240-373 Image Processing, Lecture #8 Edge detection Templates such as -1 -1 and -1 1 1 1 -1 1 A B highlight edges in an image. A identifies the horizontal edge and B identifies the vertical edge. Combining both results gives both horizontal and vertical edges. Example: Image After A After B A + B 02/01/62 240-373 Image Processing, Lecture #8

Storing the convolution results Convolution results normally need examination and transformation before storage. In most applications, images are held as one array of bytes (or three arrays of bytes for color images). Each byte hold 0-255 unsigned integer. The results of an operation must be transformed to within the range. Scaling can be done to adjust the result range. Other method is to use a floating point variable to hold each pixel value. This needs more memory, scaling and rounding. 02/01/62 240-373 Image Processing, Lecture #8

Other window operations Technique 4: Median filtering USE: Noise removal while preserving edges in an image. OPERATION: Median filter is a low-pass filter that attempts to remove noisy pixels while keeping the edges intact. The value of the pixels in the window are sorted and the median--the middle value in the sorted list--is chosen. Example: Noise removal with a 3x3 median filter Image Output 02/01/62 240-373 Image Processing, Lecture #8

Median Filtering Example Modal filter: similar to median filter except that the most popular value from the set of nine is chosen. 02/01/62 240-373 Image Processing, Lecture #8

240-373 Image Processing, Lecture #8 Technique 5: k-closest averaging USE: To preserve the actual values of the pixels without letting the noise get through to the final image OPERATION: All pixels in the window are sorted k pixels values closest to the target pixel (center pixel in the window) are averaged. If the target pixel is included, the effect is similar to a low-pass filter k is constant that is smaller than the area of the window To avoid pairs or triples of noisy pixels, an extension of this technique can be as follow: k values nearest to the target, but not including q values closest to and including the target. 02/01/62 240-373 Image Processing, Lecture #8

240-373 Image Processing, Lecture #8 Interest Points Interest points are identified by algorithms that can be applied first to images containing a known object, and then to images where recognition of the object is required Technique 6: Moravec operator USE: To identify a set of points on an image by which the image may be classified or compared OPERATION: Computing variance where Passing a 3x3 window and saving minimum Passing a 3x3 window and setting to zero the center pixel when its value is not maximum in the window Simplified formula 02/01/62 240-373 Image Processing, Lecture #8

240-373 Image Processing, Lecture #8 Example Image Variances After step 1 After step 2 02/01/62 240-373 Image Processing, Lecture #8

240-373 Image Processing, Lecture #8 Correlation Technique 7: Correlation USE: To find where a template matches a window in an image, To determine the existence of a known shape in an image. THEORY: If N x M image is addressed by I(X,Y) and n x m template is addressed by t(i,j) then 1 2 3 1: is constant across the image, so can be ignored 2: is t convolved with I 3: is constant only if average light from image is constant across image (often approximately true) 02/01/62 240-373 Image Processing, Lecture #8

Some comments on correlation technique If overall light intensity across the whole image is fairly constant, it is safe to use convolution instead of correlation. The object may have any orientation. The object may have any size. 02/01/62 240-373 Image Processing, Lecture #8

Two-Dimensional Geometric Transformations Scaling by sx in the x direction and by sy in the y direction (zooming in/zooming out) Translating by tx in the x direction and by ty in the y direction Rotating by a radian clockwise 02/01/62 240-373 Image Processing, Lecture #8

Inverse transformations Scaling by sx in the x direction and by sy in the y direction (zooming in/zooming out) Translating by tx in the x direction and by ty in the y direction Rotating by a radian clockwise 02/01/62 240-373 Image Processing, Lecture #8

Combination of transformations The three transformations can be combined by multiplying all transformation matrices. For example, if an image is to be zoomed-in (2x), rotated clockwise for 45 degree about it origin and then shifted 20 old pixels to the right, evaluate the following expression: giving For new pixel position (8,10) new pixel will be at (26,1) 02/01/62 240-373 Image Processing, Lecture #8

240-373 Image Processing, Lecture #8 Technique 8: Two-dimensional geometric transformations USE: To turn an image around, zoom in or pan across it OPERATION: Determine the matrix which maps every new pixel onto either an old pixel (if in range) or zero otherwise. That is: Starting a pixel (0,0), plotting left to right, calculate atx = cx; aty = cy and make Increment x and atx = atx + ax; aty = aty + ay and repeat Inew allocation. Repeat for each x in the row. For the next row, set starting values to atx = bx*y + cx; aty = by*y + cy 02/01/62 240-373 Image Processing, Lecture #8