3-D Computater Vision CSc 83020. Revisit filtering (Gaussian and Median) Introduction to edge detection. Linear Filters. Given an image In ( x , y ) generate a new image Out ( x , y ): - PowerPoint PPT Presentation
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3-D Computer Vision CSc83020 / Ioannis Stamos3-D Computer Vision CSc83020 / Ioannis Stamos
Revisit filtering (Gaussian and Median)Revisit filtering (Gaussian and Median) Introduction to edge detectionIntroduction to edge detection
3-D Computer Vision CSc83020 / Ioannis Stamos3-D Computer Vision CSc83020 / Ioannis Stamos
Linear FiltersLinear Filters
Given an image Given an image InIn((xx,,yy) generate a) generate anew image new image OutOut((xx,,yy):): For each pixel (For each pixel (xx,,yy))OutOut((xx,,yy) is a linear combination of pixels) is a linear combination of pixelsin the neighborhood of in the neighborhood of InIn((xx,,yy))
This algorithm isThis algorithm is Linear in input intensityLinear in input intensity Shift invariantShift invariant
3-D Computer Vision CSc83020 / Ioannis Stamos3-D Computer Vision CSc83020 / Ioannis Stamos
Discrete ConvolutionDiscrete Convolution This is the discrete analogue of convolutionThis is the discrete analogue of convolution The pattern of weights is called the “kernel”The pattern of weights is called the “kernel”
of the filterof the filter Will be useful in smoothing, edge detectionWill be useful in smoothing, edge detection
3-D Computer Vision CSc83020 / Ioannis Stamos3-D Computer Vision CSc83020 / Ioannis Stamos
Computing ConvolutionsComputing Convolutions
What happens near edges of image?What happens near edges of image? Ignore (Ignore (OutOut is smaller than is smaller than InIn)) Pad with zeros (edges get dark)Pad with zeros (edges get dark) Replicate edge pixelsReplicate edge pixels Wrap aroundWrap around ReflectReflect Change filterChange filter
i j
jyixInjifyxOut ),(),(),(
3-D Computer Vision CSc83020 / Ioannis Stamos3-D Computer Vision CSc83020 / Ioannis Stamos
3-D Computer Vision CSc83020 / Ioannis Stamos3-D Computer Vision CSc83020 / Ioannis Stamos
Gaussian FiltersGaussian Filters
One-dimensional GaussianOne-dimensional Gaussian
Two-dimensional GaussianTwo-dimensional Gaussian
2
2
21 2
1)(
x
exG
2
22
22 2
1),(
yx
eyxG
3-D Computer Vision CSc83020 / Ioannis Stamos3-D Computer Vision CSc83020 / Ioannis Stamos
Gaussian FiltersGaussian Filters
3-D Computer Vision CSc83020 / Ioannis Stamos3-D Computer Vision CSc83020 / Ioannis Stamos
Gaussian FiltersGaussian Filters
3-D Computer Vision CSc83020 / Ioannis Stamos3-D Computer Vision CSc83020 / Ioannis Stamos
Gaussian FiltersGaussian Filters Gaussians are used because:Gaussians are used because:
SmoothSmooth Decay to zero rapidlyDecay to zero rapidly Simple analytic formulaSimple analytic formula Limit of applying multiple filters is GaussianLimit of applying multiple filters is Gaussian
3-D Computer Vision CSc83020 / Ioannis Stamos3-D Computer Vision CSc83020 / Ioannis Stamos
Size of the maskSize of the mask
3-D Computer Vision CSc83020 / Ioannis Stamos3-D Computer Vision CSc83020 / Ioannis Stamos
Edges & Edge DetectionEdges & Edge Detection
What are Edges?What are Edges? Theory of Edge Detection.Theory of Edge Detection. Edge Operators (Convolution Masks)Edge Operators (Convolution Masks) Edge Detection in the Brain?Edge Detection in the Brain? Edge Detection using Resolution PyramidsEdge Detection using Resolution Pyramids
3-D Computer Vision CSc83020 / Ioannis Stamos3-D Computer Vision CSc83020 / Ioannis Stamos
EdgesEdges
3-D Computer Vision CSc83020 / Ioannis Stamos3-D Computer Vision CSc83020 / Ioannis Stamos
What are Edges?What are Edges?
Rapid Changes of intensity in small region
3-D Computer Vision CSc83020 / Ioannis Stamos3-D Computer Vision CSc83020 / Ioannis Stamos
What are Edges?What are Edges?
Surface-Normal discontinuity
Depth discontinuity
Surface-Reflectance Discontinuity
Illumination Discontinuity
Rapid Changes of intensity in small region
3-D Computer Vision CSc83020 / Ioannis Stamos3-D Computer Vision CSc83020 / Ioannis Stamos
Local Edge DetectionLocal Edge Detection
3-D Computer Vision CSc83020 / Ioannis Stamos3-D Computer Vision CSc83020 / Ioannis Stamos
What is an Edge?What is an Edge?
Edge easy to findEdge easy to find
3-D Computer Vision CSc83020 / Ioannis Stamos3-D Computer Vision CSc83020 / Ioannis Stamos
What is an Edge?What is an Edge?
Where is edge? Single pixel wide or multiple pixels?Where is edge? Single pixel wide or multiple pixels?
3-D Computer Vision CSc83020 / Ioannis Stamos3-D Computer Vision CSc83020 / Ioannis Stamos
What is an Edge?What is an Edge?
Noise: have to distinguish noise from actual edgeNoise: have to distinguish noise from actual edge
3-D Computer Vision CSc83020 / Ioannis Stamos3-D Computer Vision CSc83020 / Ioannis Stamos
What is an Edge?What is an Edge?
Is this one edge or two?Is this one edge or two?
3-D Computer Vision CSc83020 / Ioannis Stamos3-D Computer Vision CSc83020 / Ioannis Stamos
What is an Edge?What is an Edge?
Texture discontinuityTexture discontinuity
3-D Computer Vision CSc83020 / Ioannis Stamos3-D Computer Vision CSc83020 / Ioannis Stamos
Local Edge DetectionLocal Edge Detection
Edge TypesEdge Types
Ideal Step Edges
Ideal Ridge Edges
Ideal Roof Edges
3-D Computer Vision CSc83020 / Ioannis Stamos3-D Computer Vision CSc83020 / Ioannis Stamos
Real EdgesReal EdgesI
x
Problems: Noisy Images Discrete Images
3-D Computer Vision CSc83020 / Ioannis Stamos3-D Computer Vision CSc83020 / Ioannis Stamos
Real EdgesReal EdgesWe want an Edge Operator that produces: