Edges and Contours Chapter 7 Visual perception We

Edges and Contours– Chapter 7

Visual perception • We don’t need to see all the color detail to recognize the scene content of an image • That is, some data provides critical information for recognition, other data provides information that just makes things look “good”

Visual perception • Sometimes we see things that are not really there!!! Kanizsa Triangle (and variants)

Edges • Edges (single points) and contours (chains of edges) play a dominant role in (various) biological vision systems – Edges are spatial positions in the image where the intensity changes along some orientation (direction) – The larger the change in intensity, the stronger the edge – Basis of edge detection is the first derivative of the image intensity “function”

First derivative – continuous f(x) • Slope of the line at a point tangent to the function

First derivative – discrete f(u) • Slope of the line joining two adjacent (to the selected point) point u-1 u u+1

Discrete edge detection • Formulated as two partial derivatives – Horizontal gradients yield vertical edges – Vertical gradients yield horizontal edges – Upon detection we can learn the magnitude (strength) and orientation of the edge • More in a minute…

NOTE • In the following images, only the positive magnitude edges are shown • This is an artifact of Image. J Process->Filters->Convolve… command • Implemented as an edge operator, the code would have to compensate for this

Detecting edges – sharp image Image Vertical Edges Horizontal Edges

Detecting edges – blurry image Image Vertical Edges Horizontal Edges

The problem… • Localized (small neighborhood) detectors are susceptible to noise

The solution • Extend the neighborhood covered by the filter – Make the filter 2 dimensional • Perform a smoothing step prior to the derivative – Since the operators are linear filters, we can combine the smoothing and derivative operations into a single convolution

Edge operator • The following edge operators produce two results – A “magnitude” edge map (image) – An “orientation” edge map (image)

Prewitt operator • 3 x 3 neighborhood • Equivalent to averaging followed by derivative – Note that these are convolutions, not matrix multiplications

Prewitt – sharp image

Prewitt – blurry image

Prewitt – noisy image • Clearly this is not a good solution…what went wrong? – The smoothing just smeared out the noise • How could you fix it? – Perform non-linear noise removal first

Prewitt magnitude and direction

Prewitt magnitude and direction

Sobel operator • 3 x 3 neighborhood • Equivalent to averaging followed by derivative – Note that these are convolutions, not matrix multiplications – Same as Prewitt but the center row/column is weighted heavier

Sobel – sharp image

Sobel – blurry image

Sobel – noisy image • Clearly this is not a good solution…what went wrong? – The smoothing just smeared out the noise • How could you fix it? – Perform non-linear noise removal first

Sobel magnitude and direction

Sobel magnitude and direction

Sobel magnitude and direction • Still not good…how could we fix this now? • Using the information of the direction (lots of randomly oriented, non-homogeneous directions) can help to eliminate edged due to noise – This is a “higher level” (intelligent) function

Roberts operator • Looks for diagonal gradients rather than horizontal/vertical • Everything else is similar to Prewitt and Sobel operators

Roberts magnitude and direction

Roberts magnitude and direction

Roberts magnitude and direction

Compass operators • An alternative to computing edge orientation as an estimate derived from two oriented filters (horizontal and vertical) • Compass operators employ multiple oriented filters • To most famous are – Kirsch – Nevatia-Babu

Kirsch Filter • Eight 3 x 3 kernel – Theoretically must perform eight convolutions – Realistically, only compute four convolutions, the other four are merely sign changes • The kernel that produces the maximum response is deemed the winner – Choose its magnitude – Choose its direction

Kirsch filter kernels Vertical edges L-R diagonal edges Horizontal edges R-L diagonal edges

Kirsch filter

Nevatia-Babu Filter • Twelve 5 x 5 kernel – Theoretically must perform twelve convolutions – Increments of approximately 30° – Realistically, only compute six convolutions, the other six are merely sign changes • The kernel that produces the maximum response is deemed the winner – Choose its magnitude – Choose its direction

Nevatia-Babu filter