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Edge detection

Origin of edges, characterizing edges, image gradient, finite difference filters, effects of noise,. As the main contents of the lecture "Edge detection". Each of your content and references for additional lectures will serve the needs of learning and research. | Edge detection Goal: Identify sudden changes (discontinuities) in an image Intuitively, most semantic and shape information from the image can be encoded in the edges More compact than pixels Ideal: artist’s line drawing (but artist is also using object-level knowledge) Source: D. Lowe Origin of edges Edges are caused by a variety of factors: depth discontinuity surface color discontinuity illumination discontinuity surface normal discontinuity Source: Steve Seitz Characterizing edges An edge is a place of rapid change in the image intensity function image intensity function (along horizontal scanline) first derivative edges correspond to extrema of derivative The gradient points in the direction of most rapid increase in intensity Image gradient The gradient of an image: The gradient direction is given by Source: Steve Seitz The edge strength is given by the gradient magnitude How does this direction relate to the direction of the edge? give definition of partial derivative: lim h->0 [f(x+h,y) – f(x,y)]/h Differentiation and convolution Recall, for 2D function, f(x,y): This is linear and shift invariant, so must be the result of a convolution. We could approximate this as (which is obviously a convolution) -1 1 Source: D. Forsyth, D. Lowe Finite difference filters Other approximations of derivative filters exist: Source: K. Grauman Finite differences: example Which one is the gradient in the x-direction (resp. y-direction)? Effects of noise Consider a single row or column of the image Plotting intensity as a function of position gives a signal Where is the edge? Source: S. Seitz How to fix? Effects of noise Finite difference filters respond strongly to noise Image noise results in pixels that look very different from their neighbors Generally, the larger the noise the stronger the response What is to be done? Smoothing the image should help, by forcing pixels different from their neighbors (=noise pixels?) to look more like . | Edge detection Goal: Identify sudden changes (discontinuities) in an image Intuitively, most semantic and shape information from the image can be encoded in the edges More compact than pixels Ideal: artist’s line drawing (but artist is also using object-level knowledge) Source: D. Lowe Origin of edges Edges are caused by a variety of factors: depth discontinuity surface color discontinuity illumination discontinuity surface normal discontinuity Source: Steve Seitz Characterizing edges An edge is a place of rapid change in the image intensity function image intensity function (along horizontal scanline) first derivative edges correspond to extrema of derivative The gradient points in the direction of most rapid increase in intensity Image gradient The gradient of an image: The gradient direction is given by Source: Steve Seitz The edge strength is given by the gradient magnitude How does this direction relate to the direction of the edge? give definition of partial