1. 1 Image Databases  Conventional relational databases, the user types in a query and obtains an answer in response  It is different in image databases  a police officer may issue a query: “ Retrieve all pictures from the image database that are “similar” to this person and give the identities of the people.”  This query is fundamentally different from ordinary queries for 2 reasons:  1. The query includes a picture as part of the query  2. The query asks about similar pictures and therefore uses a notion of “imprecise match”

2. 2 Raw images  the content of an image consists of all “interesting” objects in that image  each object is characterized by  a shape descriptor: that describes the shape/location of the region within which the object is located inside the image  a property descriptor that describes the properties of individual pixels (e.g. RGB values of the pixel, RGB values aggregated over a group of pixels, grayscale levels)  a property consists of F a property name, e.g., red, green, blue, texture F a property domain - range of values that a property can assume {0, 1,..7}

3. 3 Images  Every image is associated with a pair of positive integers (m,n), called grid-resolution, which divides the image into (m  n) cells of equal size (called image grid)  Each cell consists of a collection of pixels  A cell property: (Name, Values, Method)  Example F (bwcolor, {b,w}, bwalgo}, where the possible values are b(black) and w(white), and bwalgo is an algorithm that takes a cell as an input and returns either black or white by somehow combining the black/white levels of the pixels in the cell F (graylevel, [0,1], grayalgo), where the possible values are real numbers within the interval [0,1].

4. 4 Image Database  Image Database: (GI,Prop,Rec)  GI is a set of gridded images (Image,m,n)  Prop is a set of cell properties  Rec is a mapping that associates with each image, a set of rectangles denoting objects (in fact this does not necessarily have to be rectangle)

5. 5 Problems with image databases  Images are often very large  infeasible to explicitly store the properties on a pixel by pixel basis  This led to a family of image “compression” techniques: attempt to compress the image into one containing fewer pixels  There is a need to determine the “features” of the image (compressed or raw)  done by “segmentation” : breaking up the image into a set of homogeneous rectangular regions called segments  Need to support “match” operations that compare either a whole image or a segmented image against another

6. 6 Image Compression  Lossy Compression  Image may contain details that human eye cannot recognize  get rid of those details F DCT(Discrete Cosine Transform) F DFT(Discrete Fourier Transform) F DWT(Discrete Wavelet Transform) convert images from time domain(Spatial) to frequency domain get rid of the frequencies which do not contain information.  Transforms  DCT and DFT are similar concepts F From time domain to signal domain F Given a signal of length “n”, these transforms return a sequence of n frequencies. Sample1, Sample2,......., Sample n transforms to : Freq1, Freq2,........., Freq n.

7. 7 Why do we use the transform  Noise removal is easier in the frequency domain  Various filters are easier to implement in frequency domain  Compression (gathers similar values together)

8. 8 Desirable Properties of Transforms  DFT  Invertibility: It is possible to get back the original image I from its DFT representation. (useful for decompression)  Note: practical implementations of DFT often use DFT with other non-invertible operations: thus sacrifice invertibility  Distance preservation: DFT preserves Euclidean distance. F This is important in image matching applications where we often use distance measures to represent similarity levels  DCT  DCT preserves all the above  a given signal can be represented with fewer frequencies  DWT  DFT and DCT have no temporal locality F a change in one single part of data changes all frequencies  wavelets introduce locality

9. 9 Distance preservation

10. 10 Distance preservation

11. 11 Fractal Compression  Transform-based approaches benefit from the difference in visual perception in different frequencies  What else can we use for compression ?  Self similarity F We can find self similarities in a given image and describe the image in terms of these similarities.

12. 12 Fractal Compression

13. 13 Image Processing: Segmentation  A process of taking an image as input and cutting up the image into disjoint homogeneous regions  Connected region (R):  is a set of cells C 1.. C n in R such that the Euclidean distance between C i and C i+1 for all i < n is 1  Example  R1,R2,R3 is connected  R1  R2 is connected  R2  R3 is connected  R1  R2  R3 is connected  R1  R3 is not connected  Because the Euclidian  distance between (2,3)  and (3,4) is  2>1 R3 R1 R2 1 2 3 4 4 3 2 1

14. 14 Measuring Homogeneity  Homogeneity predicate: is a function H that takes any connected region as input and returns either true or false  Example 1:  Suppose  is some real number between 0 and 1  H  bw can be defined as H  bw (R) is true if over (100*  )% of cells in R have the same color Region # of black #of white cells cells R1 800 200 R2 900 100 R3 100 900 Region H 0.8 bw H 0.89 bw H 0.92 bw R1 true false false R2 true true false R3 true true false

15. 15 Measuring Homogeneity  Example 1:  Suppose each cell has a real value between 0, 1, this value is bw-level  Suppose f assigns a value between 0 and 1 to each cell  Assume  is the noise factor and  a threshold  H ,f,  (R) is true if {(x,y)| |bwlevel(x,y)-f(x,y)| 

16. 16 Segmentation  Given an image I with (m  n) cells, a segmentation of I wrt a homogeneity predicate P is a set of R1,.Rk such that  Ri  Rj =  for all 1  i  j  k  I = R1 ..  Rk  H(Ri) = true for all i  j  k  for all distinct i,j, 1  I, j  n such that Ri  Rj is a connected region, it is the case that H(Ri  Rj) = false

17. 17 An Example of Segmentation Row/Col 1 2 3 4 1 0.1 0.25 0.5 0.5 2 0.05 0.30 0.6 0.6 3 0.35 0.30 0.55 0.8 4 0.6 0.63 0.85 0.90  For H dyn,0.03 (R) of the following (4  4) image will yield the following segmentation  R1 = {(1,1),(1,2)}  R2 = {(1,3),(2,1),(2,2),(2,3)}  R3 = {(3,1),(3,2),(3,3),(4,1),(4,2)}  R4 = {(3,4),(4,3),(4,4)}  R5 = {(1,4),(2,4)} Row/Col 1 2 3 4 1 0.1 0.25 0.5 0.5 2 0.05 0.30 0.6 0.6 3 0.35 0.30 0.55 0.8 4 0.6 0.63 0.85 0.90

18. 18 Segmentation Algorithm  Split:  if the whole image is homogeneous, we are done  otherwise, split the image into two parts and recursively repeat this process till we find a set of R1.. Rn such that each region is homogeneous  Merge:  check whether any of the Ri’s can be merged together  at the end of this step, we obtain a valid segmentation R1,..Rk

19. 19 Similarity Based Retrieval

20. 20 Similarity Based Retrieval

21. 21 Similarity Based Retrieval  The Metric Approach:  Uses a distance measure d that can compare tow images  The smaller the distance, the more similar they are  I.e., given an input image I, find the “nearest neighbor” of I in the image archive  The Transformation Approach:  The metric approach assumes that the notion of similarity is fixed  Whereas the transformation approach computes the cost of transforming one image into another based on user-specified cost functions that may vary from one query to another

22. 22 The Metric Approach  We define a distance function on a k dimensional space (k=n+2)  the distance function satisfies the following properties  d(x,y) = d(y,x)  d(x,z)  d(x,z) + d(z,y)  d(x,x) = 0  Example: Let the image object consists of (256  256) cells with 3 attributes (red,green,blue) each of which assumes a value from {0,…7}  d i (o 1,o 2 ) =    (diff r [i,j]+diff g [i,j]+diff b [i,j])  where diff r [i,j] = (o 1 [i,j].red - o 2 [i,j].red) 2  diff g [i,j] = (o 1 [i,j].green - o 2 [i,j].green) 2  diff b [i,j] = (o 1 [i,j].blue - o 2 [i,j].blue) 2  Such computations can be cumbersome (65536 expressions being computed inside the sum)

23. 23 The Metric Approach  How can this massive similarity computation be avoided?  Through feature extraction!  Use a good feature extraction function fe and use it to map objects into single points in a s-dimensional space where s would typically be pretty small compared to n+2  This leads to two reductions  an object is originally is a set of points in an (n+2) dimensional space. In contrast, fe(0) is a single point  fe(o) is a point in s-dimensional space where s << (n+2)  The feature extraction mapping must preserve the distance relationships in the original space  (n+2) dim space  s-dim space  indexing algorithm  index  object repository (could be quadtree, R-tree for s- dim data)

24. 24 Searching  Finding the best matches  find the nearest neighbors of fe(o) in the tree using a nearest neighbor search technique.  Finding sufficiently similar objects  execute a range query in the tree with center fe(o) and radius 

25. 25 The Transformation Approach  The main principle  the level of dis-similarity between o 1,o 2 is proportional to the cost of transforming o 1 into o 2, or vice-versa  Transformation operators  translation  rotation  scaling (uniform and nonuniform)  excision  Transformation of o into o’ is a sequence of transformation operations (to 1,to 2,..to r ) such that  to 1 (o) = o 1  …...  To(o r ) = o’  Cost of transformation, cost(TS) =  cost(to i )

26. 26 Example

27. 27 Example

28. 28 Example

29. 29 Transformation vs. Metric  Advantages of the transformation model  user can setup his own notion of similarity by specifying certain transformation operators  user may associate a cost function with each transformation operator  Advantages of the metric model  by forcing the user to use only one similarity metric, the system can facilitate the indexing of data so as to optimize nearest neighbor search