Slide 1Slide 2Slide 3Slide 4Slide 5Slide 6Slide 7Slide 8Slide 9Slide 10Digital Image Processing, 3rd ed.www.ImageProcessingPlace.com© 1992–2008 R. C. Gonzalez & R. E. Woods Gonzalez & WoodsChapter 5Image Restoration and Reconstruction•Elements of Visual Perception•Image Formation in the Eye (and relation to a photographic camera).•Brightness Adaption and Discrimination.•Light and the Electromagnetic Spectrum•Gamma rays, visible spectrum (Violet – Infrared), Radio waves.•Visible spectrum spans the range from ~0.4 µm (violet) to about ~0.7 µm (red). •Light that does not have color is called monochromatic light (i.e. each band of an RGB image).•Attribute of monochromatic light is intensity.Chromatic color spans the range ~0.4 µm through ~0.7 µm.•Image Sensing and Acquisition•Depending on the source, illumination is reflected from, or transmitted through objects.•Principal sensor arrangements used to transform energy into digital images: single sensor, line sensor, array sensor.•Image acquisition using array sensors.•A simple image formation model: . The reflectance value is bounded by 0 (total absorption) and1 (total reflectance). Review for Exam I, EE552 2/2009),(),(),( yxryxiyxf=Digital Image Processing, 3rd ed.www.ImageProcessingPlace.com© 1992–2008 R. C. Gonzalez & R. E. Woods Gonzalez & WoodsChapter 5Image Restoration and Reconstruction•Image Sampling and Quantization•To create a digital image we need to convert the continuous sensed data into digital form using two processes: sampling and quantization.•Digitizing the coordinates is sampling, digitizing the amplitude is called quantization.•Representing Digital Images. A real plane spanned by the coordinates of an image is called the spatial domain.•The number of intensity levels in an image is L=2k.•The number of bits required to store a digitized image is b=M×N×k•Image interpolation: nearest neighbors, bilinear ( ), bicubic interpolation ( ).•Basic Relationships Between Pixels•A pixel has 4-neighbors, diagonal neighbors, and 8-neighbors.•Two pixels can be 4-adjacent, 8-adjacent, and m-adjacent.•Distance measures: Euclidean ( ), city-block distance ( ), chessboard distance ( ). Review for Exam I, EE552 2/2009dcxybyaxyxv+++=),(∑ ∑= ==3030),(i jjiijyxayxv2/122])()[(),( tysxqpD−+−=||||),( tysxqpD−+−=|)||max(|),( tysxqpD−+−=Digital Image Processing, 3rd ed.www.ImageProcessingPlace.com© 1992–2008 R. C. Gonzalez & R. E. Woods Gonzalez & WoodsChapter 5Image Restoration and Reconstruction•Mathematical Tools Used in DIP•Array versus matrix operations.•Linear versus nonlinear operations.•Arithmetic operations: summation, subtraction, multiplication, division between corresponding pixels.•Applications of arithmetic operations:Reduction/removal of noise in a corrupted noise (noise uncorrelated and zero mean).Shading correction (multiplication by the inverse of the shading function h(x,y)).Masking, also called region of interest (ROI) operations. Scaling of images (linear).•Basic set and logical operations: A is a subset of B ( ), intersection ( ), union ( ).•Spatial operations: single-pixel operations (transformation functions), neighborhood operations (involves a neighborhood of m×n pixels), geometric spatial transformations (scaling, rotation, translation, shear (vertical) and shear (horizontal)). Review for Exam I, EE552 2/2009BA⊆BA∩BA∪Digital Image Processing, 3rd ed.www.ImageProcessingPlace.com© 1992–2008 R. C. Gonzalez & R. E. Woods Gonzalez & WoodsChapter 5Image Restoration and Reconstruction•Vector and Matrix Operations•Vector and matrix operations are routinely used in multispectral image processing.•Euclidean distance between a pixel vector z and an arbitrary point a in n-dimensional space is • Image transforms. Image processing tasks are best formulated by transforming the input image, carrying a specified task, and then applying the inverse transform.•Forward and inverse transforms can be separable ( ) and symmetric( ). Review for Exam I, EE552 2/20092/1)]()[(),( azazazDT−−=),(2),(1),,,( vyruxrvuyxr=),(1),(1),,,( vyruxrvuyxr=Digital Image Processing, 3rd ed.www.ImageProcessingPlace.com© 1992–2008 R. C. Gonzalez & R. E. Woods Gonzalez & WoodsChapter 5Image Restoration and Reconstruction•Intensity Transformation and Spatial Filtering•Basic spatial domain process is .•Intensity (gray-level or mapping) transformation function .•Image negatives are obtained using the negative transformation . •Log transformations have the form .•Power-Law (Gamma) transformations .•Contrast stretching is used to expand the range of intensity levels in an image.•Intensity-level slicing is used to highlight a specific range of intensities in an image.•Histogram Processing•Transformation (intensity mapping) of the form . •A transformation function of particular importance in DIP is which performs a histogram equalization or histogram linearization transformation.•Histogram matching is used to generate a processed image that has a specified histogram and .•Global histogram processing can be adapted to local enhancement (local histogram processing).•Local mean and variance can be used to change an image based on local characteristics in a neighborhood , i.e. change the intensity of a pixel if the local mean is larger/smaller than global mean. Review for Exam I, EE552 2/2009rLs−−=1yxS,)],([),( yxfTyxg=)1log( rcs+=γcrs=)(rTs=10)(−≤≤=LrrTs∑=−==kjjrkkrpLrTs0)()1()(∑=−==kjjrkkrpLrTs0)()1()()()()1()(10kqqiizkqsGzandzpLszG−==−==∑Digital Image Processing, 3rd ed.www.ImageProcessingPlace.com© 1992–2008 R. C. Gonzalez & R. E. Woods Gonzalez & WoodsChapter 5Image Restoration and Reconstruction•Fundamentals of Spatial Filtering•A spatial filter consists of (1) a neighborhood, and (2) a predefined operation.•Spatial correlation and convolution. Correlation is the process of moving a filter mask over the image and computing the sum of products. Convolution consists in a similar process but the filter is first rotated 180˚.•Vector representation of linear filtering; , where w are the