Dr. D. J. Jackson Lecture 5-1Electrical & Computer EngineeringComputer Vision &Digital Image ProcessingIntensity Transformations and Spatial FilteringDr. D. J. Jackson Lecture 5-2Electrical & Computer EngineeringIntensity Transformations and Spatial Filtering Basics• Operations take place in the spatial domain– Operate directly on pixel values– Often more computationally efficient and requires less resources• General form for operations is:• Where f(x,y) is the input image, g(x,y) is an output image, T is an operator on f defined over a neighborhood of point (x,y))],([),( yxfTyxg=Dr. D. J. Jackson Lecture 5-3Electrical & Computer EngineeringIntensity Transformations and Spatial Filtering Basics (continued)• The operator can apply to a single image or to a set of images• The point (x,y) shown is an arbitrary point in the image• The region containing the point is a neighborhood of (x,y)• Typically the neighborhood is rectangular, centered on (x,y) and is much smaller than the imageDr. D. J. Jackson Lecture 5-4Electrical & Computer EngineeringIntensity Transformations and Spatial Filtering Basics (continued)• Spatial filtering– Generally involves operations over the entire image– Operations take place involving pixels within a neighborhood of a point of interest (x,y)– Also involves a predefined operation called a spatial filter– The spatial filter is also commonly referred to as:• Spatial mask• Kernel• Template• WindowDr. D. J. Jackson Lecture 5-5Electrical & Computer EngineeringPoint Processing• The smallest neighborhood of a pixel is 1×1 in size• Here, g depends only on the value of f at (x,y)• T becomes an intensity transformation function of the form• where s and r represent the intensity of g and f at any point (x,y)• Also called a gray-level or mapping function)(rTs=Dr. D. J. Jackson Lecture 5-6Electrical & Computer EngineeringIntensity Transformation ExampleDr. D. J. Jackson Lecture 5-7Electrical & Computer EngineeringSome Basic Intensity Transformation Functions• Here, T is a transformation that maps a pixel value rinto a pixel value s• Since we are concerned with digital data, the transformation can generally be implemented with a simple lookup table• Three basic types of transformations– Linear (negative and identity transformations)– Logarithmic (log and inverse-log transformations)– Power-law (nthpower and nthroot transformations)Dr. D. J. Jackson Lecture 5-8Electrical & Computer EngineeringGeneral Form for Basic Intensity TransformationsDr. D. J. Jackson Lecture 5-9Electrical & Computer EngineeringImage Negatives• The negative of an image with intensity levels in the range [0,L-1] can be described by:rLs−−=1Dr. D. J. Jackson Lecture 5-10Electrical & Computer EngineeringLog Transformations• General form:• c is a constant and r≥0• Maps a narrow range of low intensity values in input to a wider output range• The opposite is true for high intensity input values• Compresses the dynamic range of images with large variations in pixel values)1log( rcs+=Dr. D. J. Jackson Lecture 5-11Electrical & Computer EngineeringLog Transformation Example• A plot (image) of the Fourier Spectrum is enhanced usually has a fairly large dynamic range• The image can be enhanced by applying the log transformationDr. D. J. Jackson Lecture 5-12Electrical & Computer EngineeringPower-Law (Gamma) Transformations• Basic form• Where c and γ are positive constants• Power-law curves with fractional values of γ map a narrow range of dark input values to a wider range of output values• The opposite is true for higher values of input levels• There exists a family of possible transformation curves by varying γγcrs =Dr. D. J. Jackson Lecture 5-13Electrical & Computer EngineeringPower-Law Transformation CurvesDr. D. J. Jackson Lecture 5-14Electrical & Computer EngineeringGamma Correction• Many devices used for image capture, display and printing respond according to a power law• The exponent in the power-law equation is referred to as gamma• The process of correcting for the power-law response is referred to as gamma correction• Example:– CRT devices have an intensity-to-voltage response that is a power function (exponents typically range from 1.8-2.5)– Gamma correction in this case could be achieved by applying the transformation s=r1/2.5=r0.4Dr. D. J. Jackson Lecture 5-15Electrical & Computer EngineeringGamma Correction ExampleDr. D. J. Jackson Lecture 5-16Electrical & Computer EngineeringGamma Correction (MRI Example)Dr. D. J. Jackson Lecture 5-17Electrical & Computer EngineeringGamma Correction (Aerial Example)Dr. D. J. Jackson Lecture 5-18Electrical & Computer EngineeringPiecewise-Linear Transformations• Piecewise functions can be arbitrarily complex• A disadvantage is that their specification requires significant user input• Example functions– Contrast stretching– Intensity-level slicing– Bit-plane slicingDr. D. J. Jackson Lecture 5-19Electrical & Computer EngineeringContrast Stretching• Contrast stretchingexpands the range of intensity levels in an image so it spans a given (full) intensity range• Control points (r1,s1) and (r2,s2) control the shape of the transform T(r)• r1=r2, s1=0 and s2=L-1 yields a thresholdingfunctionDr. D. J. Jackson Lecture 5-20Electrical & Computer EngineeringIntensity-level Slicing• Used to highlight a specific range of intensities in an image that might be of interest• Two common approaches– Set all pixel values within a range of interest to one value (white) and all others to another value (black)• Produces a binary image– Brighten (or darken) pixel values in a range of interest and leave all others unchangedDr. D. J. Jackson Lecture 5-21Electrical & Computer EngineeringIntensity-level Slicing (Angiogram Example)Dr. D. J. Jackson Lecture 5-22Electrical & Computer EngineeringBit-plane Slicing• Pixels are digital values composed of bits• For example, a pixel in a 256-level gray-scale image is comprised of 8 bits• We can highlight the contribution made to total image appearance by specific bits• For example, we can display an image that only shows the contribution of a specific bit planeDr. D. J. Jackson Lecture 5-23Electrical & Computer EngineeringBit-plane Slicing (Example)Dr. D. J. Jackson Lecture 5-24Electrical & Computer EngineeringBit-plane Slicing (continued)• Bit-plane slicing is useful in– Determining