Census transformation

The Census Transform (CT) (Engl. Census Transform ) proposed by Zabih and Woodfill and calculated for each square pixel area of an image a bit string as a signature.

Thereby, in particular on the Hamming distance strings bit fast matching portions of the images are determined of the - for example, for generating a disparity map as a preliminary step for determining the optical flow ( optical flow ) or a stereo disparity ( stereo matching ) of time following or images captured at the same time.

algorithm

The gray value of the central pixel is compared individually with its neighbors (number N ) and the result (N × 1 bit) is saved as a number (bit string) - with the bit "0" being a value greater and the bit "1" being a value identifies less than or equal to the gray value of the central pixel. Usually a 3 × 3 environment is considered and the trivial comparison with itself is omitted (3 × 3 - 1 = 8 bits = 1 byte). However, the consideration of a 5 × 5 environment is also common (5 × 5 - 1 = 24 bits).

The order of the result bits is arbitrary (but fixed) and can, for example, be arranged clockwise.

${\displaystyle \mathbf {F} ={\begin{bmatrix}1&2&3\\8&C&4\\7&6&5\end{bmatrix}}}$

This creates a signature vector (e.g. "11001011" in a 3x3 environment) for the central pixel, which can be compared with other signature vectors.

Trivalent census transformation

The census transformation proposed by Zabih and Woodfill was extended by Stein by a parameter , whereby similar pixels can be represented (and thus a certain blurring or noise is tolerated). This creates a 3-valued ( three-moded ) census transformation, which is shown here in the definition chosen by Stein together with an example: ${\displaystyle \epsilon }$

${\displaystyle \xi (P,P')={\begin{cases}0,&{\text{wenn }}P-P'>\epsilon \\1,&{\text{wenn }}|P-P'|\leq \epsilon \\2,&{\text{wenn }}P'-P>\epsilon \end{cases}}\qquad {\begin{array}{|c|c||c|}\hline 124&74&32\\\hline 124&64&18\\\hline 157&116&84\\\hline \end{array}}\longrightarrow {\begin{array}{|c|c|c|}\hline 2&1&0\\\hline 2&x&0\\\hline 2&2&2\\\hline \end{array}}\longrightarrow 21002222}$

In the case of the three-value census transformation, two bits are required, which doubles the length of the comparison vector.

Modified Census Transformation

On the other hand, in the modified census transformation ( modified CT , MCT) proposed for the first time by Fröba and Ernst, the environment (neighbors and central pixels) is compared with the mean value of the 3 × 3 environment. As a result, the filter response of each pixel has one bit more (9 or 25 bits).

properties

• hardly dependent on fluctuations in brightness (exposure time, regional shadows)
• distinguishes between rotation and mirroring
• local filter
• Loss of information (i.e. the image cannot be reconstructed from the filter response)

Applications

The census transformation can be used to calculate the optical flow ( feature tracking ), for image segmentation or for face recognition . Its concept is similar to the BRIEF features (a descriptor) and is used several times in the calculation of Local Binary Patterns (LBP).

Individual evidence

1. ↑ ZABIH, Ramin; WOODFILL, John. Non-parametric local transforms for computing visual correspondence. In: European conference on computer vision. Springer, Berlin, Heidelberg, 1994. pp. 151-158. doi : 10.1007 / BFb0028345
2. ↑ PEÑA, Dexmont; SUTHERLAND, Alistair. Non-parametric image transforms for sparse disparity maps. In: Machine Vision Applications (MVA), 14th IAPR International Conference on. IEEE, 2015. pp. 291-294. doi : 10.1109 / MVA.2015.7153188

swell

• Ramin Zabih, John Woodfill: Non-parametric local transforms for computing visual correspondence . In: Jan-Olof Eklundh (Ed.): Computer Vision - ECCV '94 . tape 801 . Springer-Verlag, Berlin / Heidelberg, ISBN 3-540-57957-5 , pp. 151-158 , doi : 10.1007 / BFb0028345 .
• Fridtjof Stein: Efficient Computation of Optical Flow Using the Census Transform . In: Pattern Recognition . tape 3175 . Springer, Berlin / Heidelberg 2004, ISBN 978-3-540-22945-2 , pp. 79-86 , doi : 10.1007 / 978-3-540-28649-3_10 .
• Bernhard FRÖBA, Andreas ERNST: Face Detection with the Modified Census Transform . In: Proceedings of the Sixth IEEE International Conference on Automatic Face and Gesture Recognition (FGR'04) . doi : 10.1109 / AFGR.2004.1301514 .
• Zucheul LEE, Jason JUANG, Truong Q. NGUYEN: Local Disparity Estimation With Three-Moded Cross Census and Advanced Support Weight . In: IEEE Transactions on Multimedia . tape 15 , no. 8 , 2013, p. 1855–1864 , doi : 10.1109 / TMM.2013.2270456 .
• CYGANEK, Bogusław: Comparison of Nonparametric Transformations and Bit Vector Matching for Stereo Correlation In: Klette R., Žunić J. (eds) Combinatorial Image Analysis. IWCIA 2004. In: Lecture Notes in Computer Science (LNCS) . tape 3322 , 2004, pp. 534-547 , doi : 10.1007 / 978-3-540-30503-3_39 .

• Michael Calonder, Vincent Lepetit, Christoph Strecha, Pascal Fua: BRIEF: Binary Robust Independent Elementary Features . In: Computer Vision - ECCV 2010 . tape 6314 . Springer, Berlin / Heidelberg 2010, ISBN 978-3-642-15560-4 , p. 778-792 , doi : 10.1007 / 978-3-642-15561-1_56 ( online ).