults to 0.5.

 0.5
beta float

The scaling factor for the binarization process. A higher value makes the transition sharper. Defaults to np.inf, which results in a hard threshold.

 inf

Returns:

Type Description
ndarray

The binarized array with elements scaled to 0 or 1.
Source code in prefab/geometry.py 
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def binarize(
    device_array: np.ndarray, eta: float = 0.5, beta: float = np.inf
) -> np.ndarray:
    """
    Binarize the input ndarray based on a threshold and a scaling factor.

    Parameters
    ----------
    device_array : np.ndarray
        The input array to be binarized.
    eta : float, optional
        The threshold value for binarization. Defaults to 0.5.
    beta : float, optional
        The scaling factor for the binarization process. A higher value makes the
        transition sharper. Defaults to np.inf, which results in a hard threshold.

    Returns
    -------
    np.ndarray
        The binarized array with elements scaled to 0 or 1.
    """
    return (np.tanh(beta * eta) + np.tanh(beta * (device_array - eta))) / (
        np.tanh(beta * eta) + np.tanh(beta * (1 - eta))
    )

binarize_hard(device_array, eta=0.5)

Apply a hard threshold to binarize the input ndarray. The binarize function is generally preferred for most use cases, but it can create numerical artifacts for large beta values.

Parameters:

Name Type Description Default
device_array ndarray

The input array to be binarized.

 required
eta float

The threshold value for binarization. Defaults to 0.5.

 0.5

Returns:

Type Description
ndarray

The binarized array with elements set to 0 or 1 based on the threshold.
Source code in prefab/geometry.py 
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def binarize_hard(device_array: np.ndarray, eta: float = 0.5) -> np.ndarray:
    """
    Apply a hard threshold to binarize the input ndarray. The `binarize` function is
    generally preferred for most use cases, but it can create numerical artifacts for
    large beta values.

    Parameters
    ----------
    device_array : np.ndarray
        The input array to be binarized.
    eta : float, optional
        The threshold value for binarization. Defaults to 0.5.

    Returns
    -------
    np.ndarray
        The binarized array with elements set to 0 or 1 based on the threshold.
    """
    return np.where(device_array < eta, 0.0, 1.0)

binarize_monte_carlo(device_array, threshold_noise_std, threshold_blur_std)

Binarize the input ndarray using a Monte Carlo approach with Gaussian blurring.

This function applies a dynamic thresholding technique where the threshold value is determined by a base value perturbed by Gaussian-distributed random noise. The threshold is then spatially varied across the array using Gaussian blurring, simulating a potentially more realistic scenario where the threshold is not uniform across the device.

Parameters:

Name Type Description Default
device_array ndarray

The input array to be binarized.

 required
threshold_noise_std float

The standard deviation of the Gaussian distribution used to generate noise for the threshold values. This controls the amount of randomness in the threshold.

 required
threshold_blur_std float

The standard deviation for the Gaussian kernel used in blurring the threshold map. This controls the spatial variation of the threshold across the array.

 required

Returns:

Type Description
ndarray

The binarized array with elements set to 0 or 1 based on the dynamically generated threshold.
Source code in prefab/geometry.py 
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def binarize_monte_carlo(
    device_array: np.ndarray,
    threshold_noise_std: float,
    threshold_blur_std: float,
) -> np.ndarray:
    """
    Binarize the input ndarray using a Monte Carlo approach with Gaussian blurring.

    This function applies a dynamic thresholding technique where the threshold value is
    determined by a base value perturbed by Gaussian-distributed random noise. The
    threshold is then spatially varied across the array using Gaussian blurring,
    simulating a potentially more realistic scenario where the threshold is not uniform
    across the device.

    Parameters
    ----------
    device_array : np.ndarray
        The input array to be binarized.
    threshold_noise_std : float
        The standard deviation of the Gaussian distribution used to generate noise for
        the threshold values. This controls the amount of randomness in the threshold.
    threshold_blur_std : float
        The standard deviation for the Gaussian kernel used in blurring the threshold
        map. This controls the spatial variation of the threshold across the array.

    Returns
    -------
    np.ndarray
        The binarized array with elements set to 0 or 1 based on the dynamically
        generated threshold.
    """
    device_array = np.squeeze(device_array)
    base_threshold = np.clip(np.random.normal(loc=0.5, scale=0.5 / 2), 0.4, 0.6)
    threshold_noise = np.random.normal(
        loc=0, scale=threshold_noise_std, size=device_array.shape
    )
    spatial_threshold = cv2.GaussianBlur(
        threshold_noise, ksize=(0, 0), sigmaX=threshold_blur_std
    )
    dynamic_threshold = base_threshold + spatial_threshold
    binarized_array = np.where(device_array < dynamic_threshold, 0.0, 1.0)
    binarized_array = np.expand_dims(binarized_array, axis=-1)
    return binarized_array

binarize_sem(sem_array)

Binarize a grayscale scanning electron microscope (SEM) image.

This function applies Otsu's method to automatically determine the optimal threshold value for binarization of a grayscale SEM image.

Parameters:

Name Type Description Default
sem_array ndarray

The input SEM image array to be binarized.

 required

Returns:

Type Description
ndarray

The binarized SEM image array with elements scaled to 0 or 1.
Source code in prefab/geometry.py 
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def binarize_sem(sem_array: np.ndarray) -> np.ndarray:
    """
    Binarize a grayscale scanning electron microscope (SEM) image.

    This function applies Otsu's method to automatically determine the optimal threshold
    value for binarization of a grayscale SEM image.

    Parameters
    ----------
    sem_array : np.ndarray
        The input SEM image array to be binarized.

    Returns
    -------
    np.ndarray
        The binarized SEM image array with elements scaled to 0 or 1.
    """
    return cv2.threshold(
        sem_array.astype("uint8"), 0, 1, cv2.THRESH_BINARY + cv2.THRESH_OTSU
    )[1]

blur(device_array, sigma=1.0)

Apply Gaussian blur to the input ndarray and normalize the result.

Parameters:

Name Type Description Default
device_array ndarray

The input array to be blurred.

 required
sigma float

The standard deviation for the Gaussian kernel. This controls the amount of blurring. Defaults to 1.0.

 1.0

Returns:

Type Description
ndarray

The blurred and normalized array with values scaled between 0 and 1.
Source code in prefab/geometry.py 
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def blur(device_array: np.ndarray, sigma: float = 1.0) -> np.ndarray:
    """
    Apply Gaussian blur to the input ndarray and normalize the result.

    Parameters
    ----------
    device_array : np.ndarray
        The input array to be blurred.
    sigma : float, optional
        The standard deviation for the Gaussian kernel. This controls the amount of
        blurring. Defaults to 1.0.

    Returns
    -------
    np.ndarray
        The blurred and normalized array with values scaled between 0 and 1.
    """
    return np.expand_dims(
        normalize(cv2.GaussianBlur(device_array, ksize=(0, 0), sigmaX=sigma)), axis=-1
    )

dilate(device_array, kernel_size)

Dilate the input ndarray using a specified kernel size.

Parameters:

Name Type Description Default
device_array ndarray

The input array representing the device geometry to be dilated.

 required
kernel_size int

The size of the kernel used for dilation.

 required

Returns:

Type Description
ndarray

The dilated array.
Source code in prefab/geometry.py 
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def dilate(device_array: np.ndarray, kernel_size: int) -> np.ndarray:
    """
    Dilate the input ndarray using a specified kernel size.

    Parameters
    ----------
    device_array : np.ndarray
        The input array representing the device geometry to be dilated.
    kernel_size : int
        The size of the kernel used for dilation.

    Returns
    -------
    np.ndarray
        The dilated array.
    """
    kernel = np.ones((kernel_size, kernel_size), dtype=np.uint8)
    return np.expand_dims(cv2.dilate(device_array, kernel=kernel), axis=-1)

erode(device_array, kernel_size)

Erode the input ndarray using a specified kernel size and number of iterations.

Parameters:

Name Type Description Default
device_array ndarray

The input array representing the device geometry to be eroded.

 required
kernel_size int

The size of the kernel used for erosion.

 required

Returns:

Type Description
ndarray

The eroded array.
Source code in prefab/geometry.py 
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def erode(device_array: np.ndarray, kernel_size: int) -> np.ndarray:
    """
    Erode the input ndarray using a specified kernel size and number of iterations.

    Parameters
    ----------
    device_array : np.ndarray
        The input array representing the device geometry to be eroded.
    kernel_size : int
        The size of the kernel used for erosion.

    Returns
    -------
    np.ndarray
        The eroded array.
    """
    kernel = np.ones((kernel_size, kernel_size), dtype=np.uint8)
    return np.expand_dims(cv2.erode(device_array, kernel=kernel), axis=-1)

flatten(device_array)

Flatten the input ndarray by summing the vertical layers and normalizing the result.

Parameters:

Name Type Description Default
device_array ndarray

The input array to be flattened.

 required

Returns:

Type Description
ndarray

The flattened array with values scaled between 0 and 1.
Source code in prefab/geometry.py 
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def flatten(device_array: np.ndarray) -> np.ndarray:
    """
    Flatten the input ndarray by summing the vertical layers and normalizing the result.

    Parameters
    ----------
    device_array : np.ndarray
        The input array to be flattened.

    Returns
    -------
    np.ndarray
        The flattened array with values scaled between 0 and 1.
    """
    return normalize(np.sum(device_array, axis=-1, keepdims=True))

normalize(device_array)

Normalize the input ndarray to have values between 0 and 1.

Parameters:

Name Type Description Default
device_array ndarray

The input array to be normalized.

 required

Returns:

Type Description
ndarray

The normalized array with values scaled between 0 and 1.
Source code in prefab/geometry.py 
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def normalize(device_array: np.ndarray) -> np.ndarray:
    """
    Normalize the input ndarray to have values between 0 and 1.

    Parameters
    ----------
    device_array : np.ndarray
        The input array to be normalized.

    Returns
    -------
    np.ndarray
        The normalized array with values scaled between 0 and 1.
    """
    return (device_array - np.min(device_array)) / (
        np.max(device_array) - np.min(device_array)
    )

rotate(device_array, angle)

Rotate the input ndarray by a given angle.

Parameters:

Name Type Description Default
device_array ndarray

The input array to be rotated.

 required
angle float

The angle of rotation in degrees. Positive values mean counter-clockwise rotation.

 required

Returns:

Type Description
ndarray

The rotated array.
Source code in prefab/geometry.py 
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def rotate(device_array: np.ndarray, angle: float) -> np.ndarray:
    """
    Rotate the input ndarray by a given angle.

    Parameters
    ----------
    device_array : np.ndarray
        The input array to be rotated.
    angle : float
        The angle of rotation in degrees. Positive values mean counter-clockwise
        rotation.

    Returns
    -------
    np.ndarray
        The rotated array.
    """
    center = (device_array.shape[1] / 2, device_array.shape[0] / 2)
    rotation_matrix = cv2.getRotationMatrix2D(center=center, angle=angle, scale=1)
    rotated_device_array = cv2.warpAffine(
        flatten(device_array),
        M=rotation_matrix,
        dsize=(device_array.shape[1], device_array.shape[0]),
    )
    return np.expand_dims(rotated_device_array, axis=-1)

ternarize(device_array, eta1=1 / 3, eta2=2 / 3)

Ternarize the input ndarray based on two thresholds. This function is useful for flattened devices with angled sidewalls (i.e., three segments).

Parameters:

Name Type Description Default
device_array ndarray

The input array to be ternarized.

 required
eta1 float

The first threshold value for ternarization. Defaults to 1/3.

 1 / 3
eta2 float

The second threshold value for ternarization. Defaults to 2/3.

 2 / 3

Returns:

Type Description
ndarray

The ternarized array with elements set to 0, 0.5, or 1 based on the thresholds.
Source code in prefab/geometry.py 
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def ternarize(
    device_array: np.ndarray, eta1: float = 1 / 3, eta2: float = 2 / 3
) -> np.ndarray:
    """
    Ternarize the input ndarray based on two thresholds. This function is useful for
    flattened devices with angled sidewalls (i.e., three segments).

    Parameters
    ----------
    device_array : np.ndarray
        The input array to be ternarized.
    eta1 : float, optional
        The first threshold value for ternarization. Defaults to 1/3.
    eta2 : float, optional
        The second threshold value for ternarization. Defaults to 2/3.

    Returns
    -------
    np.ndarray
        The ternarized array with elements set to 0, 0.5, or 1 based on the thresholds.
    """
    return np.where(device_array < eta1, 0.0, np.where(device_array >= eta2, 1.0, 0.5))

trim(device_array, buffer_thickness=0)

Trim the input ndarray by removing rows and columns that are completely zero.

Parameters:

Name Type Description Default
device_array ndarray

The input array to be trimmed.

 required
buffer_thickness int

The thickness of the buffer to leave around the non-zero elements of the array. Defaults to 0, which means no buffer is added.

 0

Returns:

Type Description
ndarray

The trimmed array, potentially with a buffer around the non-zero elements.
Source code in prefab/geometry.py 
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def trim(device_array: np.ndarray, buffer_thickness: int = 0) -> np.ndarray:
    """
    Trim the input ndarray by removing rows and columns that are completely zero.

    Parameters
    ----------
    device_array : np.ndarray
        The input array to be trimmed.
    buffer_thickness : int, optional
        The thickness of the buffer to leave around the non-zero elements of the array.
        Defaults to 0, which means no buffer is added.

    Returns
    -------
    np.ndarray
        The trimmed array, potentially with a buffer around the non-zero elements.
    """
    flattened_device_array = np.squeeze(flatten(device_array))
    nonzero_rows, nonzero_cols = np.nonzero(flattened_device_array)
    row_min = max(nonzero_rows.min() - buffer_thickness, 0)
    row_max = min(
        nonzero_rows.max() + buffer_thickness + 1,
        device_array.shape[0],
    )
    col_min = max(nonzero_cols.min() - buffer_thickness, 0)
    col_max = min(
        nonzero_cols.max() + buffer_thickness + 1,
        device_array.shape[1],
    )
    return device_array[
        row_min:row_max,
        col_min:col_max,
    ]