def filter_green_pen(rgb, output_type="bool"):
"""
Create a mask to filter out green pen marks from a slide.
Args:
rgb: RGB image as a NumPy array.
output_type: Type of array to return (bool, float, or uint8).
Returns:
NumPy array representing the mask.
"""
t = Time()
result = filter_green(rgb, red_upper_thresh=150, green_lower_thresh=160, blue_lower_thresh=140) & \
filter_green(rgb, red_upper_thresh=70, green_lower_thresh=110, blue_lower_thresh=110) & \
filter_green(rgb, red_upper_thresh=45, green_lower_thresh=115, blue_lower_thresh=100) & \
filter_green(rgb, red_upper_thresh=30, green_lower_thresh=75, blue_lower_thresh=60) & \
filter_green(rgb, red_upper_thresh=195, green_lower_thresh=220, blue_lower_thresh=210) & \
filter_green(rgb, red_upper_thresh=225, green_lower_thresh=230, blue_lower_thresh=225) & \
filter_green(rgb, red_upper_thresh=170, green_lower_thresh=210, blue_lower_thresh=200) & \
filter_green(rgb, red_upper_thresh=20, green_lower_thresh=30, blue_lower_thresh=20) & \
filter_green(rgb, red_upper_thresh=50, green_lower_thresh=60, blue_lower_thresh=40) & \
filter_green(rgb, red_upper_thresh=30, green_lower_thresh=50, blue_lower_thresh=35) & \
filter_green(rgb, red_upper_thresh=65, green_lower_thresh=70, blue_lower_thresh=60) & \
filter_green(rgb, red_upper_thresh=100, green_lower_thresh=110, blue_lower_thresh=105) & \
filter_green(rgb, red_upper_thresh=165, green_lower_thresh=180, blue_lower_thresh=180) & \
filter_green(rgb, red_upper_thresh=140, green_lower_thresh=140, blue_lower_thresh=150) & \
filter_green(rgb, red_upper_thresh=185, green_lower_thresh=195, blue_lower_thresh=195)
if output_type == "bool":
pass
elif output_type == "float":
result = result.astype(float)
else:
result = result.astype("uint8") * 255
util.np_info(result, "Filter Green Pen", t.elapsed())
return result
def filter_binary_dilation(np_img,
disk_size=5,
iterations=1,
output_type="uint8"):
"""
Dilate a binary object (bool, float, or uint8).
Args:
np_img: Binary image as a NumPy array.
disk_size: Radius of the disk structuring element used for dilation.
iterations: How many times to repeat the dilation.
output_type: Type of array to return (bool, float, or uint8).
Returns:
NumPy array (bool, float, or uint8) where edges have been dilated.
"""
t = Time()
if np_img.dtype == "uint8":
np_img = np_img / 255
result = sc_morph.binary_dilation(np_img,
sk_morphology.disk(disk_size),
iterations=iterations)
if output_type == "bool":
pass
elif output_type == "float":
result = result.astype(float)
else:
result = result.astype("uint8") * 255
util.np_info(result, "Binary Dilation", t.elapsed())
return result
def filter_adaptive_equalization(np_img,
nbins=256,
clip_limit=0.01,
output_type="uint8"):
"""
Filter image (gray or RGB) using adaptive equalization to increase contrast in image, where contrast in local regions
is enhanced.
Args:
np_img: Image as a NumPy array (gray or RGB).
nbins: Number of histogram bins.
clip_limit: Clipping limit where higher value increases contrast.
output_type: Type of array to return (float or uint8).
Returns:
NumPy array (float or uint8) with contrast enhanced by adaptive equalization.
"""
t = Time()
adapt_equ = sk_exposure.equalize_adapthist(np_img,
nbins=nbins,
clip_limit=clip_limit)
if output_type == "float":
pass
else:
adapt_equ = (adapt_equ * 255).astype("uint8")
util.np_info(adapt_equ, "Adapt Equalization", t.elapsed())
return adapt_equ
def filter_binary_closing(np_img,
disk_size=3,
iterations=1,
output_type="uint8"):
"""
Close a binary object (bool, float, or uint8). Closing is a dilation followed by an erosion.
Closing can be used to remove small holes.
Args:
np_img: Binary image as a NumPy array.
disk_size: Radius of the disk structuring element used for closing.
iterations: How many times to repeat.
output_type: Type of array to return (bool, float, or uint8).
Returns:
NumPy array (bool, float, or uint8) following binary closing.
"""
t = Time()
if np_img.dtype == "uint8":
np_img = np_img / 255
result = sc_morph.binary_closing(np_img,
sk_morphology.disk(disk_size),
iterations=iterations)
if output_type == "bool":
pass
elif output_type == "float":
result = result.astype(float)
else:
result = result.astype("uint8") * 255
util.np_info(result, "Binary Closing", t.elapsed())
return result
def save_tile_data(tile_summary):
"""
Save tile data to csv file.
Args
tile_summary: TimeSummary object.
"""
time = Time()
csv = summary_title(tile_summary) + "\n" + summary_stats(tile_summary)
csv += "\n\n\nTile Num,Row,Column,Tissue %,Tissue Quantity,Col Start,Row Start,Col End,Row End,Col Size,Row Size," + \
"Color Factor,S and V Factor,Quantity Factor,Score\n"
for t in tile_summary.tiles:
line = "%d,%d,%d,%4.2f,%s,%d,%d,%d,%d,%d,%d,%4.0f,%4.2f,%4.2f,%0.4f\n" % (
t.tile_num, t.r, t.c, t.tissue_percentage,
t.tissue_quantity().name, t.c_s, t.r_s, t.c_e, t.r_e,
t.c_e - t.c_s, t.r_e - t.r_s, t.color_factor, t.s_and_v_factor,
t.quantity_factor, t.score)
csv += line
data_path = slide.get_tile_data_path(tile_summary.slide_name)
csv_file = open(data_path, "w")
csv_file.write(csv)
csv_file.close()
print("%-20s | Time: %-14s Name: %s" %
("Save Tile Data", str(time.elapsed()), data_path))
def filter_canny(np_img,
sigma=1,
low_threshold=0,
high_threshold=25,
output_type="uint8"):
"""
Filter image based on Canny algorithm edges.
Args:
np_img: Image as a NumPy array.
sigma: Width (std dev) of Gaussian.
low_threshold: Low hysteresis threshold value.
high_threshold: High hysteresis threshold value.
output_type: Type of array to return (bool, float, or uint8).
Returns:
NumPy array (bool, float, or uint8) representing Canny edge map (binary image).
"""
t = Time()
can = sk_feature.canny(np_img,
sigma=sigma,
low_threshold=low_threshold,
high_threshold=high_threshold)
if output_type == "bool":
pass
elif output_type == "float":
can = can.astype(float)
else:
can = can.astype("uint8") * 255
util.np_info(can, "Canny Edges", t.elapsed())
return can
def filter_remove_small_holes(np_img, min_size=3000, output_type="uint8"):
"""
Filter image to remove small holes less than a particular size.
Args:
np_img: Image as a NumPy array of type bool.
min_size: Remove small holes below this size.
output_type: Type of array to return (bool, float, or uint8).
Returns:
NumPy array (bool, float, or uint8).
"""
t = Time()
rem_sm = sk_morphology.remove_small_holes(np_img, min_size=min_size)
if output_type == "bool":
pass
elif output_type == "float":
rem_sm = rem_sm.astype(float)
else:
rem_sm = rem_sm.astype("uint8") * 255
util.np_info(rem_sm, "Remove Small Holes", t.elapsed())
return rem_sm
def filter_grays(rgb, tolerance=15, output_type="bool"):
"""
Create a mask to filter out pixels where the red, green, and blue channel values are similar.
Args:
np_img: RGB image as a NumPy array.
tolerance: Tolerance value to determine how similar the values must be in order to be filtered out
output_type: Type of array to return (bool, float, or uint8).
Returns:
NumPy array representing a mask where pixels with similar red, green, and blue values have been masked out.
"""
t = Time()
(h, w, c) = rgb.shape
rgb = rgb.astype(np.int)
rg_diff = abs(rgb[:, :, 0] - rgb[:, :, 1]) <= tolerance
rb_diff = abs(rgb[:, :, 0] - rgb[:, :, 2]) <= tolerance
gb_diff = abs(rgb[:, :, 1] - rgb[:, :, 2]) <= tolerance
result = ~(rg_diff & rb_diff & gb_diff)
if output_type == "bool":
pass
elif output_type == "float":
result = result.astype(float)
else:
result = result.astype("uint8") * 255
util.np_info(result, "Filter Grays", t.elapsed())
return result
def singleprocess_filtered_images_to_tiles(display=False,
save_summary=True,
save_data=True,
save_top_tiles=True,
html=True,
image_list=None):
"""
Generate tile summaries and tiles for training images using a single process.
Args:
display: If True, display tile summary images to screen.
save_summary: If True, save tile summary images.
save_data: If True, save tile data to csv file.
save_top_tiles: If True, save top tiles to files.
html: If True, generate HTML page to display tiled images
image_list: Optionally specify a list of image slide names.
"""
t = Time()
print("Generating tile summaries\n")
if image_list is not None:
image_list, tile_summaries_dict = image_list_to_tiles(
image_list, display, save_summary, save_data, save_top_tiles)
else:
num_training_slides = slide.get_num_training_slides()
image_list, tile_summaries_dict = image_range_to_tiles(
1, num_training_slides, display, save_summary, save_data,
save_top_tiles)
print("Time to generate tile summaries: %s\n" % str(t.elapsed()))
if html:
generate_tiled_html_result(image_list, tile_summaries_dict, save_data)
def save_top_tiles_on_original_image(pil_img, slide_name):
"""
Save a top tiles on original image and thumbnail to the file system.
Args:
pil_img: Image as a PIL Image.
slide_name: The slide name.
"""
t = Time()
filepath = slide.get_top_tiles_on_original_image_path(slide_name)
pil_img.save(filepath)
print("%-20s | Time: %-14s Name: %s" %
("Save Top Orig", str(t.elapsed()), filepath))
def save_tile_summary_image(pil_img, slide_name):
"""
Save a tile summary image and thumbnail to the file system.
Args:
pil_img: Image as a PIL Image.
slide_name: The slide name.
"""
t = Time()
filepath = slide.get_tile_summary_image_path(slide_name)
pil_img.save(filepath)
print("%-20s | Time: %-14s Name: %s" %
("Save Tile Sum", str(t.elapsed()), filepath))
def save_filtered_image(np_img, slide_name, filter_num, filter_text):
"""
Save a filtered image to the file system.
Args:
np_img: Image as a NumPy array.
slide_name: The slide number.
filter_num: The filter number.
filter_text: Descriptive text to add to the image filename.
"""
t = Time()
filepath = slide.get_filter_image_path(slide_name, filter_num, filter_text)
pil_img = util.np_to_pil(np_img)
pil_img.save(filepath)
print("%-20s | Time: %-14s Name: %s" %
("Save Image", str(t.elapsed()), filepath))
def filter_local_equalization(np_img, disk_size=50):
"""
Filter image (gray) using local equalization, which uses local histograms based on the disk structuring element.
Args:
np_img: Image as a NumPy array.
disk_size: Radius of the disk structuring element used for the local histograms
Returns:
NumPy array with contrast enhanced using local equalization.
"""
t = Time()
local_equ = sk_filters.rank.equalize(np_img,
selem=sk_morphology.disk(disk_size))
util.np_info(local_equ, "Local Equalization", t.elapsed())
return local_equ
def filter_complement(np_img, output_type="uint8"):
"""
Obtain the complement of an image as a NumPy array.
Args:
np_img: Image as a NumPy array.
type: Type of array to return (float or uint8).
Returns:
Complement image as Numpy array.
"""
t = Time()
if output_type == "float":
complement = 1.0 - np_img
else:
complement = 255 - np_img
util.np_info(complement, "Complement", t.elapsed())
return complement
def filter_rgb_to_hsv(np_img, display_np_info=True):
"""
Filter RGB channels to HSV (Hue, Saturation, Value).
Args:
np_img: RGB image as a NumPy array.
display_np_info: If True, display NumPy array info and filter time.
Returns:
Image as NumPy array in HSV representation.
"""
if display_np_info:
t = Time()
hsv = sk_color.rgb2hsv(np_img)
if display_np_info:
util.np_info(hsv, "RGB to HSV", t.elapsed())
return hsv
def filter_green_channel(np_img,
green_thresh=200,
avoid_overmask=True,
overmask_thresh=90,
output_type="bool"):
"""
Create a mask to filter out pixels with a green channel value greater than a particular threshold, since hematoxylin
and eosin are purplish and pinkish, which do not have much green to them.
Args:
np_img: RGB image as a NumPy array.
green_thresh: Green channel threshold value (0 to 255). If value is greater than green_thresh, mask out pixel.
avoid_overmask: If True, avoid masking above the overmask_thresh percentage.
overmask_thresh: If avoid_overmask is True, avoid masking above this threshold percentage value.
output_type: Type of array to return (bool, float, or uint8).
Returns:
NumPy array representing a mask where pixels above a particular green channel threshold have been masked out.
"""
t = Time()
g = np_img[:, :, 1]
gr_ch_mask = (g < green_thresh) & (g > 0)
mask_percentage = mask_percent(gr_ch_mask)
if (mask_percentage >= overmask_thresh) and (green_thresh < 255) and (
avoid_overmask is True):
new_green_thresh = math.ceil((255 - green_thresh) / 2 + green_thresh)
#print(
#"Mask percentage %3.2f%% >= overmask threshold %3.2f%% for Remove Green Channel green_thresh=%d, so try %d" % (
#mask_percentage, overmask_thresh, green_thresh, new_green_thresh))
gr_ch_mask = filter_green_channel(np_img, new_green_thresh,
avoid_overmask, overmask_thresh,
output_type)
np_img = gr_ch_mask
if output_type == "bool":
pass
elif output_type == "float":
np_img = np_img.astype(float)
else:
np_img = np_img.astype("uint8") * 255
util.np_info(np_img, "Filter Green Channel", t.elapsed())
return np_img
def filter_remove_small_objects(np_img,
min_size=3000,
avoid_overmask=True,
overmask_thresh=95,
output_type="uint8"):
"""
Filter image to remove small objects (connected components) less than a particular minimum size. If avoid_overmask
is True, this function can recursively call itself with progressively smaller minimum size objects to remove to
reduce the amount of masking that this filter performs.
Args:
np_img: Image as a NumPy array of type bool.
min_size: Minimum size of small object to remove.
avoid_overmask: If True, avoid masking above the overmask_thresh percentage.
overmask_thresh: If avoid_overmask is True, avoid masking above this threshold percentage value.
output_type: Type of array to return (bool, float, or uint8).
Returns:
NumPy array (bool, float, or uint8).
"""
t = Time()
rem_sm = np_img.astype(bool) # make sure mask is boolean
rem_sm = sk_morphology.remove_small_objects(rem_sm, min_size=min_size)
mask_percentage = mask_percent(rem_sm)
if (mask_percentage >=
overmask_thresh) and (min_size >= 1) and (avoid_overmask is True):
new_min_size = min_size / 2
#print("Mask percentage %3.2f%% >= overmask threshold %3.2f%% for Remove Small Objs size %d, so try %d" % (
#mask_percentage, overmask_thresh, min_size, new_min_size))
rem_sm = filter_remove_small_objects(np_img, new_min_size,
avoid_overmask, overmask_thresh,
output_type)
np_img = rem_sm
if output_type == "bool":
pass
elif output_type == "float":
np_img = np_img.astype(float)
else:
np_img = np_img.astype("uint8") * 255
util.np_info(np_img, "Remove Small Objs", t.elapsed())
return np_img
def filter_contrast_stretch(np_img, low=40, high=60):
"""
Filter image (gray or RGB) using contrast stretching to increase contrast in image based on the intensities in
a specified range.
Args:
np_img: Image as a NumPy array (gray or RGB).
low: Range low value (0 to 255).
high: Range high value (0 to 255).
Returns:
Image as NumPy array with contrast enhanced.
"""
t = Time()
low_p, high_p = np.percentile(np_img, (low * 100 / 255, high * 100 / 255))
contrast_stretch = sk_exposure.rescale_intensity(np_img,
in_range=(low_p, high_p))
util.np_info(contrast_stretch, "Contrast Stretch", t.elapsed())
return contrast_stretch
def singleprocess_apply_filters_to_images(save=True,
display=False,
html=False,
image_name_list=None):
"""
Apply a set of filters to training images and optionally save and/or display the filtered images.
Args:
save: If True, save filtered images.
display: If True, display filtered images to screen.
html: If True, generate HTML page to display filtered images.
image_name_list: Optionally specify a list of image slide names.
"""
t = Time()
print("Applying filters to images\n")
if image_name_list is not None:
_, info = apply_filters_to_image_list(image_name_list, save, display)
print("Time to apply filters to all images: %s\n" % str(t.elapsed()))
def filter_rgb_to_grayscale(np_img, output_type="uint8"):
"""
Convert an RGB NumPy array to a grayscale NumPy array.
Shape (h, w, c) to (h, w).
Args:
np_img: RGB Image as a NumPy array.
output_type: Type of array to return (float or uint8)
Returns:
Grayscale image as NumPy array with shape (h, w).
"""
t = Time()
# Another common RGB ratio possibility: [0.299, 0.587, 0.114]
grayscale = np.dot(np_img[..., :3], [0.2125, 0.7154, 0.0721])
if output_type != "float":
grayscale = grayscale.astype("uint8")
util.np_info(grayscale, "Gray", t.elapsed())
return grayscale
def filter_kmeans_segmentation(np_img, compactness=10, n_segments=800):
"""
Use K-means segmentation (color/space proximity) to segment RGB image where each segment is
colored based on the average color for that segment.
Args:
np_img: Binary image as a NumPy array.
compactness: Color proximity versus space proximity factor.
n_segments: The number of segments.
Returns:
NumPy array (uint8) representing 3-channel RGB image where each segment has been colored based on the average
color for that segment.
"""
t = Time()
labels = sk_segmentation.slic(np_img,
compactness=compactness,
n_segments=n_segments)
result = sk_color.label2rgb(labels, np_img, kind='avg')
util.np_info(result, "K-Means Segmentation", t.elapsed())
return result
def filter_hed_to_eosin(np_img, output_type="uint8"):
"""
Obtain Eosin channel from HED NumPy array and rescale it (for example, to 0 to 255 for uint8) for increased
contrast.
Args:
np_img: HED image as a NumPy array.
output_type: Type of array to return (float or uint8).
Returns:
NumPy array for Eosin channel.
"""
t = Time()
eosin = np_img[:, :, 1]
if output_type == "float":
eosin = sk_exposure.rescale_intensity(eosin, out_range=(0.0, 1.0))
else:
eosin = (sk_exposure.rescale_intensity(
eosin, out_range=(0, 255))).astype("uint8")
util.np_info(eosin, "HED to Eosin", t.elapsed())
return eosin
def filter_rgb_to_hed(np_img, output_type="uint8"):
"""
Filter RGB channels to HED (Hematoxylin - Eosin - Diaminobenzidine) channels.
Args:
np_img: RGB image as a NumPy array.
output_type: Type of array to return (float or uint8).
Returns:
NumPy array (float or uint8) with HED channels.
"""
t = Time()
hed = sk_color.rgb2hed(np_img)
if output_type == "float":
hed = sk_exposure.rescale_intensity(hed, out_range=(0.0, 1.0))
else:
hed = (sk_exposure.rescale_intensity(hed,
out_range=(0,
255))).astype("uint8")
util.np_info(hed, "RGB to HED", t.elapsed())
return hed
def filter_otsu_threshold(np_img, output_type="uint8"):
"""
Compute Otsu threshold on image as a NumPy array and return binary image based on pixels above threshold.
Args:
np_img: Image as a NumPy array.
output_type: Type of array to return (bool, float, or uint8).
Returns:
NumPy array (bool, float, or uint8) where True, 1.0, and 255 represent a pixel above Otsu threshold.
"""
t = Time()
otsu_thresh_value = sk_filters.threshold_otsu(np_img)
otsu = (np_img > otsu_thresh_value)
if output_type == "bool":
pass
elif output_type == "float":
otsu = otsu.astype(float)
else:
otsu = otsu.astype("uint8") * 255
util.np_info(otsu, "Otsu Threshold", t.elapsed())
return otsu
def filter_green(rgb,
red_upper_thresh,
green_lower_thresh,
blue_lower_thresh,
output_type="bool",
display_np_info=False):
"""
Create a mask to filter out greenish colors, where the mask is based on a pixel being below a
red channel threshold value, above a green channel threshold value, and above a blue channel threshold value.
Note that for the green ink, the green and blue channels tend to track together, so we use a blue channel
lower threshold value rather than a blue channel upper threshold value.
Args:
rgb: RGB image as a NumPy array.
red_upper_thresh: Red channel upper threshold value.
green_lower_thresh: Green channel lower threshold value.
blue_lower_thresh: Blue channel lower threshold value.
output_type: Type of array to return (bool, float, or uint8).
display_np_info: If True, display NumPy array info and filter time.
Returns:
NumPy array representing the mask.
"""
if display_np_info:
t = Time()
r = rgb[:, :, 0] < red_upper_thresh
g = rgb[:, :, 1] > green_lower_thresh
b = rgb[:, :, 2] > blue_lower_thresh
result = ~(r & g & b)
if output_type == "bool":
pass
elif output_type == "float":
result = result.astype(float)
else:
result = result.astype("uint8") * 255
if display_np_info:
util.np_info(result, "Filter Green", t.elapsed())
return result
def filter_binary_fill_holes(np_img, output_type="bool"):
"""
Fill holes in a binary object (bool, float, or uint8).
Args:
np_img: Binary image as a NumPy array.
output_type: Type of array to return (bool, float, or uint8).
Returns:
NumPy array (bool, float, or uint8) where holes have been filled.
"""
t = Time()
if np_img.dtype == "uint8":
np_img = np_img / 255
result = sc_morph.binary_fill_holes(np_img)
if output_type == "bool":
pass
elif output_type == "float":
result = result.astype(float)
else:
result = result.astype("uint8") * 255
util.np_info(result, "Binary Fill Holes", t.elapsed())
return result
def save_display_tile(tile, save=True, display=False):
"""
Save and/or display a tile image.
Args:
tile: Tile object.
save: If True, save tile image.
display: If True, dispaly tile image.
"""
tile_pil_img = tile_to_pil_tile(tile)
if save:
t = Time()
img_path = slide.get_tile_image_path(tile)
dir = os.path.dirname(img_path)
if not os.path.exists(dir):
os.makedirs(dir)
tile_pil_img.save(img_path)
print("%-20s | Time: %-14s Name: %s" %
("Save Tile", str(t.elapsed()), img_path))
if display:
tile_pil_img.show()
def filter_histogram_equalization(np_img, nbins=256, output_type="uint8"):
"""
Filter image (gray or RGB) using histogram equalization to increase contrast in image.
Args:
np_img: Image as a NumPy array (gray or RGB).
nbins: Number of histogram bins.
output_type: Type of array to return (float or uint8).
Returns:
NumPy array (float or uint8) with contrast enhanced by histogram equalization.
"""
t = Time()
# if uint8 type and nbins is specified, convert to float so that nbins can be a value besides 256
if np_img.dtype == "uint8" and nbins != 256:
np_img = np_img / 255
hist_equ = sk_exposure.equalize_hist(np_img, nbins=nbins)
if output_type == "float":
pass
else:
hist_equ = (hist_equ * 255).astype("uint8")
util.np_info(hist_equ, "Hist Equalization", t.elapsed())
return hist_equ
def filter_threshold(np_img, threshold, output_type="bool"):
"""
Return mask where a pixel has a value if it exceeds the threshold value.
Args:
np_img: Binary image as a NumPy array.
threshold: The threshold value to exceed.
output_type: Type of array to return (bool, float, or uint8).
Returns:
NumPy array representing a mask where a pixel has a value (T, 1.0, or 255) if the corresponding input array
pixel exceeds the threshold value.
"""
t = Time()
result = (np_img > threshold)
if output_type == "bool":
pass
elif output_type == "float":
result = result.astype(float)
else:
result = result.astype("uint8") * 255
util.np_info(result, "Threshold", t.elapsed())
return result
def filter_hysteresis_threshold(np_img, low=50, high=100, output_type="uint8"):
"""
Apply two-level (hysteresis) threshold to an image as a NumPy array, returning a binary image.
Args:
np_img: Image as a NumPy array.
low: Low threshold.
high: High threshold.
output_type: Type of array to return (bool, float, or uint8).
Returns:
NumPy array (bool, float, or uint8) where True, 1.0, and 255 represent a pixel above hysteresis threshold.
"""
t = Time()
hyst = sk_filters.apply_hysteresis_threshold(np_img, low, high)
if output_type == "bool":
pass
elif output_type == "float":
hyst = hyst.astype(float)
else:
hyst = (255 * hyst).astype("uint8")
util.np_info(hyst, "Hysteresis Threshold", t.elapsed())
return hyst