Image Processing

LabNo4\mathbf{Lab\space No4}Lab No4

StudentInfo\mathbb {Student\space Info}Student Info

Name: Xiao Shitong
HDU ID: 19321123
ITMO ID: 293647

Content

Purpose\mathbb{Purpose}Purpose

• Getting know about basic digital images morphological analysis principles
• Using basic digital images operations
• Combine them to implement object splitting algorithm

Theory\mathbb{Theory}Theory

Basicmorphologicaloperations\mathbb{Basic\space morphological\space operations}Basic morphological operations

1. Dilation

   A⊕BA\oplus BA⊕B, where A is a binary image and B is an structural element. Its calculation formula can be written as dst(x,y)=max(src(x+x′,y+y′)),(x′,y′):element(x′,y′)≠0dst(x,y) = max (src(x+x', y+y')), (x',y'):element(x',y') \neq 0dst(x,y)=max(src(x+x′,y+y′)),(x′,y′):element(x′,y′)​=0

2. Erosion

   The simliar operation as dilation, but the maxmaxmax function in formula changes to minminmin function. Thus, it’s A⊖BA\ominus BA⊖B, and the calculation formula is dst(x,y)=max(src(x+x′,y+y′)),(x′,y′):element(x′,y′)≠0dst(x,y) = max (src(x+x', y+y')), (x',y'):element(x',y') \neq 0dst(x,y)=max(src(x+x′,y+y′)),(x′,y′):element(x′,y′)​=0

3. Open

   Open operation is a combination of dilation and erosion. It can be written as (A⊖B)⊕B(A\ominus B)\oplus B(A⊖B)⊕B.

   This operation can be used to remove small objects, split object by the thin junction.

4. Close

   Close operation is also a combination of dilation and erosion. It can be written as (A⊕B)⊖B(A\oplus B)\ominus B(A⊕B)⊖B.

   This operation can be used to remove some little black holes in the image.

5. Bwareaopen

   This operation can be used to remove small connectivity object from the image.

6. Contour detection

   Contour consists of internal contour and external contour.

   For the internal contour detection, the formula is A−(A⊖B)A - (A\ominus B)A−(A⊖B).

   For the external contour detection, the formula is A−(A⊕B)A - (A\oplus B)A−(A⊕B).

Separatingobjects\mathbb{Separating\space objects}Separating objects

1. First, we should change the gray image into binary value image.
2. Then, we erode this binary value image and got one image whose object areas are smaller.
3. We do several dilation operation, we can detect the approximate contour between objects.
4. Last, we just combine the contour together with the original gray image. Thus, the result image will look like separating the objects.

Watershedsegmentation\mathbb{Watershed\space segmentation}Watershed segmentation

The watershed segmentation algorithm assume that the garyscale image as a geological watershed.

And the value of gary pixel is regarded as the altitude, where higher altitude means much whiter.

Then we drop water into the watershed, and the lower altitude will be first drown, and then higher altitude. During the dropping, we can add isolation between each puddle. Thus, we can separate the objects.

Assignmentprogress\mathbb{Assignment\space progress}Assignment progress

Basicoperations\mathbb{Basic\space operations}Basic operations

Originalimages\mathbb{Original\space images}Original images

Chinese characters	Photo

Resultimages\mathbb{Result\space images}Result images

Erosion	Dilation	Open	Close	Bwarea open	Internal contour	External contour

Code\mathbb{Code}Code

# Do erode and dilate
kernel = cv.getStructuringElement(cv.MORPH_RECT, (15, 15))chinese_eroded = cv.erode(chinese, kernel)
cv.imshow("chinese eroded", chinese_eroded)chinese_dilated = cv.dilate(chinese, kernel)
cv.imshow("chinese dilated", chinese_dilated)# Do open and close
kernel = cv.getStructuringElement(cv.MORPH_RECT, (15, 15))chinese_closed = cv.morphologyEx(chinese, cv.MORPH_CLOSE, kernel, iterations=1)
cv.imshow("chinese closed", chinese_closed)chinese_opened = cv.morphologyEx(chinese, cv.MORPH_OPEN, kernel, iterations=1)
cv.imshow("chinese opened", chinese_opened)chinese_opened_closed = cv.morphologyEx(chinese_opened, cv.MORPH_CLOSE, kernel, iterations=2)
cv.imshow("chinese opened closed", chinese_opened_closed)# Do bwarea open
photo_bwareaopen = utils.bwareaopen(photo, 20000)
cv.imshow("photo bwareaopen", photo_bwareaopen)#
chinese_inner_contour = cv.subtract(chinese, chinese_eroded)
cv.imshow("Inner contour (I - erosion)", chinese_inner_contour)
chinese_outer_contour = cv.subtract(chinese_dilated, chinese)
cv.imshow("Outer contour (dilation - I)", chinese_outer_contour)# End of basic operations

Comments\mathbb{Comments}Comments

For the digital images morphological operations, the erosion and dilation are the basical operations for other operations. The open, close and bwarea open operations are based on the combination of erosion and dilation.

Separatingobjects\mathbb{Separating\space objects}Separating objects

Originalimage\mathbb{Original\space image}Original image

Resultimage\mathbb{Result\space image}Result image

Binary value coins	Erosion	Contour	Result

Code\mathbb{Code}Code

coins = cv.cvtColor(coins_color, cv.COLOR_BGR2GRAY
retval, coins_threshold = cv.threshold(coins, 160, 255, cv.THRESH_BINARY_INV) # Make it change into binary image
kernel = cv.getStructuringElement(cv.MORPH_ELLIPSE, (5, 5))# Erode
coins_threshold_eroded = cv.morphologyEx(coins_threshold, cv.MORPH_ERODE, kernel, iterations=14, borderType=cv.BORDER_CONSTANT, borderValue=(0))  # Erode the binary image then after several dilations, the contour can be detected
cv.imshow("coins_threshold_eroded", coins_threshold_eroded)# Dilate
T = np.zeros_like(coins_threshold)
while cv.countNonZero(coins_threshold_eroded) < coins_threshold_eroded.size:dilated = cv.dilate(coins_threshold_eroded, kernel, borderType=cv.BORDER_CONSTANT, borderValue=(0))closed = cv.morphologyEx(dilated, cv.MORPH_CLOSE, kernel, borderType=cv.BORDER_CONSTANT, borderValue=(0))split = cv.subtract(closed, dilated)T = cv.bitwise_or(split, T)coins_threshold_eroded = dilated# Border close
kernel = cv.getStructuringElement(cv.MORPH_ELLIPSE, (3, 3))
T = cv.morphologyEx(T, cv.MORPH_CLOSE, kernel, iterations=14, borderType=cv.BORDER_CONSTANT, borderValue=(255))
T_eroded = cv.morphologyEx(~T, cv.MORPH_ERODE, kernel, iterations=1)
T_contour = cv.subtract(~T, T_eroded)
cv.imshow("T", T)# Remove border
coins_threshold = cv.bitwise_and(~T, coins_threshold)
coins_threshold[T_contour > 0] = 255
result = cv.bitwise_and(coins_threshold, coins)cv.imshow("result", result)

Comments\mathbb{Comments}Comments

First, we should convert the original image into gray scale, and then change it into binary value image via implementing threshold filter.

Then we should remove some small noise on the image, so that these small noises won’t cause bad effect in the coming contour detection.

After that, we can use several steps of dilation, so that we can find the contours between coins.

Then, we can add contour onto the original gray coins images. So that, we implement the separating objects.

Watershedsegmentation\mathbb{Watershed\space segmentation}Watershed segmentation

Originalimage\mathbb{Original\space image}Original image

Resultimage\mathbb{Result\space image}Result image

Code\mathbb{Code}Code

coins_gray = cv.cvtColor(coins_color, cv.COLOR_BGR2GRAY)
ret, thresh = cv.threshold(coins_gray, 0, 255, cv.THRESH_BINARY_INV + cv.THRESH_OTSU)# noise removal
kernel = np.ones((9, 9), np.uint8)
opening = cv.morphologyEx(thresh, cv.MORPH_OPEN, kernel, iterations=2)# sure background area
sure_bg = cv.dilate(opening, kernel, iterations=3)# Finding sure foreground area
dist_transform = cv.distanceTransform(opening, cv.DIST_L2, 5)
cv.imshow("distance", dist_transform)
ret, sure_fg = cv.threshold(dist_transform, 0.7 * dist_transform.max(), 255, 0)# Finding unknown region
sure_fg = np.uint8(sure_fg)
unknown = cv.subtract(sure_bg, sure_fg)# Marker labelling
ret, markers = cv.connectedComponents(sure_fg)# Add one to all labels so that sure background is not 0, but 1
markers = markers + 1# Now, mark the region of unknown with zero
markers[unknown == 255] = 0markers = cv.watershed(coins_color, markers)
coins_color[markers == -1] = [255, 0, 0]cv.imshow("Result", coins_color)

Comments\mathbb{Comments}Comments

The basic algorithm about watershed has been already told in theory part.

But when implementing it, we should also remove small noises, just as part 2 of work.

Conclusion\mathbb{Conclusion}Conclusion

When we work with digital images morphological operations, we are actually working with erosion, dilation and their various combinations.

Answers\mathbb{Answers}Answers

1. Does the opening result include the closing result?
   The calculation of open operation is (A⊖B)⊕B(A\ominus B)\oplus B(A⊖B)⊕B, and the calcution of close operation is (A⊕B)⊖B(A\oplus B)\ominus B(A⊕B)⊖B. There is no connection between these two operations.

2. What morphological filter should be applied to remove ledges from an object?
   Open.

3. How can you find the object edges using morphological operations?
   Use formula: A′=A−(A⊖B)A' = A - (A\ominus B)A′=A−(A⊖B).

4. What is morphology?
   Morphology is one brunch of image processing, where the color and brightness are not important factors.

   We only take care of the shape and position of objects.

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