prof. heikki kälviäinen lappeenranta university of technolog y, finland

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LAPPEENRANTA UNIVERSITY OF TECHNOLOGYTHE DEPARTMENT OF INFORMATION TECHNOLOGY

Prof. Heikki KälviäinenProf. Heikki KälviäinenLappeenranta University of Lappeenranta University of

TechnologTechnology, Finlandy, Finland

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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

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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


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.

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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.

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Compression, Similarity, Matching, Object Recognition

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Feature extraction using Hough Transform

End-pointdetection

Encoding

Input Image

Feature Image

Hough Transform

FEATURE EXTRACTION

Line parameters

Reconstruction

Feature File

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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

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LAPPEENRANTA UNIVERSITY OF TECHNOLOGYTHE DEPARTMENT OF INFORMATION TECHNOLOGY Hough

Transform(SHT)

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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.

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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.

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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.

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1. Infinite scope parameter space.

2. Arbitrarily high parameter resolution.

3. High computational speed.

4. Small storage.

Advances of RHT over SHT

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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.

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More complex images

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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.

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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.

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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.

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Detecting partially deformed motion

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Detecting multiple objects

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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

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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.

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Pure classes with mixed pixels and outliers

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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.

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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.

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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

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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

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Context-based compression

Output Image

Featureextraction

Compression Decompression

COMPRESSION DECOMPRESSION

Input Image

Feature File

vecto

r

Filtering

raster

data

RetrievalAnalysisEditing

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Feature extraction using Hough transform

End-pointdetection

Encoding

Input Image

Feature Image

Hough Transform

FEATURE EXTRACTION

Line parameters

Reconstruction

Feature File

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Feature-based context modeling (HTC)

Output Image

Featureextraction

Coding Decoding


Input Image

Contextmodelling

Contextmodelling

Feature File

Reconstruction

Feature Image Feature Imageras

ter da

tave

ctor

JBIG compression JBIG decompression

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Feature-based filtering: Near-lossless compression system (HTF-JBIG)

Output Image

Featureextraction

JBIGcompression

JBIGdecompression


Input Image

Feature File

Feature Image

rast

er d

ata

vect

orFiltering

OPTIONAL

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Noise removal procedure

Output Image

Isolatedpixel

extraction

XOR

Input image

Feature Image

XOR

NOISE REMOVAL

Isolated mismatch pixels

Mismatch pixels

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Filtering procedure

Output Image

Input imageFeature Image

FILTERING

Dilation

Erosion

Noiseremoval

Noiseremoval

Noiseremoval

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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)

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Original, filtered, and difference images

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Test images: Bolt, Plan, House

Chair, Module, Plus

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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

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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

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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

)

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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?



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



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.



Generated 3D images: query images



Generated 3D images: test database

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Symbol library: noisy and rotated test images

prof. heikki kälviäinen lappeenranta university of technolog y, finland

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