Using and Processing Binary Images

Question 1

What are connected components?

Answer 1

Pixels which are connected i.e. neighbours to at least one other connected pixel.
Connected can mean either 4 or 8 neighbours

Question 2

What are the problems with calculating connected components?

Answer 2

They are slow, and often a bottleneck in image processing

Question 3

How can you find connected components?

Answer 3

Using a sequential algorithm (example uses 4 neighbours) - keeps a separate output array for labels, with two passes over the image

Question 4

What does the first pass entail with connected components?

Answer 4

Scan image top left to bottom right (like reading a book)
Look at top and left neighbours (already given labels)
If the current pixel is foreground, then you use one of the three cases:
left = top = background - assign current pixel a new label
One of left and top is background, the other foreground - assign current pixel the foreground pixel’s label
Left = top = foreground - assign current pixel one of their labels and note that their labels are equal in an equivalence table
Step 3 detects mergers between two previously separate components

Question 5

What does the 2nd pass entail within connected components?

Answer 5

Consider each equivalent pair of labels. Set all instances of the higher label to the lower.
i.e. if you are using 4 neighbour solution, then anything that is connected in a + shape around the pixel will now become part of that connected component (the biggest component overrides). If using 8, then anything nearby the pixel will now become part of that connected component.

Question 6

What can you do with connected components?

Answer 6

Can compute features of and apply tests to components to process the underlying image e.g. apply a size threshold T to the number of pixels in the component
Shape is captured by measures like area/boundary length

Question 7

What is mathematical morphology, and where is it used?

Answer 7

A branch of image processing which treats images as sets of pixels, and uses set theoretic operations to process them.
They were developed for binary images, and were extended to be used on grey level images.
Elements of sets are (x,y) coordinates of either black or white pixels.
You perform operations by combining two sets:
A patch of the binary image to be processed, and a structuring element

Question 8

What are structuring elements?

Answer 8

Binary masks which identify rather than weigh pixels

Question 9

What are the different types of morphological operations?

Answer 9

Dilation expands a foreground (or background) object A using structuring element B
Erosion shrinks a foreground (or background) object A using structural element B

Question 10

What happens when using either dilation or erosion? (general effects)

Answer 10

The boundaries between foreground and background are often smoothed in the process.
The amount and the way objects grow or shrink depend upon the choice of the structuring element.

Question 11

What is dilation, and how does it work?

Answer 11

Takes two inputs - binary image to dilate, and a set of points to be considered (a structuring element), of which the origin is the central element.
The algorithm superimposes the structuring element on each of the background pixels such that the origin of the structuring element coincides with the input pixel position.
If any of the ‘1’ pixels in the structuring element overlap with the foreground, then the background pixel is also set to foreground.

Question 12

What are the effects of dilating an image?

Answer 12

Gradually enlarges the boundaries of regions of foreground pixels i.e. white pixels typically.
Areas of foreground pixels grow in size while holes within those regions become smaller

Question 13

How do you perform edge detection with dilation?

Answer 13

Dilate the input image (note, that does cause the corners to become round, rather than straight edges)
Subtract from the original
Edges remain (pixels on the outside of the boundary)

Question 14

What is erosion, and how does it work?

Answer 14

Two inputs:
binary image to erode, and a set of points to be considered - a structuring element, where the origin is the central element
The algorithm erodes the foreground by superimposing the structural element on each of the foreground pixels such that the original of the structuring element coincides with the input pixel position
If any of the ‘1’ pixels in the structuring element overlap with the background, then the foreground pixel is also set to background.

Question 15

How can erosion be used in a different way?

Answer 15

It can be used to separate joint together objects, for clearer edge detection

Question 16

What is opening, and what is the result of applying it?

Answer 16

To perform opening, first erode the image A with structuring element B
Then, after that, immediately dilate A with B
This smoothes contours, and eliminates protrusions

Question 17

What is closing, and what is the result of applying it?

Answer 17

First, dilate image A with structuring element B.
Afterwards, immediately erode A with B
Smoothes sections of contours, fuses narrow breaks and long thin gulfs, eliminates small holes and fills gaps in contours

Question 18

What happens if you apply either opening or closing multiple times?

Answer 18

Trick question - nothing happens. The effect only happens the first time around, and nothing more.

Question 19

What is an ROI?

Answer 19

A Region of Interest
This is a portion of an image that you want to filter or operate on in some way. In Matlab, you can represent ROI as a binary mask image. In the mask, pixels that belong to the ROI are set to 1, whereas anything else is set to 0.