Detecting image intensity changes

Detecting intensity changes Smooth the image intensities reduces effect of noise sets resolution or scale of analysis Differentiate the smoothed intensities transforms image into a representation that facilitates detection of intensity changes Detect and describe features in the transformed image (e.g. peaks or zero-crossings)

Smoothing a 2D image G(x,y) * I(x,y) To smooth a 2D image I(x,y), we convolve with a 2D Gaussian: result of convolution G(x,y) * I(x,y) image

Differentiation in 2D To differentiate the smoothed image, we will use the Laplacian operator: We can again combine the smoothing and derivative operations: (displayed with sign reversed)

Analyzing a 2D image image after smoothing and second derivative image black = negative white = positive zero-crossings

Convolution in two dimensions 1 8 1 3 8 1 3 8 * convolution result 2D convolution operator 24 = image

Image Convolution operator Laplacian Convolution result

Detecting intensity changes at multiple scales small σ large σ zero-crossings of convolutions of image with 2G operators

Computing the contrast of intensity changes L

Stereo viewing geometry LEFT + - RIGHT positive disparity  in front of fixation point negative disparity  behind fixation point LEFT RIGHT 1-10

Steps of the stereo process left right extract features from the left and right images, whose stereo disparity will be measured match the left and right image features and measure their disparity in position “stereo correspondence problem” use stereo disparity to compute depth 1-11 1-11

Constraints on stereo correspondence Uniqueness each feature in the left image matches with only one feature in the right (and vice versa…) Similarity matching features appear “similar” in the two images Continuity nearby image features have similar disparities Epipolar constraint simple version: matching features have similar vertical positions, but… 1-12

Solving the stereo correspondence problem 1-13