Spatial Filtering - George Mason University

Spatial Filtering - George Mason University

Spatial Filtering Enhancement 02/22/20 Spatial Filtering 1 References 1. Gonzalez and Woods, Digital Image Processing, 2nd Edition, Prentice Hall, 2002. 2. Jain, Fundamentals of Digital Image Processing, Prentice Hall 1989 02/22/20

Spatial Filtering 2 Filters Powerful Imaging Tool Frequency domain is often used Enhancement by accentuating the features of interest Spatial domain Linear Think of this as weighted average over a mask / filter region Compare to convolution imaging (smoothing) filters are often symmetric

02/22/20 Spatial Filtering 3 Spatial Filtering Computations Result for 3x3 mask g(x,y) = w(-1,-1)f(x-1,y-1) w(-1,0)f(x-1,y) + w(-1,1) f(x-1,y+1) . + w(1,1)f(x+1,y+1) +

Result for mxn mask g(x,y) = a b w(s,t) f(x+s,y+t) s=-a t=-b a = (m-1)/2 b = (n-1)/2 If image size is MxN, then x=0,1,M-1 and y=0,1,..N-1.

From [1] 02/22/20 Spatial Filtering 4 Smoothing Filters Weighted average Low pass filter

Reduce the noise; remove small artifacts Blurring of edges Two masks: Note multiplication is by 2n, divide once at end of process g(x,y) = a b a b w(s,t) f(x+s,y+t) / w(s,t) s= -a t= -b

02/22/20 Spatial Filtering s= -a t= -b 5 Smoothing - Examples Suppressed small objects in the scene 02/22/20 Spatial Filtering

6 Median Filter Example of Order Statistics Filter. Other examples max filter or min filter Effective for impulse noise (salt and pepper noise) Median half the values <= the median value NxN neighborhood, where N is odd Replace center of mask with the median value

Stray values are eliminated; uniform neighborhoods not affected 02/22/20 Spatial Filtering 7 Sharpening Filters Smoothing Blurring Averaging Sharpening is the reverse process Smoothing is the result of integration Sharpening involves differentiation Enhances discontinuities Noise Edges

De-emphasizes uniform parts of the image 02/22/20 Spatial Filtering 8 Differentiation Numeric Techniques Derivatives are defined in terms of differences First order derivative f ' (x) = (f (x) f (x - )) / Second order derivative f '' (x) = (f ' (x+) f ' (x)) / =({f (x + ) f (x)} {f (x) f (x - )}) / 2

=({f (x + ) 2f (x) f (x - )}) / 2 = smallest unit; for images = 1. 02/22/20 Spatial Filtering 9 Example of Derivative Computation Isolated point (noise?) 02/22/20 Spatial Filtering

10 Use Derivatives with care What is the gradient? Slope at a local point, may be quite different than the overall trend Often use a smoothing filter to reduce impact of noise Higher the order of the derivative, higher is the impact of local discontinuities 02/22/20 Spatial Filtering 11

Laplacian for Enhancement Second order derivatives are better at highlighting finer details Imaging requires derivatives in 2D Laplacian 2 f = fxx + fyy , where fxx = f(x+1,y) + f(x-1,y) 2 f(x,y) fyy= f(x,y+1) + f(x, y-1) 2 f(x,y)

02/22/20 Spatial Filtering 12 Composite Laplacian for Enhancement Laplacian highlights discontinuities (b and c) The uniform regions are suppressed To restore the balance, for image enhancement the original image is added to the Laplacian g(x,y)=f(x,y) - 2 f (x,y)

if 2 f (x,y) < 0 g(x,y)=f(x,y) + 2 f (x,y) if 2 f (x,y) >= 0 In difference form g(x,y)=5f(x,y)-{f(x+1,y)+ f(x-1,y)+f(x,y+1)+f(x,y-1)} Leads to new mask Next slide 02/22/20 Spatial Filtering 13 Application of Composite Masks

02/22/20 Spatial Filtering 14 High Boost Filters For image enhancement the augmented original image is added to the Laplacian g(x,y)= Af(x,y) - 2 f (x,y) if 2 f (x,y) < 0 g(x,y)= Af(x,y) + 2 f (x,y) if 2 f (x,y) >= 0 In difference form

g(x,y)=(A+4)f(x,y)-{f(x+1,y)+ f(x-1,y)+f(x,y+1)+f(x,y-1)} 02/22/20 Spatial Filtering 15 High Boost Filter with Different A - values 02/22/20 Spatial Filtering 16

The Gradient 02/22/20 Spatial Filtering 17 Roberts and Sobel Gradient Based Masks 02/22/20 Spatial Filtering 18

Sobel Mask Detects Edges 02/22/20 Spatial Filtering 19 Multiple Step Spatial Enhancement 02/22/20 Spatial Filtering 20

Recently Viewed Presentations

  • Quadratic Sequences

    Quadratic Sequences

    The nth term for the sequence below is 5?25, 20, 45, 80, 125, Find the nth term for the sequence below: *4, 13, 28, 49, 76 But there is a key difference!
  • 슬라이드 1 - Daum

    슬라이드 1 - Daum

    하악골의 측사위촬영법(Lateral oblique projection of mandible) 1) 하악체 촬영법(Mandibular body projection) 2) 하악지 촬영법(Mandibular ramus projection) 두부 방사선사진촬영법(Skull projection) 1) PA skull projection 2) lateral skull projection 3) Waters 촬영법 4) Reverse-Towne 촬영법 5) 이하두정 ...
  • PLANNING AND IMPLEMENTING CENSUS MAPPING PROGRAMME United Nations

    PLANNING AND IMPLEMENTING CENSUS MAPPING PROGRAMME United Nations

    An example of a planning process Realization of a test Acquisition of cartography (aerial and satellite imagery, paper maps, vector files, etc.) for the pilot area Importing and integrating administrative records, spatial levels and EA boundaries of previous censuses Development...
  • Update: Privacy Issues Karyn Hogan Region of Peel

    Update: Privacy Issues Karyn Hogan Region of Peel

    Karyn Hogan [email protected] 905-791-7800 ext. 4379 Generator Standard: Site requirements Source documentation Issue: Exclusions for municipalities (ECAs) Sept 1st deadline (extension) + payments * Issue: contractual component + obligated materials (OES) Non-Ontario WEEE + Best ...
  • Elementary Logic - Southern Illinois University Carbondale

    Elementary Logic - Southern Illinois University Carbondale

    Argument form. All arguments have forms, though some are easier to find than others. All (deductive) argument forms are either valid or invalid. Disjunctive syllogism, for instance, is valid. Seventh Inning Stretch ... Elementary Logic Last modified by:
  • Was Hurricane Katrina Good for The Education of Students in ...

    Was Hurricane Katrina Good for The Education of Students in ...

    WAS HURRICANE KATRINA GOOD FOR THE EDUCATION OF STUDENTS IN NEW ORLEANS? By Caroline Harris Pre-Katrina The education system in New Orleans was already struggling prior to Hurricane Katrina. New Orleans was known as the lowest performing school district in...
  • Role Based Access Control Models

    Role Based Access Control Models

    Role Based Access Control Models ... we assumed the presence of a single security officer Normally have a small administrative team to mange RBAC Propagation of rights Management Model Management Model Proposed Administrative roles and permissions are disjoint from regular...
  • Shakespeare PowerPoint - Lawndale High School

    Shakespeare PowerPoint - Lawndale High School

    Fie on 't! Ah, fie!" - Hamlet Sonnet 12 When I do count the clock that tells the time, And see the brave day sunk in hideous night; When I behold the violet past prime, And sable curls, all silvered...