Morphology – Chapter 10

Binary image processing Often it is advantageous to reduce an image from gray level (multiple bits/pixel) to binary (1 bit/pixel) –Threshold the gray level image to isolate objects –Edge detect and threshold the edge magnitude map –Special lighting (assembly line manufacturing applications) The goal is to separate the image into foreground and background components

Binarization

But, the process is not always perfect (is rarely perfect?) –Foreground objects have holes (background shows through)

Binarization But, the process is not always perfect (is rarely perfect?) –Contours get broken

Morphology Morphology is a set of processes that allow us to alter the structure of the binary image Foundations in set theory –The image forms one set – the set of pixels that make up the foreground –The structuring element forms the other set – much like a convolution kernel

Structuring element Looks like a convolution kernel –Contains only 0 and 1 –Has a designated hot spot (origin) –The hot spot is placed over the “current pixel” (like the center of the convolution kernel) –The hot spot need not be in the center –The hot spot can be either 0 or 1

The operations All are based on set theory –Definitions are based on intersections and unions of the image and the structuring element (logical AND/OR operations) The two fundamental operations are –Dilation – growing the foreground of the image –Erosion – shrinking the foreground of the image

Dilation No need to show the set theory definition – better to just see the words Place the hot spot on top of an image pixel that is in the set (a foreground pixel) Copy the 1’s of the structuring element into the image set Note that this must be done using double buffering (don’t overwrite the original image)

Dilation

Erosion No need to show the set theory definition – better to just see the words Place the hot spot on top of an image pixel that is in the set (a foreground pixel) Place a 1 in the image only if all of the 1’s of the structuring element align with 1’s in the image Note that this must be done using double buffering (don’t overwrite the original image)

Erosion

Dilation/Erosion usage Among other things… –Dilation is good for filling small holes –Erosion is good for removing small tails Dilation of the foreground can be achieved by erosion of the background –See next slide for explanation

Dilation/Erosion Dilation operation Erosion operation Reflection of the structuring element (change coordinates from – to +, + to -) Reflect All this really means is that implementation is easy

Typical… The shape of the structuring element is often a circular disk (approximate) –This results in a symmetrical dilation or erosion (which is often desired) There is no easy (i.e. efficient) way to do this stuff –Lots of nested loops is all you can do

Composite operations Opening –Erosion followed by dilation (same structuring element) Erosion removes small elements (like noise) Dilation puts the remaining stuff [almost] back to how it was Closing –Dilation followed by erosion (same structuring element) Dilation removes small holes and notches Erosion puts the remaining stuff [almost] back to how it was

Composite operations Opening the foreground is equivalent to closing the background –Again, this just means implementation is easy –To do opening, invert the image (swap foreground and background) and perform a closing operation

Grayscale morphology Instead of checking for values equal to 1 or 0 (and copying into the result image, etc.) you check for minimum and maximum values From my experience this isn’t done very much –The book doesn’t go into details –ImageJ doesn’t implement –So I’m going to just move on