EC-433 Digital Image Processing

Transcription

1 EC-433 Digital Image Processing Lecture 4 Digital Image Fundamentals Dr. Arslan Shaukat Acknowledgement: Lecture slides material from Dr. Rehan Hafiz, Gonzalez and Woods

2 Interpolation Required in image resizing such as shrinking and zooming Using known data to estimate data at unknown points

3 1D Interpolation Linear Interpolation: Fit a linear function piecewise between the points

4 1D Interpolation Quadratic: Fit a Quadratic Polynomial between the three points

5 Interpolation Fitting Polynomial to data points

6 Nearest Neighbor Interpolation Simply replicate the value from neighboring pixels

7 Nearest Neighbor Interpolation Severe distortion of straight edges

8 Bilinear Interpolation Use the four nearest neighbors to estimate the intensity at a given location

9 Bicubic Interpolation Involves the 16 nearest neighbors

10 Comparison of Interpolation Approaches Nearest Neighbor Bi-Linear Bi-Cubic

11 Basic Pixel Relationships

12 Neighborhood of a Pixel Co-located in space Not necessarily in intensity value N 4 (p) 4-neighbors Set of horizontal and vertical neighbors (x+1,y), (x-1,y), (x,y+1), (x,y-1) N D (p) diagonal neighbors Set of 4 diagonal neighbors (x+1,y+1), (x+1,y-1), (x-1,y+1), (x-1,y-1) N 8 (p) 8-neighbors Union of N 4 (p) & N D (p)

13 Neighbors N D (p) N 4 (p)

14 Adjacency Two pixels that are neighbours and have the same/(similar) grey-levels are adjacent In a binary image, V = {1} if we are referring to adjacency of pixels with value 1 Two pixels p & q have: 4-Adjacency if q is in the set N 4 (p); p & q belong to V 8-Adjacency if q is in the set N 8 (p); p & q belong to V Diagonal-Adjacency if q is in the set N D (p); p & q belong to V m-adjacency (mixed adjacency): If q is in set N 4 (p); p & q belong to V OR If q is Diagonally-Adjacent BUT p & q DO NOT have any common 4-adjacent neighbours belonging to set V

15 Adjacency Mixed adjacency is a modification of 8-adjacency and is used to eliminate the multiple path connections that often arise when 8-adjacency is used.

16 Path A path from pixel p with coordinates (x,y) to pixel q with coordinates (s,t) is a sequence of distinct pixels: (x 0,y 0 ), (x 1,y 1 ),, (x n,y n ), where (x 0,y 0 ) = (x,y), (x n,y n ) = (s,t) (x i,y i ) is adjacent to (x i-1,y i -1 ), for 1 i n n is the length of the path. If (xo, yo) = (xn, yn) closed path 4, 8 and m-paths depending on adjacency m-adjacency pixels m-path Resolves the direction where to go first Preferably m-adjacency

17 Path

18 m-path

19 Closed m-path

20 Connectivity Connectivity in a subset S of an image Two pixels are connected if there is a path between them that lies completely within S Connected Component The set of all pixels in S that are connected to a given pixel Connected Set If S has only one connected component

21 Connected Components & Connected Set

22 Connectivity

23 Regions In an image sub-section, R is a region if it is a connected set Adjacent Regions Two regions are Adjacent if their union is again a connected set Disjoint Regions Not Adjacent Adjacency to consider: 4 & 8 adjacency

24 Regions & their adjacency Adjacency

25 Regions are connected sets The red box is not a region because it is not connected set

26 Labeling Components

27 Foreground and Background Let there be K disjoint Regions: R k None touches the image border Let R u be the union of all K-regions Foreground Points in R u Background Complement of Points in R u

28 Light green = Background Yellow = Foreground

29 Inner Boundary Boundary, Contour Set of points of R that are adjacent to points in the complement of R or The set of pixels in R that have at least one neighbor from background Must specify the connectivity Preferably 8-Adjacency

30 Find the boundary Assuming 4-Adjacency

31 Boundary / Contour = GREEN Assuming 4-Adjacency Some yellow boxes should be green as well if we consider 8-adjacency Even 8-Adjacency may not form a closed path Assuming 4-Adjacency 1 1 1

32 To get outer boundary Outer Boundary Let Rc be the background; than Set of points in Rc that are adjacent to points in the R OR The set of pixels in Rc that have at least one neighbor from R Useful for border following algorithms

33 Inner Boundary / Contour = GREEN Assuming 4-Adjacency

34 Assuming 4-Adjacency 4-Adjacent 1 Outer Boundary = Gray

35 8-Adjacnet Outer Boundary = Gray 1 1 Forms closed Path

36 If a region corresponds to the whole image, 1 st and last rows & columns are treated as boundary Difference Edges Intensity Discontinuities Boundaries Closed Path Some Notes