NON MAXIMUM SUPPRESSION FOR TENSORFLOW OBJECT DETECTION API - tensorflow

I am implementing a Faster RCNN v2 Inception in Tensorflow Object Detection API. To remove redundant overlapping detections, I read that NMS should be applied.
One way of doing this is adjusting the NMS IOU Threshold in the config file first_stage_nms_iou_threshold.
Questions
What is this parameter exactly? To what value should this parameter be adjusted to (default value is 0.7)
Why is it called first_stage_nms_iou_threshold? Why first stage only?
Is there another easy and more effective way of removing redundant detections?

I can't anwser your first and second question but i had the same problem with overlapping bounding boxes and use the following code to fix them manually... You have to know the x1,y1,x2,y2 coordinates of your bounding boxes which are overlapping...
# import the necessary packages
from nms import non_max_suppression_slow
import numpy as np
import cv2
# path to your image
# and the coordinates x1,x2,y1,y2 of the overlapping bounding boxes
images = [
("path/to/your/image", np.array([
(664, 0, 988, 177),
(670, 10, 1000, 188),
(685, 20, 1015, 193),
(47, 100, 357, 500),
(55, 105, 362, 508),
(68, 120, 375, 520),
(978, 80, 1093, 206)]))]
# loop over the images
for (imagePath, boundingBoxes) in images:
# load the image and clone it
print("[x] %d initial bounding boxes" % (len(boundingBoxes)))
image = cv2.imread(imagePath)
orig = image.copy()
# loop over the bounding boxes for each image and draw them
for (startX, startY, endX, endY) in boundingBoxes:
cv2.rectangle(orig, (startX, startY), (endX, endY), (0, 0, 255), 2)
# perform non-maximum suppression on the bounding boxes
pick = non_max_suppression_slow(boundingBoxes, 0.3)
print("[x] after applying non-maximum, %d bounding boxes" % (len(pick)))
# loop over the picked bounding boxes and draw them
for (startX, startY, endX, endY) in pick:
cv2.rectangle(image, (startX, startY), (endX, endY), (0, 255, 0), 2)
# display the images
cv2.imshow("Original", orig)
cv2.imshow("After NMS", image)
cv2.waitKey(0)
and still need this :
# import the necessary packages
import numpy as np
def non_max_suppression_slow(boxes, overlapThresh):
# if there are no boxes, return an empty list
if len(boxes) == 0:
return []
# initialize the list of picked indexes
pick = []
# grab the coordinates of the bounding boxes
x1 = boxes[:,0]
y1 = boxes[:,1]
x2 = boxes[:,2]
y2 = boxes[:,3]
# compute the area of the bounding boxes and sort the bounding
# boxes by the bottom-right y-coordinate of the bounding box
area = (x2 - x1 + 1) * (y2 - y1 + 1)
idxs = np.argsort(y2)
# keep looping while some indexes still remain in the indexes
# list
while len(idxs) > 0:
# grab the last index in the indexes list, add the index
# value to the list of picked indexes, then initialize
# the suppression list (i.e. indexes that will be deleted)
# using the last index
last = len(idxs) - 1
i = idxs[last]
pick.append(i)
suppress = [last]
# loop over all indexes in the indexes list
for pos in range(0, last):
# grab the current index
j = idxs[pos]
# find the largest (x, y) coordinates for the start of
# the bounding box and the smallest (x, y) coordinates
# for the end of the bounding box
xx1 = max(x1[i], x1[j])
yy1 = max(y1[i], y1[j])
xx2 = min(x2[i], x2[j])
yy2 = min(y2[i], y2[j])
# compute the width and height of the bounding box
w = max(0, xx2 - xx1 + 1)
h = max(0, yy2 - yy1 + 1)
# compute the ratio of overlap between the computed
# bounding box and the bounding box in the area list
overlap = float(w * h) / area[j]
# if there is sufficient overlap, suppress the
# current bounding box
if overlap > overlapThresh:
suppress.append(pos)
# delete all indexes from the index list that are in the
# suppression list
idxs = np.delete(idxs, suppress)
# return only the bounding boxes that were picked
return boxes[pick]

Related

make sure text falls within plot using matplotlib

I am trying to generate random images of text and store them as image files in my computer so that I can use them to train a model later. But I don't know how make sure all the characters falls within the image boundaries. When I plot them out in python they always show, but if I looked at the saved image, some times the strings are cut. Also, I want to automate the process instead of plotting each out to check.
Furthermore, setting bbox_inches='tight' changes the image size, while I want to be able to specify the image size.
This is what I have tried so far
import matplotlib.pyplot as plt
import numpy as np
dpi = 100
h, w = 50, 100
plt.figure(figsize=(w / dpi, h / dpi), dpi=dpi)# so I will get w columns and h rows
text = str(np.random.uniform(100000, 1000000))# my string will always only be 6 characters
x = np.random.uniform(0, .3)# random positions
y = np.random.uniform(0, .5)
size = np.random.uniform(16, 23)# random text size
plt.text(x, y, text, fontdict={'size': size})
plt.axis('off')
plt.savefig(text + '.jpg'))
I figured a way to get around this. .get_window_extent() can help locate the edges of the text. Since I just want to generate random images, I can drop the image and generate the next one if the text it out of bounds. For non-random text, I suppose one can also use it to determine which way to shift text if it goes out of bounds.
Here is a sample solution with my random text case:
import matplotlib.pyplot as plt
import numpy as np
dpi = 100
w = 120 # number of columns
h = 50 # number of rows
N = 100 # number of random images to generate
count = 0
while count < N:
fig = plt.figure(frameon=False, dpi=dpi)
fig.set_size_inches(w / dpi, h / dpi)
ax = plt.Axes(fig, [0., 0., 1., 1.])
ax.set_axis_off()
fig.add_axes(ax)
number = str(np.random.randint(100000, 1000000))# random text
x = np.random.uniform(0, .1)# random position
y = np.random.uniform(0, .5)
size = np.random.uniform(w / dpi * 72 / 6, w / dpi * 72 / 3.3)
text = ax.text(x, y, number, fontdict={'size': size})
bbox = text.get_window_extent(fig.canvas.get_renderer())# !!! get the extent of the text
if (bbox.x1 < w) & (bbox.y1 < h):# !!! make sure the extent is within bounds before save
plt.savefig(f'{number}.jpg'), pad_inches=0, dpi=dpi)
count += 1
plt.close()# remember to close else bad for memory(?)

how to counting white pixels in every rectangle in over image?

I have thousands of images 1000X2000 px and I want count only white pixels in each small windows of image 100X200 and write count number in vector array
please how can I do that by python openCV?
Sample Image:
Opencv and Numpy are pretty good at this. You can use numpy slicing to target each box and numpy.sum to count the number of white pixels in the slice.
import cv2
import numpy as np
# count white pixels per box
def boxCount(img, bw, bh):
# declare output list
counts = [];
h, w = img.shape[:2];
for y in range(0, h - bh + 1, bh):
line = [];
for x in range(0, w - bw + 1, bw):
# slice out box
box = img[y:y+bh, x:x+bw];
# count
count = np.sum(box == 255);
line.append(count);
counts.append(line);
return counts;
# load image
img = cv2.imread("jump.png");
img = cv2.resize(img, (1000, 2000));
gray = cv2.cvtColor(img, cv2.COLOR_BGR2GRAY);
# define box search params
box_width = 100;
box_height = 200;
# get counts
counts = boxCount(img, box_width, box_height);
for line in counts:
print(line);

PiCamera mmal Error in Raspberrypi W Zero

I Do Detecting Mask Project on Raspberrypi W Zero. But I can't catch the error.
This is my Tensorflow and openCV Code
# import the necessary packages
from tensorflow.keras.applications.mobilenet_v2 import preprocess_input
from tensorflow.keras.preprocessing.image import img_to_array
from tensorflow.keras.models import load_model
from imutils.video import VideoStream
import picamera
#from picamera import sleep
import numpy as np
import imutils
import time
import cv2
import os
def detect_and_predict_mask(frame, faceNet, maskNet):
# grab the dimensions of the frame and then construct a blob
# from it
(h, w) = frame.shape[:2]
blob = cv2.dnn.blobFromImage(frame, 1.0, (224, 224),
(104.0, 177.0, 123.0))
# pass the blob through the network and obtain the face detections
faceNet.setInput(blob)
detections = faceNet.forward()
print(detections.shape)
# initialize our list of faces, their corresponding locations,
# and the list of predictions from our face mask network
faces = []
locs = []
preds = []
# loop over the detections
for i in range(0, detections.shape[2]):
# extract the confidence (i.e., probability) associated with
# the detection
confidence = detections[0, 0, i, 2]
# filter out weak detections by ensuring the confidence is
# greater than the minimum confidence
if confidence > 0.5:
# compute the (x, y)-coordinates of the bounding box for
# the object
box = detections[0, 0, i, 3:7] * np.array([w, h, w, h])
(startX, startY, endX, endY) = box.astype("int")
# ensure the bounding boxes fall within the dimensions of
# the frame
(startX, startY) = (max(0, startX), max(0, startY))
(endX, endY) = (min(w - 1, endX), min(h - 1, endY))
# extract the face ROI, convert it from BGR to RGB channel
# ordering, resize it to 224x224, and preprocess it
face = frame[startY:endY, startX:endX]
face = cv2.cvtColor(face, cv2.COLOR_BGR2RGB)
face = cv2.resize(face, (224, 224))
face = img_to_array(face)
face = preprocess_input(face)
# add the face and bounding boxes to their respective
# lists
faces.append(face)
locs.append((startX, startY, endX, endY))
# only make a predictions if at least one face was detected
if len(faces) > 0:
# for faster inference we'll make batch predictions on *all*
# faces at the same time rather than one-by-one predictions
# in the above `for` loop
faces = np.array(faces, dtype="float32")
preds = maskNet.predict(faces, batch_size=32)
# return a 2-tuple of the face locations and their corresponding
# locations
return (locs, preds)
# load our serialized face detector model from disk
prototxtPath = r"/home/pi/Desktop/pi/face_detector/deploy.prototxt"
weightsPath = r"/home/pi/Desktop/pi/face_detector/res10_300x300_ssd_iter_140000.caffemodel"
faceNet = cv2.dnn.readNet(prototxtPath, weightsPath)
# load the face mask detector model from disk
maskNet = load_model("./mask_detector.model")
# initialize the video stream
print("[INFO] starting video stream...")
vs = VideoStream(src=0).start()
cap = picamera.PiCamera()
# loop over the frames from the video stream
while(cap.isOpened()):
# grab the frame from the threaded video stream and resize it
# to have a maximum width of 400 pixels
frame = vs.read()
frame = imutils.resize(frame, width=400)
# detect faces in the frame and determine if they are wearing a
# face mask or not
(locs, preds) = detect_and_predict_mask(frame, faceNet, maskNet)
# loop over the detected face locations and their corresponding
# locations
for (box, pred) in zip(locs, preds):
# unpack the bounding box and predictions
(startX, startY, endX, endY) = box
(mask, withoutMask) = pred
# determine the class label and color we'll use to draw
# the bounding box and text
label = "Mask" if mask > withoutMask else "No Mask"
color = (0, 255, 0) if label == "Mask" else (0, 0, 255)
# include the probability in the label
label = "{}: {:.2f}%".format(label, max(mask, withoutMask) * 100)
# display the label and bounding box rectangle on the output
# frame
cv2.putText(frame, label, (startX, startY - 10),
cv2.FONT_HERSHEY_SIMPLEX, 0.45, color, 2)
cv2.rectangle(frame, (startX, startY), (endX, endY), color, 2)
# show the output frame
cv2.imshow("Frame", frame)
key = cv2.waitKey(1) & 0xFF
# if the `q` key was pressed, break from the loop
if key == ord("q"):
cap.close()
break
# do a bit of cleanup
cv2.destroyAllWindows()
vs.stop()
And I run this Tensorflow and openCV code in Raspberrypi W Zero... But This Error Bothering Me..
mmal: mmal_vc_port_enable: failed to enable port vc.null_sink:in:0(OPQV): ENOSPC
mmal: mmal_port_enable: failed to enable connected port (vc.null_sink:in:0(OPQV))0x34600e0 (ENOSPC)
mmal: mmal_connection_enable: output port couldn't be enabled
Traceback (most recent call last):
File "detect_mask_video.py", line 88, in <module>
cap = picamera.PiCamera()
File "/usr/lib/python3/dist-packages/picamera/camera.py", line 433, in __init__
self._init_preview()
File "/usr/lib/python3/dist-packages/picamera/camera.py", line 513, in _init_preview
self, self._camera.outputs[self.CAMERA_PREVIEW_PORT])
File "/usr/lib/python3/dist-packages/picamera/renderers.py", line 558, in __init__
self.renderer.inputs[0].connect(source).enable()
File "/usr/lib/python3/dist-packages/picamera/mmalobj.py", line 2212, in enable
prefix="Failed to enable connection")
File "/usr/lib/python3/dist-packages/picamera/exc.py", line 184, in mmal_check
raise PiCameraMMALError(status, prefix)
picamera.exc.PiCameraMMALError: Failed to enable connection: Out of resources
I Search this error in google But I can't fix this...Please Help me.. :D
What I've done so far :
raspberrypi update
Increasing memory
Reconnect PiCamera
Enter the following command on the terminal:
sudo modprobe bcm2835-v4l2
To access the mmal device as a standard v4l(video for Linux) device.

how to use tensorflow::ops::NonMaxSuppression in label_image tensorflow cpp example to remove multi rectangle predicted for one object?

i used Tensorflow label_image example https://github.com/tensorflow/tensorflow/tree/master/tensorflow/examples/label_image to detect and localize 10 class objects from image . now i want remove multi predicted rectangle for one object with tensorflow::ops::NonMaxSuppression . i don't know how to use it in my code . please help me to solve it. like this picture
You can use the below function to draw boxes which surpass the threshold, I am taking it from Tensorflow object detection API.
https://github.com/tensorflow/models/blob/master/research/object_detection/utils/visualization_utils.py
def visualize_boxes_and_labels_on_image_array(
image,
boxes,
classes,
scores,
category_index,
instance_masks=None,
instance_boundaries=None,
keypoints=None,
track_ids=None,
use_normalized_coordinates=False,
max_boxes_to_draw=20,
min_score_thresh=.5,
agnostic_mode=False,
line_thickness=4,
groundtruth_box_visualization_color='black',
skip_scores=False,
skip_labels=False,
skip_track_ids=False):
"""Overlay labeled boxes on an image with formatted scores and label names.
This function groups boxes that correspond to the same location
and creates a display string for each detection and overlays these
on the image. Note that this function modifies the image in place, and returns
that same image.
Args:
image: uint8 numpy array with shape (img_height, img_width, 3)
boxes: a numpy array of shape [N, 4]
classes: a numpy array of shape [N]. Note that class indices are 1-based,
and match the keys in the label map.
scores: a numpy array of shape [N] or None. If scores=None, then
this function assumes that the boxes to be plotted are groundtruth
boxes and plot all boxes as black with no classes or scores.
category_index: a dict containing category dictionaries (each holding
category index `id` and category name `name`) keyed by category indices.
instance_masks: a numpy array of shape [N, image_height, image_width] with
values ranging between 0 and 1, can be None.
instance_boundaries: a numpy array of shape [N, image_height, image_width]
with values ranging between 0 and 1, can be None.
keypoints: a numpy array of shape [N, num_keypoints, 2], can
be None
track_ids: a numpy array of shape [N] with unique track ids. If provided,
color-coding of boxes will be determined by these ids, and not the class
indices.
use_normalized_coordinates: whether boxes is to be interpreted as
normalized coordinates or not.
max_boxes_to_draw: maximum number of boxes to visualize. If None, draw
all boxes.
min_score_thresh: minimum score threshold for a box to be visualized
agnostic_mode: boolean (default: False) controlling whether to evaluate in
class-agnostic mode or not. This mode will display scores but ignore
classes.
line_thickness: integer (default: 4) controlling line width of the boxes.
groundtruth_box_visualization_color: box color for visualizing groundtruth
boxes
skip_scores: whether to skip score when drawing a single detection
skip_labels: whether to skip label when drawing a single detection
skip_track_ids: whether to skip track id when drawing a single detection
Returns:
uint8 numpy array with shape (img_height, img_width, 3) with overlaid boxes.
"""
# Create a display string (and color) for every box location, group any boxes
# that correspond to the same location.
box_to_display_str_map = collections.defaultdict(list)
box_to_color_map = collections.defaultdict(str)
box_to_instance_masks_map = {}
box_to_instance_boundaries_map = {}
box_to_keypoints_map = collections.defaultdict(list)
box_to_track_ids_map = {}
if not max_boxes_to_draw:
max_boxes_to_draw = boxes.shape[0]
for i in range(min(max_boxes_to_draw, boxes.shape[0])):
if scores is None or scores[i] > min_score_thresh:
box = tuple(boxes[i].tolist())
if instance_masks is not None:
box_to_instance_masks_map[box] = instance_masks[i]
if instance_boundaries is not None:
box_to_instance_boundaries_map[box] = instance_boundaries[i]
if keypoints is not None:
box_to_keypoints_map[box].extend(keypoints[i])
if track_ids is not None:
box_to_track_ids_map[box] = track_ids[i]
if scores is None:
box_to_color_map[box] = groundtruth_box_visualization_color
else:
display_str = ''
if not skip_labels:
if not agnostic_mode:
if classes[i] in six.viewkeys(category_index):
class_name = category_index[classes[i]]['name']
else:
class_name = 'N/A'
display_str = str(class_name)
if not skip_scores:
if not display_str:
display_str = '{}%'.format(int(100*scores[i]))
else:
display_str = '{}: {}%'.format(display_str, int(100*scores[i]))
if not skip_track_ids and track_ids is not None:
if not display_str:
display_str = 'ID {}'.format(track_ids[i])
else:
display_str = '{}: ID {}'.format(display_str, track_ids[i])
box_to_display_str_map[box].append(display_str)
if agnostic_mode:
box_to_color_map[box] = 'DarkOrange'
elif track_ids is not None:
prime_multipler = _get_multiplier_for_color_randomness()
box_to_color_map[box] = STANDARD_COLORS[
(prime_multipler * track_ids[i]) % len(STANDARD_COLORS)]
else:
box_to_color_map[box] = STANDARD_COLORS[
classes[i] % len(STANDARD_COLORS)]
# Draw all boxes onto image.
for box, color in box_to_color_map.items():
ymin, xmin, ymax, xmax = box
if instance_masks is not None:
draw_mask_on_image_array(
image,
box_to_instance_masks_map[box],
color=color
)
if instance_boundaries is not None:
draw_mask_on_image_array(
image,
box_to_instance_boundaries_map[box],
color='red',
alpha=1.0
)
draw_bounding_box_on_image_array(
image,
ymin,
xmin,
ymax,
xmax,
color=color,
thickness=line_thickness,
display_str_list=box_to_display_str_map[box],
use_normalized_coordinates=use_normalized_coordinates)
if keypoints is not None:
draw_keypoints_on_image_array(
image,
box_to_keypoints_map[box],
color=color,
radius=line_thickness / 2,
use_normalized_coordinates=use_normalized_coordinates)
return image

want to smooth a contour from a masked array

I have a masked array which is used by matplotlib.plt.contourf to project a temperature contour on a glabal map. I was trying to smooth the contour, but unfortunately none of the proposed solutions seems to be able to handle masked array. I tested these solutions:
-scipy.ndimage.gaussian_filter - moving averages
scipy.ndimage.zoom
none of them works(they count in the masked values also). Is there any way I can smooth my contour on maskedArray
I have added this part after trying the proposed 'inpaint' solution and the results were unchanged. here is the code (if it helps)
import Scientific.IO.NetCDF as S
import mpl_toolkits.basemap as bm
import numpy.ma as MA
import numpy as np
import matplotlib.pyplot as plt
import inpaint
def main():
fileobj = S.NetCDFFile('Bias.ANN.tas_A1_1.nc', mode='r')
# take the values
set1 = {'time', 'lat', 'lon'}
set2 = set(fileobj.variables.keys())
set3 = set2 - set1
datadim = set3.pop()
print "******************datadim: "+datadim
data = fileobj.variables[datadim].getValue()[0,:,:]
lon = fileobj.variables['lon'].getValue()
lat = fileobj.variables['lat'].getValue()
fileobj.close()
data, lon = bm.shiftgrid(180.,data, lon,start=False)
data = MA.masked_equal(data, 1.0e20)
#data2 = inpaint.replace_nans(data, 10, 0.25, 2, 'idw')
#- Make 2-D longitude and latitude arrays:
[lon2d, lat2d] =np.meshgrid(lon, lat)
#- Set up map:
mapproj = bm.Basemap(projection='cyl',
llcrnrlat=-90.0, llcrnrlon=-180.00,
urcrnrlat=90.0, urcrnrlon=180.0)
mapproj.drawcoastlines(linewidth=.5)
mapproj.drawmapboundary(fill_color='.8')
#mapproj.drawparallels(N.array([-90, -45, 0, 45, 90]), labels=[1,0,0,0])
#mapproj.drawmeridians(N.array([0, 90, 180, 270, 360]), labels=[0,0,0,1])
lonall, latall = mapproj(lon2d, lat2d)
cmap=plt.cm.Spectral
#- Make a contour plot of the temperature:
mymapf = plt.contourf(lonall, latall, data, 20, cmap=cmap)
#plt.clabel(mymapf, fontsize=12)
plt.title(cmap.name)
plt.colorbar(mymapf, orientation='horizontal')
plt.savefig('sample2.png', dpi=150, edgecolor='red', format='png', bbox_inches='tight', pad_inches=.2)
plt.close()
if __name__ == "__main__":
main()
I am comparing the output from this code (the first figure), with output of the same datafile from Panoply. Zoomin in and looking more precisely it seems like it is not the smoothness problem, but the pyplot model provides one stripe slimmer, or the contours are cut earlier (the outer boundaries shows this clearly, and inner contours are different due to this fact). It makes it to look like that the pyplot model is not as smooth as the Panoply one. how can I get (nearly) the same model? Am I distinguishing it right?
I had similar problem and google pointed me to this: blog post. Basically he's using inpaint algorithm to interpolate missing values and produce valid array for filtering.
The code is at the end of the post, and you can save it to site-packages (or else) and load it as module (i.e. inpaint.py):
import inpaint
filled = inpaint.replace_nans(NANMask, 5, 0.5, 2, 'idw')
I'm happy with the result, and I guess it will suite missing temperature values just fine. There is also next version here: github but code will need some cleaning for general usage as it's part of a project.
For reference, easy use and preservation sake I'll post the code (of initial version) here:
# -*- coding: utf-8 -*-
"""A module for various utilities and helper functions"""
import numpy as np
#cimport numpy as np
#cimport cython
DTYPEf = np.float64
#ctypedef np.float64_t DTYPEf_t
DTYPEi = np.int32
#ctypedef np.int32_t DTYPEi_t
##cython.boundscheck(False) # turn of bounds-checking for entire function
##cython.wraparound(False) # turn of bounds-checking for entire function
def replace_nans(array, max_iter, tol,kernel_size=1,method='localmean'):
"""Replace NaN elements in an array using an iterative image inpainting algorithm.
The algorithm is the following:
1) For each element in the input array, replace it by a weighted average
of the neighbouring elements which are not NaN themselves. The weights depends
of the method type. If ``method=localmean`` weight are equal to 1/( (2*kernel_size+1)**2 -1 )
2) Several iterations are needed if there are adjacent NaN elements.
If this is the case, information is "spread" from the edges of the missing
regions iteratively, until the variation is below a certain threshold.
Parameters
----------
array : 2d np.ndarray
an array containing NaN elements that have to be replaced
max_iter : int
the number of iterations
kernel_size : int
the size of the kernel, default is 1
method : str
the method used to replace invalid values. Valid options are
`localmean`, 'idw'.
Returns
-------
filled : 2d np.ndarray
a copy of the input array, where NaN elements have been replaced.
"""
# cdef int i, j, I, J, it, n, k, l
# cdef int n_invalids
filled = np.empty( [array.shape[0], array.shape[1]], dtype=DTYPEf)
kernel = np.empty( (2*kernel_size+1, 2*kernel_size+1), dtype=DTYPEf )
# cdef np.ndarray[np.int_t, ndim=1] inans
# cdef np.ndarray[np.int_t, ndim=1] jnans
# indices where array is NaN
inans, jnans = np.nonzero( np.isnan(array) )
# number of NaN elements
n_nans = len(inans)
# arrays which contain replaced values to check for convergence
replaced_new = np.zeros( n_nans, dtype=DTYPEf)
replaced_old = np.zeros( n_nans, dtype=DTYPEf)
# depending on kernel type, fill kernel array
if method == 'localmean':
print 'kernel_size', kernel_size
for i in range(2*kernel_size+1):
for j in range(2*kernel_size+1):
kernel[i,j] = 1
print kernel, 'kernel'
elif method == 'idw':
kernel = np.array([[0, 0.5, 0.5, 0.5,0],
[0.5,0.75,0.75,0.75,0.5],
[0.5,0.75,1,0.75,0.5],
[0.5,0.75,0.75,0.5,1],
[0, 0.5, 0.5 ,0.5 ,0]])
print kernel, 'kernel'
else:
raise ValueError( 'method not valid. Should be one of `localmean`.')
# fill new array with input elements
for i in range(array.shape[0]):
for j in range(array.shape[1]):
filled[i,j] = array[i,j]
# make several passes
# until we reach convergence
for it in range(max_iter):
print 'iteration', it
# for each NaN element
for k in range(n_nans):
i = inans[k]
j = jnans[k]
# initialize to zero
filled[i,j] = 0.0
n = 0
# loop over the kernel
for I in range(2*kernel_size+1):
for J in range(2*kernel_size+1):
# if we are not out of the boundaries
if i+I-kernel_size < array.shape[0] and i+I-kernel_size >= 0:
if j+J-kernel_size < array.shape[1] and j+J-kernel_size >= 0:
# if the neighbour element is not NaN itself.
if filled[i+I-kernel_size, j+J-kernel_size] == filled[i+I-kernel_size, j+J-kernel_size] :
# do not sum itself
if I-kernel_size != 0 and J-kernel_size != 0:
# convolve kernel with original array
filled[i,j] = filled[i,j] + filled[i+I-kernel_size, j+J-kernel_size]*kernel[I, J]
n = n + 1*kernel[I,J]
# divide value by effective number of added elements
if n != 0:
filled[i,j] = filled[i,j] / n
replaced_new[k] = filled[i,j]
else:
filled[i,j] = np.nan
# check if mean square difference between values of replaced
#elements is below a certain tolerance
print 'tolerance', np.mean( (replaced_new-replaced_old)**2 )
if np.mean( (replaced_new-replaced_old)**2 ) < tol:
break
else:
for l in range(n_nans):
replaced_old[l] = replaced_new[l]
return filled
def sincinterp(image, x, y, kernel_size=3 ):
"""Re-sample an image at intermediate positions between pixels.
This function uses a cardinal interpolation formula which limits
the loss of information in the resampling process. It uses a limited
number of neighbouring pixels.
The new image :math:`im^+` at fractional locations :math:`x` and :math:`y` is computed as:
.. math::
im^+(x,y) = \sum_{i=-\mathtt{kernel\_size}}^{i=\mathtt{kernel\_size}} \sum_{j=-\mathtt{kernel\_size}}^{j=\mathtt{kernel\_size}} \mathtt{image}(i,j) sin[\pi(i-\mathtt{x})] sin[\pi(j-\mathtt{y})] / \pi(i-\mathtt{x}) / \pi(j-\mathtt{y})
Parameters
----------
image : np.ndarray, dtype np.int32
the image array.
x : two dimensions np.ndarray of floats
an array containing fractional pixel row
positions at which to interpolate the image
y : two dimensions np.ndarray of floats
an array containing fractional pixel column
positions at which to interpolate the image
kernel_size : int
interpolation is performed over a ``(2*kernel_size+1)*(2*kernel_size+1)``
submatrix in the neighbourhood of each interpolation point.
Returns
-------
im : np.ndarray, dtype np.float64
the interpolated value of ``image`` at the points specified
by ``x`` and ``y``
"""
# indices
# cdef int i, j, I, J
# the output array
r = np.zeros( [x.shape[0], x.shape[1]], dtype=DTYPEf)
# fast pi
pi = 3.1419
# for each point of the output array
for I in range(x.shape[0]):
for J in range(x.shape[1]):
#loop over all neighbouring grid points
for i in range( int(x[I,J])-kernel_size, int(x[I,J])+kernel_size+1 ):
for j in range( int(y[I,J])-kernel_size, int(y[I,J])+kernel_size+1 ):
# check that we are in the boundaries
if i >= 0 and i <= image.shape[0] and j >= 0 and j <= image.shape[1]:
if (i-x[I,J]) == 0.0 and (j-y[I,J]) == 0.0:
r[I,J] = r[I,J] + image[i,j]
elif (i-x[I,J]) == 0.0:
r[I,J] = r[I,J] + image[i,j] * np.sin( pi*(j-y[I,J]) )/( pi*(j-y[I,J]) )
elif (j-y[I,J]) == 0.0:
r[I,J] = r[I,J] + image[i,j] * np.sin( pi*(i-x[I,J]) )/( pi*(i-x[I,J]) )
else:
r[I,J] = r[I,J] + image[i,j] * np.sin( pi*(i-x[I,J]) )*np.sin( pi*(j-y[I,J]) )/( pi*pi*(i-x[I,J])*(j-y[I,J]))
return r
#cdef extern from "math.h":
# double sin(double)
A simple smoothing function that works with masked data will solve this. One can then avoid the approaches that involve making up data (ie, interpolating, inpainting, etc); and making up data should always be avoided.
The main issue that arises when smoothing masked data is that for each point, smoothing uses the neighboring values to calculate a new value at a center point, but when those neighbors are masked, the new value for the center point will also become masked due to the rules of masked arrays. Therefore, one needs to do the calculation with unmasked data, and explicitly account for the mask. That's easy to do, and is not in the function smooth below.
from numpy import *
import pylab as plt
# make a grid and a striped mask as test data
N = 100
x = linspace(0, 5, N, endpoint=True)
grid = 2. + 1.*(sin(2*pi*x)[:,newaxis]*sin(2*pi*x)>0.)
m = resize((sin(pi*x)>0), (N,N))
plt.imshow(grid.copy(), cmap='jet', interpolation='nearest')
plt.colorbar()
plt.title('original data')
def smooth(u, mask):
m = ~mask
r = u*m # set all 'masked' points to 0. so they aren't used in the smoothing
a = 4*r[1:-1,1:-1] + r[2:,1:-1] + r[:-2,1:-1] + r[1:-1,2:] + r[1:-1,:-2]
b = 4*m[1:-1,1:-1] + m[2:,1:-1] + m[:-2,1:-1] + m[1:-1,2:] + m[1:-1,:-2] # a divisor that accounts for masked points
b[b==0] = 1. # for avoiding divide by 0 error (region is masked so value doesn't matter)
u[1:-1,1:-1] = a/b
# run the data through the smoothing filter a few times
for i in range(10):
smooth(grid, m)
mg = ma.array(grid, mask=m) # put together the mask and the data
plt.figure()
plt.imshow(mg, cmap='jet', interpolation='nearest')
plt.colorbar()
plt.title('smoothed with mask')
plt.show()
The main point is that at the boundary of the mask, the masked values are not used in the smoothing. (This is also where the grid squares switch values, so it would be clear in the figure if the masked neighboring values were being used.)
We also just had this problem and the astropy package has us covered:
import numpy as np
import matplotlib.pyplot as plt
# Some Axes
x = np.arange(100)
y = np.arange(100)
#Some Interesting Shape
z = np.array(np.outer(np.sin((x+y)/10),np.sin(y/3)),dtype=float)
# some mask
mask = np.outer(np.sin((x+y)/20),np.sin(y/5))**2>.9
# masked data represent noise, so lets put in some trash into the masked points
z[mask] = (np.random.random(size = (100,100))*10)[mask]
# masked data
z_masked = np.ma.masked_array(z, mask)
# "Conventional" filter
filter_kernelsize = 2
import scipy.ndimage
z_filtered_bad = scipy.ndimage.gaussian_filter(z_masked,filter_kernelsize)
# Lets filter it
import astropy.convolution.convolve
from astropy.convolution import Gaussian2DKernel
k = Gaussian2DKernel(1.5)
z_filtered = astropy.convolution.convolve(z_masked, k, boundary='extend')
### Plots:
fig, axes = plt.subplots(2,2)
plt.sca(axes[0,0])
plt.title('Raw Data')
plt.imshow(z)
plt.colorbar()
plt.sca(axes[0,1])
plt.title('Raw Data Masked')
plt.imshow(z_masked)
plt.colorbar()
plt.sca(axes[1,0])
plt.title('ndimage filter (ignores mask)')
plt.imshow(z_filtered_bad)
plt.colorbar()
plt.sca(axes[1,1])
plt.title('astropy filter (uses mask)')
plt.imshow(z_filtered)
plt.colorbar()
plt.tight_layout()
Output plot of the code