View
219
Download
0
Embed Size (px)
Citation preview
1
LAPPEENRANTA UNIVERSITY OF TECHNOLOGYTHE DEPARTMENT OF INFORMATION TECHNOLOGY
Prof. Heikki KälviäinenProf. Heikki KälviäinenLappeenranta University of Lappeenranta University of
TechnologTechnology, Finlandy, Finland
2
LAPPEENRANTA UNIVERSITY OF TECHNOLOGYTHE DEPARTMENT OF INFORMATION TECHNOLOGY
Applications of Hough Transform for Image Processing and Analysis
Heikki Kälviäinen
Professor, Computer Science
*Machine Vision and Pattern Recognition LaboratoryDepartment of Information Technology
Lappeenranta University of Technology (LUT), FINLAND [email protected] http/www.lut.fi/~kalviai
**Centre for Vision, Speech, and Signal Processing (CVSSP)University of Surrey, UNITED KINGDOM
3
LAPPEENRANTA UNIVERSITY OF TECHNOLOGYTHE DEPARTMENT OF INFORMATION TECHNOLOGY
L ondonBer lin
Mosc ow
S t.Petersburg
Tall inn
Lappeenranta
Os lo
S tockholm
Hels ink i
July 17, 2000 ICVGIP 2000, December 20-22, 2000, Bangalore, India
LAPPEENRANTA UNIVERSITY OF TECHNOLOGYTHE DEPARTMENT OF INFORMATION TECHNOLOGY
Hough Transform
• Shape detection– Lines, circles, ellipses, arbitrary shapes.
• Motion detection and estimation– Simple and robust methods in 2D.
• Mixed pixel classification– Large data sets of mixed pixels.
• Image compression– Compression and better image quality.
• Image databases– Matching of images.
5
LAPPEENRANTA UNIVERSITY OF TECHNOLOGYTHE DEPARTMENT OF INFORMATION TECHNOLOGY
Hough surveys and comparisons
• J. Illingworth, J. Kittler, A Survey of the Hough Transform, Computer Vision, Graphics, and Image Processing, 1988, vol. 44, pp. 87-116.
• V.F. Leavers, Survey: Which Hough Transform, CVGIP Image Understanding, 1993, vol. 58, no. 2, pp. 250‑264.
• H. Kälviäinen , P. Hirvonen, L. Xu, E. Oja, Probabilistic, non-probabilistic Hough transforms: overview and comparisons. Image, Vision Computing, 1995, vol. 13, no. 4, pp. 239‑251.
• N. Kiryati, H. Kälviäinen, S. Alaoutinen, Randomized or Probabilistic Hough Transform: Unified Performance Evaluation, Pattern Recognition Letters, 2000, vol. 21, nos. 13-14, pp. 1157-1164.
6
LAPPEENRANTA UNIVERSITY OF TECHNOLOGYTHE DEPARTMENT OF INFORMATION TECHNOLOGY
7
LAPPEENRANTA UNIVERSITY OF TECHNOLOGYTHE DEPARTMENT OF INFORMATION TECHNOLOGY
Compression, Similarity, Matching, Object Recognition
8
LAPPEENRANTA UNIVERSITY OF TECHNOLOGYTHE DEPARTMENT OF INFORMATION TECHNOLOGY
Feature extraction using Hough Transform
End-pointdetection
Encoding
Input Image
Feature Image
Hough Transform
FEATURE EXTRACTION
Line parameters
Reconstruction
Feature File
9
LAPPEENRANTA UNIVERSITY OF TECHNOLOGYTHE DEPARTMENT OF INFORMATION TECHNOLOGY
Hough Transform• A method for global feature extraction:
– y = a x + b => b = -x a + y.– For each pixel (x,y) compute a curve b = -x a + b into the parameter space.– Alternatively the normal presentation of a line:
• Hough Transform detects sets of pixels which represent geometric primitives in a binary image.
• Lines, circles, ellipses, arbitrary shapes, etc.
• Tolerant to noise and distortions in an image, but traditional versions suffer from problems with time and space complexities.
• New variants: probabilistic and deterministic Hough Transforms.
sincos yx
10
LAPPEENRANTA UNIVERSITY OF TECHNOLOGYTHE DEPARTMENT OF INFORMATION TECHNOLOGY Hough
Transform(SHT)
11
LAPPEENRANTA UNIVERSITY OF TECHNOLOGYTHE DEPARTMENT OF INFORMATION TECHNOLOGY
Kernel of the Hough Transform
1. Create the set D of all edge points in a binary picture.
2. Transform each point in the set D into a parameterized curve in the parameter space.
3. Increment the cells in the parameter space determined by the parametric curve.
4. Detect local maxima in the accumulator array. Each local maximum may correspond to a parametric curve in the image space.
5. Extract the curve segments using the knowledge of the maximum positions.
12
LAPPEENRANTA UNIVERSITY OF TECHNOLOGYTHE DEPARTMENT OF INFORMATION TECHNOLOGY
Randomized Hough Transform (RHT)• Developed in Lappeenranta Universityof Technology (LUT),FINLAND.• Xu, L., Oja, E., Kultanen, P, ”A New Curve Detection Method: Randomized Hough Transform (RHT), Pattern Recognition Letters, vol. 11, no. 5., 1990, pp. 331-338.
13
LAPPEENRANTA UNIVERSITY OF TECHNOLOGYTHE DEPARTMENT OF INFORMATION TECHNOLOGY
Kernel of the Randomized Hough Transform (RHT)
1. Create the set D of all edge points in a binary edge picture.
2. Select a point pair (d_i, d_j) randomly from the set D.
3. If the points do not satisfy the predefined distance limits, go to Step 2; otherwise continue to Step 4.
4. Solve the parameter space point (a, b) using the curve equation with the points (d_i, d_j).
5. Accumulate the cell A(a, b) in the accumulator space.
6. If the A(a, b) is equal to the threshold t, the parameters a and b describe the parameters of the detected curve; otherwise continue to Step 2.
14
LAPPEENRANTA UNIVERSITY OF TECHNOLOGYTHE DEPARTMENT OF INFORMATION TECHNOLOGY
1. Infinite scope parameter space.
2. Arbitrarily high parameter resolution.
3. High computational speed.
4. Small storage.
Advances of RHT over SHT
15
LAPPEENRANTA UNIVERSITY OF TECHNOLOGYTHE DEPARTMENT OF INFORMATION TECHNOLOGY
RHT Extensions
Kälviäinen, H.,Hirvonen, P.,
Xu, L.,Oja, E.,
”Probabilistic and Non-probabilistic
Hough Transforms:Overview andComparisons,”
Image and VisionComputing,
Vol. 13, No. 4, 1995,pp. 239-251.
16
LAPPEENRANTA UNIVERSITY OF TECHNOLOGYTHE DEPARTMENT OF INFORMATION TECHNOLOGY
More complex images
17
LAPPEENRANTA UNIVERSITY OF TECHNOLOGYTHE DEPARTMENT OF INFORMATION TECHNOLOGY
Motion Detection by RHT (MDRHT)
• 2D motion detection as sets of moving pixels.• A set of moving edge points is assumed to illustrate a
moving object frame by frame. • The majority of the points are assumed to move rigidly. • Two moving points is the simplest version. • Extensions: (a) rotation and scaling, (b) exploiting gradient
information of each edge point, (c) using three or more moving points as evidence, and (d) detecting multiple moving objects.
18
LAPPEENRANTA UNIVERSITY OF TECHNOLOGYTHE DEPARTMENT OF INFORMATION TECHNOLOGY
Motion Detection Using RHT (MDRHT)
Kälviäinen, H., ”Motion Detection
Using the Randomized Hough Transform (RHT): Exploiting
Gradient Information and
Detecting Multiple Moving Objects,” IEE Proceedings---Vision, Image and Signal Processing,
Vol. 143, No. 6, 1996, pp. 361-369.
19
LAPPEENRANTA UNIVERSITY OF TECHNOLOGYTHE DEPARTMENT OF INFORMATION TECHNOLOGY
Kernel of Motion Detection Using Randomized Hough Transform (MDRHT)
1. Create the sets B and C of edge points, each in one of two consecutive frames.
2. Select point pairs (b_i,b_j) and (c_i,c_j) randomly from sets B and C, respectively.
3. If the point pairs correspond, calculate the x- and y-translations dx=c_{ix}-b_{ix} and dy=c_{iy}-b_{iy} and go to Step 4; otherwise, go to Step 2.
4. Accumulate the cell A(dx,dy). 5. If the A(dx,dy) is equal to the threshold t, motion (dx,dy) has
been detected; otherwise, go to Step 2.
20
LAPPEENRANTA UNIVERSITY OF TECHNOLOGYTHE DEPARTMENT OF INFORMATION TECHNOLOGY
21
LAPPEENRANTA UNIVERSITY OF TECHNOLOGYTHE DEPARTMENT OF INFORMATION TECHNOLOGY
Detecting partially deformed motion
22
LAPPEENRANTA UNIVERSITY OF TECHNOLOGYTHE DEPARTMENT OF INFORMATION TECHNOLOGY
Detecting multiple objects
23
LAPPEENRANTA UNIVERSITY OF TECHNOLOGYTHE DEPARTMENT OF INFORMATION TECHNOLOGY
Mixed pixel classification
• What is in a mixed pixel?: The identification of the constituent components and their proportions in a mixed pixel.
• For applications with large pixels and/or with large sets of mixed pixels (remote sensing).
• Bosdogianni, P.*, Kälviäinen, H., Petrou, M.*, and Kittler, J.*, Robust Unmixing of Large Sets of Mixed Pixels, Pattern Recognition Letters, Vol. 18, 1997, pp. 415-424. *Centre for Vision, Speech, and Signal Processing (CVSSP), University of Surrey, UK
24
LAPPEENRANTA UNIVERSITY OF TECHNOLOGYTHE DEPARTMENT OF INFORMATION TECHNOLOGY
Linear mixing model
• w = ax + by + cz
– w: reflectance of a mixed pixel (known).
– x, y,z: reflectances of pixels that belong to three different pure classes (known).
– a,b,c: proportions of the pure classes present in the mixed pixel (unknown).
• Assuming that a+b+c=1, we obtain w - z = (x-z)a + (y-z)b.
25
LAPPEENRANTA UNIVERSITY OF TECHNOLOGYTHE DEPARTMENT OF INFORMATION TECHNOLOGY
Pure classes with mixed pixels and outliers
26
LAPPEENRANTA UNIVERSITY OF TECHNOLOGYTHE DEPARTMENT OF INFORMATION TECHNOLOGY
Mixel pixel classification by RHT
1. Select one quadruple (x_1,y_1,z_1,w_1) from the first band and another quadruple (x_2,y_2,z_2,w_2) from the second band of the same pixel randomly.
2. Using two selected quadruples compute one (a,b) value in the parametric (a,b) space by
w - z = (x-z)a + (y-z)b.
3. Accumulate the cell A(a,b) in the accumulator space.4. If the A(a, b) is equal to the threshold t, the parameters a
and b describe the parameters of the detected proportions; otherwise continue to Step 1.
27
LAPPEENRANTA UNIVERSITY OF TECHNOLOGYTHE DEPARTMENT OF INFORMATION TECHNOLOGY
Advantages and questions
• Fast computation and the small accumulator => the use of large datasets possible.
• Randomized Hough Transform needs less CPU time and memory than Standard Hough Transform when datasets are large.
• Hough methods are more robust than classical Least Square Methods in the presence of outliers.
• How high threshold? => e.g. with adaptive termination rules like a variable threshold according to data.
• More accuracy? => e.g. by averaging several RHT processes.
28
LAPPEENRANTA UNIVERSITY OF TECHNOLOGYTHE DEPARTMENT OF INFORMATION TECHNOLOGY
Image Compression with Hough Feature Extraction
*P. Fränti, *E. Ageenko, S. Kukkonen, H. Kälviäinen,
Using Hough Transform for Context-based Image Compression in Hybrid Raster/Vector Applications,
Journal Of Electrical Imaging, 2002, vol. 11, no. 2, pp. 236-245
*Department of Computer Science
University of Joensuu, Finland
29
LAPPEENRANTA UNIVERSITY OF TECHNOLOGYTHE DEPARTMENT OF INFORMATION TECHNOLOGY
Goal: To use vector features in context-based compression of binary images
• Context-based compression• Feature extraction using Hough transform • Feature-based context modeling • Feature-based filtering • Results • Conclusions
30
LAPPEENRANTA UNIVERSITY OF TECHNOLOGYTHE DEPARTMENT OF INFORMATION TECHNOLOGY
Context-based compression
Output Image
Featureextraction
Compression Decompression
COMPRESSION DECOMPRESSION
Input Image
Feature File
vecto
r
Filtering
raster
data
RetrievalAnalysisEditing
31
LAPPEENRANTA UNIVERSITY OF TECHNOLOGYTHE DEPARTMENT OF INFORMATION TECHNOLOGY
Feature extraction using Hough transform
End-pointdetection
Encoding
Input Image
Feature Image
Hough Transform
FEATURE EXTRACTION
Line parameters
Reconstruction
Feature File
32
LAPPEENRANTA UNIVERSITY OF TECHNOLOGYTHE DEPARTMENT OF INFORMATION TECHNOLOGY
Feature-based context modeling (HTC)
Output Image
Featureextraction
Coding Decoding
COMPRESSION DECOMPRESSION
Input Image
Contextmodelling
Contextmodelling
Feature File
Reconstruction
Feature Image Feature Imageras
ter da
tave
ctor
JBIG compression JBIG decompression
33
LAPPEENRANTA UNIVERSITY OF TECHNOLOGYTHE DEPARTMENT OF INFORMATION TECHNOLOGY
Feature-based filtering: Near-lossless compression system (HTF-JBIG)
Output Image
Featureextraction
JBIGcompression
JBIGdecompression
COMPRESSION DECOMPRESSION
Input Image
Feature File
Feature Image
rast
er d
ata
vect
orFiltering
OPTIONAL
34
LAPPEENRANTA UNIVERSITY OF TECHNOLOGYTHE DEPARTMENT OF INFORMATION TECHNOLOGY
Noise removal procedure
Output Image
Isolatedpixel
extraction
XOR
Input image
Feature Image
XOR
NOISE REMOVAL
Isolated mismatch pixels
Mismatch pixels
35
LAPPEENRANTA UNIVERSITY OF TECHNOLOGYTHE DEPARTMENT OF INFORMATION TECHNOLOGY
Filtering procedure
Output Image
Input imageFeature Image
FILTERING
Dilation
Erosion
Noiseremoval
Noiseremoval
Noiseremoval
36
LAPPEENRANTA UNIVERSITY OF TECHNOLOGYTHE DEPARTMENT OF INFORMATION TECHNOLOGY
Results of the filtering procedure
FIRST STAGE SECOND STAGE THIRD STAGE
Input image Filtering result (1st) Filtering result (2nd) Filtering result (3rd)
Feature image Dilated feature image Eroded feature imageHough Transformimage
Mismatch pixels (1st) Mismatch pixels (2nd) Mismatch pixels (3rd)
Filtered pixels (1st) Filtered pixels (2nd) Filtered pixels (3rd)
37
LAPPEENRANTA UNIVERSITY OF TECHNOLOGYTHE DEPARTMENT OF INFORMATION TECHNOLOGY
Original, filtered, and difference images
38
LAPPEENRANTA UNIVERSITY OF TECHNOLOGYTHE DEPARTMENT OF INFORMATION TECHNOLOGY
Test images: Bolt, Plan, House
Chair, Module, Plus
39
LAPPEENRANTA UNIVERSITY OF TECHNOLOGYTHE DEPARTMENT OF INFORMATION TECHNOLOGY
Effects of the feature-based context modeling for the Bolt image
12,966 12,598 12,177 11,549 11,514
6,438
1,7344,512702
0
2,000
4,000
6,000
8,000
10,000
12,000
14,000
16,000
18,000
JBIG Hybrid: 117segments
Hybrid: 289segments
Hybrid: 752segments
Hybrid: 1073segments
Com
pres
sed
file
size
, by
tes
Raster data Vector data
40
LAPPEENRANTA UNIVERSITY OF TECHNOLOGYTHE DEPARTMENT OF INFORMATION TECHNOLOGY
Storage sizes in bytesImage Hybrid compression Filtering
onlyFiltering +
Hybrid vector raster
(JBIG)raster (HTC)
(HTF-JBIG)
(HTF-HTC)
BOLT 6,438 12,966 11,514 10,536 9,287
PLAN 2,370 5,098 4,578 4,325 3,786
HOUSE 13,398 15,688 13,961 13,336 11,553
CHAIR 16,710 52,384 50,140 51,529 48,023
MODULE 3,468 7,671 7,222 6,431 6,057
PLUS 5,268 17,609 17,132 16,273 15,739
TOTAL 47,652 111,416 104,547 102,430 94,445
41
LAPPEENRANTA UNIVERSITY OF TECHNOLOGYTHE DEPARTMENT OF INFORMATION TECHNOLOGY
Computation times of the HT-based compression
Compression
Compression1:27
Filtering2:05
Feature extraction1:46:28
Decompression
0:00
0:20
0:40
1:00
1:20
1:40
2:00
JBIG HTC HTF-JBIG
Tim
e (m
in:s
)
42
LAPPEENRANTA UNIVERSITY OF TECHNOLOGYTHE DEPARTMENT OF INFORMATION TECHNOLOGY
Conclusions
• Two methods proposed for improving compression performance– Feature image as side information for compression
– Feature-based filtering for removing noise
• Problems – Is an exact replica of the original image always needed?
– How to improve the quality of vectorizing?
July 17, 2000 ICVGIP 2000, December 20-22, 2000, Bangalore, India
LAPPEENRANTA UNIVERSITY OF TECHNOLOGYTHE DEPARTMENT OF INFORMATION TECHNOLOGY
Image Databases and Image Matching with Hough Features
*P. Fränti, A. Mednonogov, V. Kyrki, H. KälviäinenContent-Based Matching of Line-Drawing Images Using
Hough Transform International Journal on Document Analysis and
Recognition (IJDAR)2000, vol. 3, no. 2, pp. 117-124
*Department of Computer Science, University of Joensuu, Finland
July 17, 2000 ICVGIP 2000, December 20-22, 2000, Bangalore, India
LAPPEENRANTA UNIVERSITY OF TECHNOLOGYTHE DEPARTMENT OF INFORMATION TECHNOLOGY
Applications of Hough Transform for image databases
• Content-based matching of line-drawing images using Hough Transform.
• Similarity of images in image databases.
• Hough Transform as a feature extractor.– Translation-,
– rotation-, and
– scale-invariant
features from the accumulator matrix.
July 17, 2000 ICVGIP 2000, December 20-22, 2000, Bangalore, India
LAPPEENRANTA UNIVERSITY OF TECHNOLOGYTHE DEPARTMENT OF INFORMATION TECHNOLOGY
Generated 3D images: query images
July 17, 2000 ICVGIP 2000, December 20-22, 2000, Bangalore, India
LAPPEENRANTA UNIVERSITY OF TECHNOLOGYTHE DEPARTMENT OF INFORMATION TECHNOLOGY
Generated 3D images: test database
47
LAPPEENRANTA UNIVERSITY OF TECHNOLOGYTHE DEPARTMENT OF INFORMATION TECHNOLOGY
Symbol library: noisy and rotated test images