Digital Image Processing: Image Enhancement Spatial Filtering - Duong Anh Duc

Digital Image Processing: Image Enhancement Spatial Filtering - Duong Anh Duc includes Image Enhancement - Spatial Filtering; How to specify T; Smoothing Filters; Image smoothing by averaging (lowpass spatial filtering); Image Sharpening; High-boost filtering; Prewitt operators.

Digital Image Processing Image Enhancement Spatial Filtering 21/11/15 Duong Anh Duc - Digital Image Processing Image Enhancement: Spatial Filtering  Image enhancement in the spatial domain can be represented as: Transformation Enhanced Image g(m,n) = T(f)(m,n) Given Image  The transformation T maybe linear or nonlinear We will mainly study linear operators T but will see one important nonlinear operation 21/11/15 Duong Anh Duc - Digital Image Processing How to specify T  If the operator T is linear and shift invariant (LSI), characterized by the pointspread sequence (PSS) h(m,n) , then (recall convolution) 21/11/15 Duong Anh Duc - Digital Image Processing How to specify T  In practice, to reduce computations, h(m,n) is of “finite extent: h(k,l) = for (k,l) where is a small set (called neighborhood) is also called as the support of h  In the frequency domain, this can be represented as: G(u,v) = He(u,v) Fe(u,v)  where He(u,v) and Fe(u,v) are obtained after appropriate zeropadding 21/11/15 Duong Anh Duc - Digital Image Processing How to specify T  Many LSI operations can be interpreted in the frequency domain as a “filtering operation.” It has the effect of filtering frequency components (passing certain frequency components and stopping others)  The term filtering is generally associated with such operations 21/11/15 Duong Anh Duc - Digital Image Processing How to specify T  Examples of some common filters (1-D case): Lowpass filter 21/11/15 Highpass filter Duong Anh Duc - Digital Image Processing  If h(m, n) is a by mask given by w1 w2 w3 h= w4 w5 w6 w7 w8 w9 then 21/11/15 Duong Anh Duc - Digital Image Processing  The output g(m, n) is computed by sliding the mask over each pixel of the image f(m, n) This filtering procedure is sometimes referred to as moving average filter  Special care is required for the pixels at the border of image f(m, n) This depends on the so-called boundary condition Common choices are:    21/11/15 The mask is truncated at the border (free boundary) The image is extended by appending extra rows/columns at the boundaries The extension is done by repeating the first/last row/column or by setting them to some constant (fixed boundary) The boundaries “wrap around” (periodic boundary) Duong Anh Duc - Digital Image Processing  In any case, the final output g(m, n) is restricted to the support of the original image f(m, n)  The mask operation can be implemented in MATLAB using the filter2 command, which is based on the conv2 command 21/11/15 Duong Anh Duc - Digital Image Processing Smoothing Filters  Image smoothing refers to any image-to-image transformation designed to “smooth” or flatten the image by reducing the rapid pixel-to-pixel variation in grayvalues  Smoothing filters are used for: Blurring: This is usually a preprocessing step for removing small (unwanted) details before extracting the relevant (large) object, bridging gaps in lines/curves,  Noise reduction: Mitigate the effect of noise by linear or nonlinear operations  21/11/15 Duong Anh Duc - Digital Image Processing 10 Example Original Image 21/11/15 Highpass filtering Duong Anh Duc - Digital Image Processing 26 High-boost filtering  This is a filter whose output g is produced by subtracting a lowpass (blurred) version of f from an amplified version of f g(m,n) = Af(m,n) – lowpass(f(m,n)) This is also referred to as unsharp masking 21/11/15 Duong Anh Duc - Digital Image Processing 27 High-boost filtering  Observe that g(m,n) = Af(m,n) – lowpass(f(m,n)) = (A-1)f(m,n) + f(m,n) – lowpass(f(m,n)) = (A-1)f(m,n) + hipass(f(m,n))  For > A , part of the original image is added back to the highpass filtered version of f  The result is the original image with the edges enhanced relative to the original image 21/11/15 Duong Anh Duc - Digital Image Processing 28 Example Original Image 21/11/15 Highpass filtering Duong Anh Duc - Digital Image Processing High-boost filtering 29 Derivative filter  Averaging tends to blur details in an image Averaging involves summation or integration  Naturally, differentiation or “differencing” would tend to enhance abrupt changes, i.e., sharpen edges  Most common differentiation operator is the gradient: 21/11/15 Duong Anh Duc - Digital Image Processing 30 Derivative filter  The magnitude of the gradient is:  Discrete approximations to the magnitude of the gradient is normally used 21/11/15 Duong Anh Duc - Digital Image Processing 31 Derivative filter  Consider the following image region: z1 z2 z3 z4 z5 z6 z7 z8 z9  We may use the approximation: 21/11/15 Duong Anh Duc - Digital Image Processing 32 Derivative filter  This can implemented using the masks:  As follows: 21/11/15 Duong Anh Duc - Digital Image Processing 33 Derivative filter  Alternatively, we may use the approximation:  This can implemented using the masks:  As follows: 21/11/15 Duong Anh Duc - Digital Image Processing 34 Derivative filter  The resulting maks are called Roberts cross-gradient operators  The Roberts operators and the Prewitt/Sobel operators (described later) are used for edge detection and are sometimes called edge detectors 21/11/15 Duong Anh Duc - Digital Image Processing 35 Example: Roberts cross-gradient operator 21/11/15 Duong Anh Duc - Digital Image Processing 36 Example: Roberts cross-gradient operator 21/11/15 Duong Anh Duc - Digital Image Processing 37 Prewitt operators  Better approximations to the gradient can be obtained by:  This can be implemented using the masks: as follows: 21/11/15 Duong Anh Duc - Digital Image Processing 38 Sobel operators  Another approximation is given by the masks:  The resulting masks are called Sobel operators 21/11/15 Duong Anh Duc - Digital Image Processing 39 Example Prewitt 21/11/15 Sobel Duong Anh Duc - Digital Image Processing 40 ... Duong Anh Duc - Digital Image Processing 13 Example of Image Blurring N = 11 21/11/15 N = 21 Duong Anh Duc - Digital Image Processing 14 Example of noise reduction Noise-free Image 21/11/15 Duong. .. lowpass filtering 21/11/15 Duong Anh Duc - Digital Image Processing 11 Example of Image Blurring Original Image 21/11/15 Duong Anh Duc - Digital Image Processing Avg Mask 12 Example of Image Blurring... lowpass(f(m,n)) 21/11/15 Duong Anh Duc - Digital Image Processing 25 Example Original Image 21/11/15 Highpass filtering Duong Anh Duc - Digital Image Processing 26 High-boost filtering  This is a