Content-Based Image Retrieval System by Hierarchical Color Image Region Segmentation
Shun-Wen Cho, Chiou-Shann Fuh , Kai Essig
Department of Computer Science and Information Engineering National Taiwan University
Taipei, Taiwan
fuh@csie.ntu.edu.tw, kessig@robot.csie.ntu.edu.tw
Abstract
In this paper we propose a model of a content-based image retrieval system by using the new idea of com- bining a color segmentation with relationship trees and a corresponding tree-matching method. We retain the hierarchical relationship of the regions in an image dur- ing segmentation. Using the information of the relation- ships and features of the regions, we can represent the desired objects in images more accurately. In retrieval, we compare not only region features but also region re- lationships.
Keywords: Hierarchical relationships, region extrac- tion, region merging, feature extraction, color.
1 Introduction
A content-based image/video retrieval system is a querying system that uses content as a key for the re- trieval process 1]. It is a di cult task to design an automatic retrieval system, because real world images usually contain very complex objects and color infor- mation. One problem that occurs is how to segment a real world image perfectly. Various research has been done in extracting color and spatial information from images. In recent work 7] the image is segmented into regions of constant (but unknown) re ectance to avoid unreliable results in the vicinity of an edge. The com- puted ratio of the re ectance of a region to that of its background is used for object recognition. Another ap- proach 4] derives illumination invariants of color dis- tributions in spatially ltered color images. The com- bination of this information can be used to recognize a wide range of spatial patterns in color images under unknown illumination conditions. Syeda-Mahmood 9]
presents a method of color specication in terms of per- ceptual color categories that allow a reliable extraction of color regions and their subsequent use in selection.
An e cient color segmentation algorithm which com- Corresponding Author
bines the advantages of a global region-based approach with the advantages of a local edge-based approach is presented in 3].
This paper attempts to propose the new idea of com- bining a color segmentation method that can retain the hierarchical relationships of the regions in an image with a suitable tree-matching method that uses the relation- ships and the features of the regions to build an e cient content-based image retrieval system for real world im- ages. We can describe complex real world images by decomposing the objects into some regions. These re- gions may have some relationships among them, such as overlap, relative position, and so on. By these region re- lationships, we can identify surrounding or surrounded regions hence we also know which regions consist of a simple object. Therefore we created a color segmenta- tion method to segment images and retain region rela- tions at the same time in a relationship tree. In the retrieval process, these relationships and the extracted shape and color features of the regions themselves can help us to retrieve the more desired image by matching the representations of the objects in the database to the objects in the query image. For demonstration, we build a system that can retrieve some simple objects.
2 Region Extraction
The region extraction process consists of three phases:
segmenting an image into regions, merging regions, and extracting features from regions.
The existing segmentation techniques are not suitable for our purpose because of two reasons: (i) They are based only on color information alone. They usually produce disconnected segments, which we do not want.
(ii) In complex images, selecting thresholds is almost impossible.
Region-oriented segmentation techniques use not only color information but also the pixel relationships to par- tition an image into some regions, which are usually continuous 6, 10]. Hence our hierarchical region seg-
mentation bases on region growing segmentation.
2.1 Region and Sub-Region Denitions
Before stating the process of our segmentation, we must dene the region rst.
Denition 1 (Region) Let R represent the entire image. We may consider the segmentation as a process that partitions R into n regions, R1R2:::Rn, such that the segmentation is complete, the pixels in a region are connected and that the regions must be disjoint.
Additionally two regions must be dierent in the sense of a predicate P.
Denition 2 (Subregion) We say that a region R0 is a sub-region of region R if there exists a close pixel sequence S =
h(r0c0)(r1c1)(r2c2):::(rk ;1ck ;1)(rkck)i, where (rici)2R and each pair of successive pixels in sequence are neighbors, including (r0c0) and (rkck), such that every pixel (r0c0)2R0 is surrounded by the sequenceS.
This sub-region denition identies the relationship of two regions. Every region in an image must be a sub-region of another region. In order to comply with this, we need a pseudo-region which represents the entire image. Hence, the rst level regions which are not sub- regions of any real regions are collected to be sub-regions of the pseudo-region. The sub-regions of a region are siblings. These relationships and the features of every region are su cient to represent an image.
2.2 Color Space and Color Distance
We use the original RGB model of the images, and the color distance is the Euclidean distance in RGB color space. The RGB color distance function is described as the following:
d
C(v v0) =p(r;r0)2+ (g;g0)2+ (b;b0)2 (1) where
v= (rgb) v0 = (r0g0b0)
where dC denotes the color distance function. The v and v0 denotes the two color value vectors in RGB color space. The color distance between two pixels can be represented as:
d
C(C(p)C(p0)) =
q(rp;rp0)2+ (gp;gp0)2+ (bp;bp0)2 (2) where
C(p) = (rpgpbp) p= (ij)
where C denotes a function mapping from a pixel p= (ij) in image plane to its color value (rpgpbp) in RGB
color space. Hence the C(p) and C(p0) represent the RGB color values at pixel p = (ij) and p0 = (i0j0) respectively.
2.3 Region Growing
We focus to segment the regions of the obvious objects from an image and treat the remainder as regions of the background or other obscure objects. We want the segmented regions to grow as large as possible. Hence we use the following two criteria to limit the growth:
local criterion
d
C(C(p)C(p0))<TL (3) and global criterion
d
C(CR(R(p))C(p0))<TG (4) where
p= (ij) p0 = (i+lj+k) l=;101 k=;101
C
R(R) = (
P
i2R r
i
N
P
i2R g
i
N
P
i2R b
i
N
)
N is the number of pixels in region R whereR(p) denotes the region which pixelpbelongs to and CR denotes the average color value function for a region which maps from region R to its average color value vector. Besides, the pixel p0 is a neighbor of the pixel p. Equation 3, the local criterion, means that the color distance between pixelspandp0 must be less than the local criterion threshold TL. Equation 4, the global criterion, means that the color distance between the pixel p0 and the average color value of the region which pixel p belongs to must be less than the global criterion threshold TG.
The segmented regions grow one by one in region growing segmentation. For convenience, the pixels in region and neighboring (8-neighbors) with unclassied pixels are called growing pixels. The growth process must run once for each of the growing pixels, and the region expands from these growing pixels according to the local and global criteria. Besides, there must ex- ist a seed growing pixel for every region, otherwise the growth process can not proceed. We dene the order of the pixels in entire image as an increasing order from left to right and top to bottom. The seed growing pixel of the next growing region is the unclassied pixel with the smallest order. The unclassied pixels (p0 in Equations 3 and 4) neighboring the growing pixels (pin Equations 3 and 4) in a growing region are classied into the grow- ing region when the local and global criteria are both satised. The region grows until no unclassied pixels satisfy the two criteria. After all pixels in the entire image are classied into the proper regions, the growth process terminates.
2.4 Creating Region Relationships
With the sub-region denition in Section 2.1 the re- lationships of all regions in an image can be created.
For example, if regionR2 andR3 are identied as sub- regions of regionR1by sub-region denition, and region
R
4 is a sub-region of region R2, then we can create a relationship tree as shown in Figure 1. Each node in the relationship tree represents a region in the original image. The regions which are not surrounded by any other regions respectively are considered as sub-regions of the entire image itself. For generality, we design a pseudo-region which represents the entire image itself, the node of this pseudo-region is the root node of the relationship tree. All nodes of regions which are not sub-regions of any other regions are children nodes of the root node. The relationship tree is created during
R4 R3 R2
R1
Original Image
Relationship Tree R1
R2 R1
R3
R2
R4
Root
R1
R2
R4
R3
Figure 1: Creating relationship tree.
region segmentation. The root node is created before segmentation. When a region growth completes, the node of this region is added into the relationship tree.
The position the added node is placed is determined by the sub-region relationship identication. We must mention that it is not necessary to identify each pair of regions in an image for creating the relationship tree.
The sub-region relationship identication just proceeds at the time when a node is added. The added node is placed under the lowest level node of the region which can surround the region of the added node. Because the seed growth pixel of each region is the pixel with the smallest order at the time, the sub-regions of a region must grow later than the surrounding region and the relationship tree created by sub-region identication is correct.
In order to create a unique relationship tree structure for the same object in dierent images, we sort the sub- regions under each region by their areas in descending order.
3 Merging and Eliminating Re- gions
3.1 The Merging Process
Regions with an area less than the area threshold are considered as non-signicant regions. We eliminate a non-signicant small region by merging it into a region adjacent to this small region which is most similar in color. Besides, in order to retain the correctness of the relationship tree, the tree must be corrected when two regions are merged.
The merging process proceeds during region segmenta- tion. After a region completes its growth and is placed in its proper position in the relationship tree, merging process calculates all color distances between this added region and the regions of its parent or sibling region node respectively. If the added region is placed in the
rst level of the relationship tree, merging process needs only to calculate the color distances between the added region and the region of its sibling region node. We pro- ceed the merging process after every region is generated to reduce the number of regions. Therefore, our result slightly diers from the result produced by merging after all regions are generated. This is not important because no segmentation result is absolutely correct.
The color distance function between two regions are written as
d
C(CR(R)CR(R0)): (5) The similarity criterion to judge whether two regions are similar in color is
d
C(CR(R)CR(R0))<TS: (6) This criterion means that two regions are similar in color if their color distance is less than the thresholdTS. The non-signicant criterion to judge whether a region is non-signicant is
A(R)<TN (7) whereAdenotes the area function for region. The crite- rion means that the regionRis a non-signicant region if its area is less than the area thresholdTN. If the non- signicant criterion is satised, this region is merged to the region with the closest color distance but the merg- ing process does not consider whether the similarity cri- terion satises in this situation. It must be noticed that the relation of the similar and non-signicant criteria is an `or' relation. If both two criteria are not satised, the added region is simply located into the relationship tree in the usual way.
All region features of the merged region are recalcu- lated from the features of the two original regions. Each region's contribution to these features is weighted ac- cording to its relative size. After two regions are merged together, it may result in that some regions are sur- rounded by the merged region. Hence the relationship
R6
Original Image R3 R5
R4 R2 R1
Correcting
R2
R4
R5 Move under R4 Merged R4 Uninfluenced
Nodes
Root
R1
R2 R3
R4 R5 R6
Merging
Figure 2: Correcting the tree after merging. Region R6 is added into the tree, and merged into regionR4. This results in that regionR5is surrounded by merged region
R
4. The tree must be corrected accordingly.
tree must be corrected in response to merging. It is ob- vious that the aected part of the tree structure after merging is just the sub-tree under the node of the region surrounding both merging regions. The root of the sub- tree is the parent node of the added region node. The other parts of the relationship tree are not aected. If the region being merged to is the root node of the sub- tree, the sub-tree remains correct. If the region being merged to is the sibling node of the added region node, merging process must nd the region nodes whose re- gions are surrounded by the resulted merged region from the other sibling nodes. Subsequently, all sub-trees led by the found nodes are moved to the position under the merged region node. Moreover, the children nodes of the merged region node must also be re-sorted. A correction of the tree structure after merging of two re- gions is shown in Figure 2. It is noticed that the rst generated region in the rst level nodes of the relation- ship tree may not be merged with any other adjacent regions. The reason is that the merging proceeds when every region completes its growth and the other adjacent regions are not generated at the time when the rst re- gion is generated. This problem is solved by proceeding the merging for the rst level nodes at the end of the segmentation algorithm.
3.2 Threshold Selection
We select the local, global, and similarity thresholds,
T
L, TG, andTS, in growing process adequately to pre- vent an iteration of the time-consuming merging process until all regions in an image can not be merged further.
This method does not solve the problem perfectly, but it is a reasonable compromise between the result and the
performance.
The local criterion threshold TL can not be selected too large to segment two regions. However, too small TL produces too detailed segmentation. The proper TL value is the color distance between two color values dif- fering about twenty color levels in all R, G, and B axes.
The global criterion threshold TG can be selected larger to make the segmented regions as large as pos- sible, but it also can not be too large to segment two obvious adjacent regions. The proper TG value is the distance between two color values diering about fty color levels in all R, G, and B axes.
The similarity criterion threshold TS is selected simi- lar toTL, because we hope the adjacent regions can be discriminated as pixels. Besides, in order to solve the iterative merging problem mentioned above, the value of theTG must be larger thanTS.
The last threshold is the non-signicant criterion threshold TN. If the application concerns more details in an image, we select smaller TN. Otherwise, theTN can be larger.
All threshold selection also depends on the application.
3.3 Extracting Features from Regions
After representing the region structures of the image as a relationship tree, we must extract the features of regions from the original image to improve the quality of the description of the nal relationship tree. The selected features must be insensitive to the three trans- formations, even invariant to them.
The means and standard deviations of the R, G, and B values of the pixels in a region are su cient to represent the color attributes of a region.
Table 1 shows the shape features we select: the thin- ness ratio T, the density ratioD, and the invariant mo- ment , derived from the normalized central moments
2]. These features are su cient to represent the regions of a simple object.
4 Image Retrieval
The image retrieval process itself is a matching process which matches the query data with the data in database.
Because of the hierarchical region segmentation, the re- trieval process must match not only the features but also the relationship structure of the regions in query object when querying a simple object. When querying a simple object by our approach, the relationship matching pro- cess needs only to match the sub-tree led by the region node of the outermost region of the query object with each sub-tree in all database images.
Table 1: The shape features of regionR. Equations for the selected features: 1 2 3 4
T = 4kPNk2
D= number of pixels
number of pixels including sub-regions
= N12
"
P
p=(rc)2R
(r;r )2+ P
p=(rc)2R
(c; c)2
#
4.1 Matching Region Relationships
Every tree can be represented as a string. We represent a leaf node as an `n' character, and a branch node as a
`(' character. Besides, in order to represent a sub-tree led by a branch node, we insert a `)' character after the sub-string of a sub-tree. It is noticed that the `)' char- acter does not represent any region node. Hence, the relationship tree of an image in Figure 3 can be repre- sented as a string \(((nn))(((nn)))(n))." It is obvious that when querying by an object the matching process is only to nd the sub-strings which are the same as the string of the object from the string of each image in database a common function in C run-time library.
The disadvantage of this method is that the tree struc- tures must be the same in the query object image and database images. Otherwise, the strings of the query image and database images can not be matched. How- ever, this method is the simplest and fastest method for relationship tree matching.
Original Image
Root
Relationship Tree ( ((nn)) (((nn))) (n) ) Query Object
(nn)
Figure 3: Relationship tree matching.
1
N: The number of the pixels inR.
2
P: R's perimeter, P = f(rkck) 2
Rjfall 4-neighbors of (rkck)g;R6=g.
3
p: A pixel inR, its coordinate in image plane is (rc).
4( r c): Centroid ofR.
4.2 Matching Regions
The color and shape features in our approach are represented as a nine value feature vector|
h
red
green
blue
red
green
blue
TDi. The smaller the dissimilarity score between two feature vec- tors, the more similar the two regions. The dissimilarity score functions of two regionsRandR0are described as the following:
S
color(R R0) = X
=
r ed
g r een
blue
(R);(R0)]2+
X
=
r ed
g r een
blue
(R);(R0)]2(8)
S
shape(R R0) =
T(R);T(R0)]2+D(R);D(R0)]2+(R);(R0)]2 (9)
S
region(R R0) =qScolor(R R0) +Sshape(R R0) (10) where(R) is the mean and(R) is the standard devi- ation of the regionR. The dissimilarity score is the Eu- clidean distance between the two feature vectors. Equa- tion 8 calculates the color and Equation 9 the shape dissimilarity between two regions. Equation 10 com- bines these two measures to calculate the dissimilarity score (or distance) of the two regions.
The matching process is to nd the matching sub-strings from the strings of all images in database and to calcu- late the dissimilarity score between every corresponding region pair in the found matching sub-trees. The dissim- ilarity score between two structure matching sub-trees
T andT0 is dened as
S
tree(TT0) = X
R2TR 0
2T 0
R$R 0
S
region(R R0): (11) The symbol `$' means the corresponding relation be- tween two structural matching sub-trees T and T0. Equation 11 means that the dissimilarity score between the two sub-trees is simply the summation of the dissim- ilarity scores between each corresponding region pair in the two sub-trees. The dissimilarity score for an image is the minimum dissimilarity score for a sub-tree in the image. Finally, the retrieval result is a name list of the images which contain the matching objects and is sorted by the smallest tree dissimilarity scores of all relation- ship matching images in ascending order.
5 Demonstration Program
5.1 Implementation
We implement our approach under Microsoft Windows NT Workstation 4.0 and NT Service Pack 3.0. The ma- chine we used is an AMD K6-200 PC with 128MB EDO- DRAM main memory and 512KB pipeline burst SRAM
second level cache. The development kit is Microsoft Visual C++ 5.0.
Some parts are programmed in assembly language or by Intel's MMX (MultiMedia eXtension) techniques to accelerate the algorithm.
5.2 The Thresholds in Our Experiment
The four threshold values TL, TG, TS, and TN in our experiment are listed in Table 2. Certainly, thresholds can be adjusted to make the segmentation better for an individual image.
Table 2: Threshold values.
Threshold Value
Local criterion thresholdTL 20 Global criterion thresholdTG 50 Similarity criterion thresholdTS 20 Non-signicant criterion thresholdTN 1000
5.3 Creation of Image Database
Our experimental image database contains 200 24-bit color images. These images are all photographed by Ko- dak DC-210 digital camera with its standard resolution and best quality settings. The experimental image di- mension is 320 pixels in width and 240 pixels in height.
The performance of our segmentation when creating the database with 200 24-bit color real world images is listed in Table 3.
Table 3: Performance of the segmentation.
Item Second
Maximum processing time on an image5 2.333 Minimum processing time on an image6 0.841 Average processing time on an image 1.265 Total processing time on 200 images 253.0230
Figure 4 shows one image of the image database with its segmentation result and relationship tree. The num- bers labeled in the nodes of the tree represent the labels which are assigned during segmentation. It is noticed that the regions in the same sub-tree are sorted by re- gion size in descending order.
5When processing Image086.
6When processing Image002.
(a)
(b)
(c)
Figure 4: Segmentation result and relationship tree ex- ample of wall decoration image. (a) The original image.
(b) The segmentation result. (c) The relationship tree.
6 Experimental Result
We design the experiment on our retrieval system by querying 10 objects and retrieving some images. For each query object, the images containing the same ob- ject are determined by human eye as the ground truth.
After the ground truth is determined, we apply our retrieval system to obtain a list of similar images. The length of this list can be determined by users. For each query, the e ciency of retrieval L5] for a given list of lengthLis dened as the following:
L=
N
S
NT
if NT L
N
S
L
if NT >L (12) whereNS is the number of the similar images retrieved in the result list, and NT is the number of the ground truth images for the query object. Each of the ten ex- perimental queries is respectively made at four dierent lists of lengthsL= 51015and 20.
The retrieval results of four example queries are listed in Table 4. This table just lists the numbers of the
rst twenty retrieval images for each query, because the
longest length of retrieval list is twenty. The retrieval e ciency of the ten queries at L = 51015 and 20 is shown in Table 5. Besides, the original images of the four query objects are shown in Figure 5.
In our experiment, the time spent by every query is less than one second. This time is determined by the size and structure of the database. Our experiment database does not have any special structure, and the retrieval is sequential.
The retrieval e ciency of query object 1 is not high, because it is a one-region object. Besides, the relation- ship tree of query object 1 is a simple one-node tree and the object region is very common. This results in matching with each region node in every database image. However the query object 2 has more special shape, and the retrieval e ciency is high. The reason for misdetection and false-alarm in queries 2 to 4 is the segmentation. The segmentation of some ground truth images is not similar to the query object images, es- pecially when relationship trees are dierent. Hence, these images can not be retrieved. The re ection and light condition in images can in uence the segmenta- tion results. Additionally when the sizes of the objects are much bigger or much smaller than that of the query object, the segmentation results are also dierent. The results for the more complicated query images 3 and 4 are quite good. The ranks 1 to 4 for query objects 3 and 4 are shown in Figures 6 and 7 respectively.
Table 4: Retrieval results of queries 1 to 4.
Rank Query 1 Query 2 Query 3 Query 4
1 062 *7 029 * 168 * 157 *
2 192 028 * 164 * 159 *
3 200 * 027 * 163 * 158 *
4 009 116 * 167 * 060
5 059 197 * 162 * 136 *
6 067 * 026 * 082 160 *
7 144 121 041 * 094 *
8 151 043 095 138 *
9 196 120 039 * 161 *
10 089 182 165 * 165
11 150 100 135 050
12 173 144 040 * 049
13 141 065 140 051
14 016 064 139 132
15 153 119 112 154 *
16 142 044 114 022
17 066 080 113 178
18 169 107 049 155 *
19 088 066 068 179
20 097 158 070 176
7 *: denotes similar images
Figure 5: Images of the query objects 1 to 4. Query objects are enclosed by red curves.
Figure 6: Images of rank 1 to 4 for query object 3.
Figure 7: Images of rank 1 to 4 for query object 4.
Table 5: Retrieval e ciency of ten queries at L = 51015and 20.
Query NT L= 5 L= 10 L= 15 L= 20
1 5 0.40 0.60 0.60 0.60
2 6 1 1 1 1
3 6 0.60 0.50 0.66 0.66
4 11 0.80 0.60 0.81 0.81
5 10 1 0.80 0.90 0.90
6 12 0.80 0.70 0.75 0.83
7 14 1 1 1 1
8 17 0.80 0.80 0.60 0.58
9 10 0.80 0.80 1 1
10 14 0.60 0.80 0.78 0.78
Average - 0.78 0.76 0.81 0.81
7 Conclusions and Future Work
The idea of combining a color segmentation with the cre- ation of a hierarchical relationship tree and the use of the corresponding tree-matching method leads to an image retrieval system that has a better retrieval e ciency than those systems which only use region information.
From the experiment, our approach has good retrieval e ciency when the region relationships of query objects are slightly complex. An improvement for our system is to use Color Coherence Vectors (CCV) 8] which provide more information regarding the spatial relationships of the image objects. Instead of designing the database as a continuous sequence of relationship trees, it is more e cient to use a higher level tree structure. This is es- pecially important for huge databases. A disadvantage of our algorithm is that the retrieval process relies on exact tree matching. We can calculate the distance be- tween two dierent trees by counting the number of re- label, delete, or insert operations for a node when we transfer a tree into another tree. To enable inexact matching we can also accept trees for solutions whose distance measure to the tree of the query image is be- low a denite thresholdTD. If we precompute pairwise distances between trees and also consider the smallest actual distance calculated, we are also able to eliminate trees which can not contribute to the solution 11]. We can further consider sibling relationships.
We are currently experimenting with an image database of 550 images and we also include implementation of in- exact or fuzzy matching.
Acknowledgments
This research was supported by the National Science Council of Taiwan, R.O.C., under Grants NSC 88-2213-
E-002-031 and NSC 86-2212-E-002-025, by Mechanical Industry Research Laboratories, Industrial Technology Research Institute, under Grant MIRL 873K67BN3, by the EeRise Corporation, Tekom Technologies, and Ulead Systems.
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