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Indexing Techniques for Multimedia Databases Multimedia Similarity Search Structure Image Indexing Video Indexing

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2 Traditional DBMS –Designed to manage one- dimensional datasets consisting of simple data types, such as strings and numbers –Limited kinds of queries: exact match, partial match, and range queries –Well-understood indexing methods: B-trees, hashing

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3 Characteristic of Multimedia Queries We normally retrieve a few records from a traditional DBMS through the specification of exact queries based on the notions of “equality”. The types of queries expected in an image/video DBMS are relatively vague or fuzzy, and are based on the notion of “similarity”. The indexing structure should be able to satisfy similarity-based queries for a wide range of similarity measures.

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4 Content-Based Retrieval It is necessary to extract the features which are characteristics of the image and index the image on these features. Examples: Shape descriptions, texture properties. Typically there are a few different quantitative measures which describes the various aspect of each feature. Example: The texture attribute of an image can be modeled as a 3-dimensional vector with measures of directionality, contrast, and coarseness.

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5 Introduction Multimedia require support of multi-dimensional datasets –E.g., a 256 dimensional feature vector. That implies –Specialized kinds of queries –New indexing approaches. Two choices: Map n-dimensional data to a single dimension and use traditional indexing structures (B-trees) Develop specialized indexing structures

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6 Low-Dimensional Indexing Applications Spatial Databases (GIS, CAD/CAM) –Number of dimensions: 2-4 –Spatial queries. For example: Which objects intersect a given 2D or 3D rectangle Which objects intersect a given object –Specialized indexing structures quad-tree, BSP-tree, K-D-B-tree, R-tree, R+-tree, R*-tree, X-tree, …

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7 High-Dimensional (HD) Indexing Applications Multimedia databases (Images, Sounds, Movies) –Map multimedia object to a n- dimensional point called feature vector –Number of dimensions: typically 256 - 1000 –Indexing: Actually index only feature vectors Data structures used: –same as for spatial databases (R-Trees, X- trees) –or, structures tailored to index specifically feature vectors (TV-Tree)

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8 HD Considerations (1) Main problem: –In general there is no total-ordering of d-dimensional objects that preserves spatial proximity Data comes in two forms –N-dimensional points –N-dimensional objects extended in space Objects can have rather complex shapes (extents) Typically abstract from the actual form and index some simpler shapes, such as Minimum Bounding Boxes (MBB) or n- dimensional hyper spheres

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9 HD Considerations (2) “Dimensionality curse” –As the number of dimensions increases performance tends to degrade (often exponentially) Indexing structures become inefficient for certain kinds of queries Performance is often CPU- bound, not just I/O-bound as in traditional DBMS

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10 HD Queries Overview No standard algebra or query language The set of operators strongly depends on application domain Queries are usually expressed by an extension of SQL (e.g. abstract data types) Although there are no standards, some queries are common

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11 Multiattribute and Spatial Indexing of Multimedia Objects Spatial Databases: Queries involve regions that are represented as multidimensional objects. Example: A rectangle in a 2-dimensional space involves four values: two points and two values for each point. Access methods that index on multidimensional keys yield better performance for spatial queries. Multimedia Databases: Multimedia objects typically have several attributes that characterize them. Example: Attributes of an image include coarseness, shape, color, etc. Multimedia databases are also good candidates for multikey search structures.

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12 Measure of Similarity A suitable measure of similarity between an image feature vector F and query vector Q is the weighted metric W: where A is an nxn matrix which can be used to specify suitable weighting measures.

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13 Similarity Based on Euclidean Distance FFFQ D(F 1,Q) 123 3 4 6 2 4 7 3 4 7 2 4 6 100 100 010 001 1 0 0 1 001 100 010 001 0 0 1 1 101 100 010 001 1 0 1 2 D(F 2,Q) D(F 3,Q)

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14 Similarity Based on Euclidean Distance (cont.) F1F1 F2F2 Feature 2 Feature 1 Points which lie at the same distance from the query point are all equally similar, e.g., F 1 and F 2. F 3 Q

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15 Similarity Based on Weighted Euclidean Distance where A is the diagonal. FFQA D(F 1,Q) 12 4 5 7 3 5 8 3 5 7 100 010 002 100 100 010 002 1 0 0 1 001 100 010 002 0 0 1 2 Example: D(F 2,Q) D(F 1,Q) < D(F 2,Q) F 1 is more similar to Q

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16 How to determine the weights ? A 00 00 00 S i 2 : the variance of the i- th feature measures. S 2 2 S 1 2 S 3 2 The variance of the individual feature measures can be used as their weights. Rationale: A feature with a larger variance is more discriminating.

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17 Query Types Querying in image DBMS is envisioned to be iterative in nature: Vague Queries: Queries at the earlier stage can be very “loose”. Retrieve images containing textures similar to this sample. K-nearest-neighbor-queries: The user specifies the number of close matches to the given query point. Retrieve 10 images containing textures directionally similar to this sample Range queries: An interval is given for each dimension of the feature space and all the records which fall inside this hypercube are retrieved. r is large r is small range query => vague query => 3-nearest neighbor query Q Q.Q. r............ + + +

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18 Indexing Multimedia Objects Can’t we index multiple features using a B + -tree ? –B + -tree defines a linear order –Similar objects (e.g., O 1 and O 2 ) can be far apart in the indexing order Why multidimensional indexing ? –A multidimensional index defines a “spatial order” –Conceptually similar objects are spatially near each other in the indexing order (e.g., O 1 and O 2 ) Feature X Feature Y.O1.O1 O2.O2.

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19 Some Multidimensional Search Structures Space Filling Curves k-d Trees Multidimensional Tries Grid File Point-Quad Trees R Trees, R*, TV, SS D-Trees VA files

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20 Space Filling Curves Assume that each dimension is represented by a fixed bit width number Partition the universe with a grid Label each grid cell with a unique number called the curve value For points, store that number in a traditional one-dimensional index Objects can be handled through decomposition into multiple cells Z-ordering Curve with 2 bits

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21 k-d Trees k-d tree is a multidimensional binary search tree. Each node consists of a “record” and two pointers. The pointers are either null or point to another node. Nodes have levels and each level of the tree discriminates for one attribute. The partitioning of the space with respect to various attributes alternates between the various attributes of the n-dimensional search space. Example: 2-D tree Input Sequence A = (65, 50) B = (60, 70) C = (70, 60) D = (75, 25) E = (50, 90) F = (90, 65) G = (10, 30) H = (80, 85) I = (95, 75) A(65, 50) B(60, 70) C(70, 60) G(10,30)E(50,90) D(75, 25) F(90, 65) H(80, 85)I(95, 75) Discriminator XYXYXYXY

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22 k-d Tree: Search Algorithm Notations: Algorithm: Search for P(K 1,..., K n ) Q := Root; /* Q will be used to navigate the tree */ While NOT DONE DO the following: if K i (P) = K i (Q) for i = 1,..., n then we have located the node and we are DONE Otherwise if A = Disc(Q) and K A (P) < K A (Q) then Q := Low(Q) else Q := High(Q) Performance: O(logN), where N is the number of records L M N (..., K A (L),...) M = Low(L) N = High(L) Disc(L) : The discriminator at L’s level K A (L) : The A-attribute value of L Low(L) : The left child of L High(L) : The right child of L

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23 Multidimensional Tries Multidimensional tries, or k-d tries, are similar to k-d tree except that they divide the embedding space. Each split evenly divides a region Example: Construction of a 2D tries X>75 X<=50 X>50 Y>50 X<=75 Y<=50 X<=75 X>75 Y>25 A(65,50) X<=75 Y>75 X<=62.5 X>62.5 B(60,70) C(70,60) X<=50 X>50 A(65, 50) Insert A(65,50): X<=50 X>50 Y<=50 Y>50 A(65,50) B(60, 70) Insert B(60, 70): Insert D(75, 25): B(60, 70)C(70, 60) X<=50 X>50 Y<=50 Y>50 X<=75 X>75 X<=62.5 X>62.5 Y<=75Y>75 A(65,50) Y<=25 D(75,25) Insert C(70,60): Partitioning of the space 10 20 30 40 50 60 70 102030405060708090 1 4 3 2 7 D(75,25) B(60,70) C(70, 60) A(65,50) 5 X Y 6

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24 Multidimensional Tries: Using Buckets Disadvantage: The maximum level of decomposition depends on the minimum separation between two points. A solution: Split a region only if it contains more than p points.

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25 Grid Files Split Strategy: The partitioning is done with only one hyperplane, but the split extends to all the regions in the splitting direction 1. The directory is quite sparse. 2. Many adjacent directory entries may point to the same data block. 3. For partial-match and range queries, many directory entries, but only few data blocks, may have to be scanned. linear scale Grid directory Data bucket ABCD DEFG HIJJ KKLM 100 75 50 25 0 5075100 0 25 50 75100 1234 75 50 25 0 1 2 3 4

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26 Point-Quad Trees Each node of a k-dimensional quad tree partitions the object space into k quadrants. The partitioning is performed along all search dimensions and is data dependent, like k-d trees. Example: The quad tree D(35,85) A(50,50) E(25,25) B(75,80) C(90,65) A SE SW E NW D NE B SE SW NW NE C To insert P(55, 75): Since X A < X P and Y A < Y P go to NE (i.e., B). Since X B > X P and Y B > Y P go to SW, which in this case is null. Partitioning of the space P

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27 Spatial Index Trees We will talk about data normalized in the range [0, 1] for all the dimensions. Minimum Bounding Region (MBR) refers to the smallest region (rectangle, circle) that encloses the entire shape of the objects or all the data points.

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28 R-tree R-trees are higher generalizations of B-trees. The nodes correspond to disk pages. All leaf nodes appear at the same level. Root and intermediate nodes corresponds to the smallest rectangle that encloses its child nodes, i.e., containing [r, ] pairs. Leaf nodes contain pointers to the actual objects, i.e., containing [r, ] pairs. A rectangle may be spatially contained in several nodes (e.g., J ), yet it can be associated with only one node.

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29 Hierarchy of nested d-dimensional intervals (boxes). Each node v corresponds to a disk page & d- dimensional interval,. Store MBB or MBR of n-dimensional object. Permits overlap of index entries. Index used as filter mechanism for query. Every node contains between m and M entries unless it is a root. The root node has at least 2 entries unless it is a leaf. Height-balanced. Which of the above properties are similar to - trees ? R-Trees

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30 R-tree: Insertion A new object is added to the appropriate leaf node. If insertion causes the leaf node to overflow, the node must be split, and the records distributed in the two leaf nodes. –Minimizing the total area of the covering rectangles –Minimizing the area common to the covering rectangles Splits are propagated up the tree (similar to B-tree).

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31 R-tree: Delete If a deletion causes a node to underflow, its nodes are reinserted (instead of being merged with adjacent nodes as in B-tree). There is no concept of adjacency in an R-tree.

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32 D-tree: Domain Decomposition If the number of objects inside a domain exceeds a certain thresholds, the domain is split into two subdomains. Example 1: Horizontal Split Example 2: Vertical Split A B C D F E G D A subdomain Split along longest dimension Original domain Split line G F E D B A C D B A C G E F A border object A subdomain Original domain A B C F E G

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33 D-tree: Split Examples D-tree Initial tree: D Embedding Space D After 3 insertions: null Data node D After 1 st split: D1D1 D2D2 D1D1 D2D2 After 2 nd split: D 11 D2D2 D 12 D2D2 D 11 D 12 Domain node null

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34 D-tree: Split Example (continued) D-tree Embedding Space After 3 rd split: D 11 D 121 D2D2 D 122 D 11 D2D2 D 121 D 122 After 4 th split: Internal node External node D1D2 D 11 D 121 D 122 D21D22 D 122 D 11 D 21 D 121 D 22 D22.P

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35 D-tree: Range Queries Note: A range query can be represented as a hypercube embedded in the search space. Search Strategy: Retrieve the set, say S, of all subdomains which overlap with the query cube. For each subdomain, in S, which is not fully contained in the query cube, discard the objects falling outside the query cube. Algorithm: Search(D_tree_root, search_cube) Current_node = D_tree_root For each entry in Current_node, say (D, P), if D overlaps with search_cube, we do the following: –If Current_node is an external node, retrieve the objects, in D.P, which fall within the overlap region. –If Current_node is an internal node, call Search(D.P, search_cube).

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36 D-tree: Desirable Properties D-trees are balance The search path for an object is unique No redundant searches. More splits occur in the denser regions of the search space. Objects are evenly distributed among the data nodes. Similar objects are physically clustered in the same, or neighboring data nodes. Good performance is ensured regardless of the insertion order of the data.

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37 Content-Based Image Indexing Keyword Approach –Problem: there is no commonly agreed-upon vocabulary for describing image properties. Computer Vision Techniques –Problem: General image understanding and object recognition is beyond the capability of current computer vision technology. Image Analysis Techniques –It is relatively easy to capture the primitive image properties such as prominent regions, their colors and shapes, and related layout and location information within images. –These features can be used to index image data.

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38 Possible Features Edge Region Color Shape Location Size Texture

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39 EDGE Types of Edges – Step, Ramp, Spike and Roof. 3 stages in edge detection –Filtering : Image is passed through a filter in order to remove noise. –Differentiation : highlights the locations where intensity changes are significant. –Detection

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40 Classes of edge detection schemes Prewit, Robert, Sobel, and Laplacian – 3x3 and 5x5 gradient operators Hueckel, Hartly and Haralick’s – surface fitting Canny - the derivatives of Gaussian

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41 Canny Edge Detector The results of choosing the standard deviation sigma of the edge detectors as 3. lena.gif vertical edges horizontal edges norm of the gradient after thresholding after thinning

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42 Features Acquisition: Region Segmentation Group adjacent pixels with similar color properties into one region, and segment the pixels with distinct color properties into different regions.

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43 Definition of Segmentation All pixels must have the same.. All pixels must not differ by more than.. All pixels must not differ by more than T from the mean.. The standard deviation must small..

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44 Simple Segmentation B(x, y) = 1 if T1 < f(x, y) < T2 0 otherwise Thresholds and Histogram Connected Component Algorithms –Recursive Algorithm –Sequential Algorithm

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45 Seed Segmentation 1.Compute the histogram 2.Smooth the histogram by averaging to remove small peaks 3.Identify candidates peaks and valleys 4.Detect good peaks by peakiness test 5.Segment the image using thresholds 6.Apply connected component algorithm

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46 Region Growing Split and Merge Algorithm Phagocyte Algorithm Likelihood Ratio Test

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47 Region Segmentation EDISON JSEG

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48 Color We can divide the color space into a small number of zones, each of which is clearly distinct with others for human eyes. Each of the zones is assigned a sequence number beginning from zero. Notes: It is proven that human eyes are not very sensitive to colors. In fact, users only have a vague idea about the colors they want to specify.

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49 Shape Shape feature can be measured by properties: Circularity, major axis orientation, and Moment. –Circularity: Notes: The more circular the shape, the closer to one the circularity. –Major Axis Orientation: –Moment : the first and the second r a 2a a a

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50 Location The image is divided into sub-areas. Each sub-area is labeled with a number. The region location is represented by the number of the sub-area in which the centroid (gravity center) of the region is contained. Note: When a user queries the database by visual contents, approximate feature values are used. It is meaningless to use absolute feature values as indices. 0 1 2 3 4 5 6 78 A B Location of A is 4 Location of B is 1

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51 Size Total number of pixels occupied by the region The size range is divided into groups. A region’s size is represented by the corresponding group number. Example: group number Size Range Notes: Only the regions more than one-fourth of the sub-area are registered. S: object size A sub : size of the sub-area

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52 Texture Approach based on Statistics: –angular second moment (energy, homogeneity or uniformity), entropy, correlation, inverse difference moment, contrast (inertia), variance, sum average, sum variance, difference variance, difference entropy, information measure of correlation I, information measure of correlation II, and maximal correlation coefficient. Approach based on human perception: –coarseness, contrast, directionality, line-likeness, regularity and roughness –busyness, complexity and texture strength –repetitiveness, orientation, and complexity

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53 Image Indexing by contents By applying image segmentation techniques, a set of regions are detected along with their locations, sizes, colors, texture and shapes. These features can be used to index image data.

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54 Texture Areas Texture areas and images with dominant high frequency components are beyond the capacity of image segmentation techniques. Matching on the distribution of colors (i.e., color histograms) is a simple yet effective means for these areas. Strategy: Dividing an image into sub-areas and creating a histogram for each of the sub-areas. Note: the partitioning of the image is to capture locality information. We don’t want to match an image with a red balloon on top with an image with a red car in the bottom.

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55 Histograms Gray-Level Histogram: It is a plot of the number of pixels that assume each discrete value that the quantized image intensity can take. Color Histogram: It holds information on color distribution. It is a plot of the statistics of the R, G, B components in the 3-D color space.

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56 We can use the largest, say 20, bins as the representative bins of the histogram. these 20 bins form a chain in the 3-D color space. If we can represent such chains using a numerical number, then we can index the color images using various tree structures. Connecting order: The representative bins are sorted in ascending order by their distance from the origin of the color space. Weighted Perimeter: Weighted Angle: Format of the index key: Histograms (cont.) B (0,1,1) (2,3,0) (3,2,3) (6,2,0) (8,2,6) G R 0 Most histogram bins are sparsely populated, with only a small number of bins capturing the majority of pixel counts. WP (10 bits) WA (10 bits)

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57 Color Correlogram

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