【CBIR】【Color】颜色矩（Color Moment）1

颜色矩（Color Moment）

Stricker和Orengo提出了颜色矩的方法[1]，颜色矩是一种简单有效的颜色特征表示方法，有一阶矩(均值,mean)、二阶矩(方差,viarance)和三阶矩(斜度,skewness)等，由于颜色信息主要分布于低阶矩中，所以用一阶矩，二阶矩和三阶矩足以表达图像的颜色分布，颜色矩已证明可有效地表示图像中的颜色分布，该方法的优点在于：不需要颜色空间量化，特征向量维数低；但实验发现该方法的检索效率比较低，因而在实际应用中往往用来过滤图像以缩小检索范围。

[1]Stricker, Markus A., and Markus Orengo. "Similarity of color images." IS&T/SPIE's Symposium on Electronic Imaging: Science & Technology . International Society for Optics and Photonics, 1995.

From WiKi

Color moments are scaling and rotation invariant. It is usually the case that only the first three color moments are used as features in image retrieval applications as most of the color distribution information is contained in the low-order moments.^[1] Since color moments encode both shape and color information they are a good feature to use under changing lighting conditions, but they cannot handle occlusion very successfully.^[2] Color moments can be computed for any color model. Three color moments are computed per channel (e.g. 9 moments if the color model is RGB and 12 moments if the color model is CMYK). Computing color moments is done in the same way as computing moments of a probability distribution.

Mean[edit]

Main article:  Mean

The first color moment can be interpreted as the average color in the image, and it can be calculated by using the following formula

where N is the number of pixels in the image and  is the value of the j-th pixel of the image at the i-th color channel.

Standard Deviation[edit]

Main article:  Standard_deviation

The second color moment is the standard deviation, which is obtained by taking the square root of the variance of the color distribution.

where  is the mean value, or first color moment, for the i-th color channel of the image.

Skewness[edit]

Main article:  Skewness

The third color moment is the skewness. It measures how asymmetric the color distribution is, and thus it gives information about the shape of the color distribution. Skewness can be computed with the following formula:

Kurtosis[edit]

Main article:  Kurtosis

Kurtosis is the fourth color moment, and, similarly to skewness, it provides information about the shape of the color distribution. More specifically, kurtosis is a measure of how flat or tall the distribution is in comparison to normal distribution.

Higher-order color moments[edit]

Main article:  Moment_(mathematics)#Higher_moments

Higher-order color moments are usually not part of the color moments feature set in image retrieval tasks as they require more data in order to obtain a good estimate of their value, and also the lower-order moments generally provide enough information.

Color indexing[edit]

Color indexing is the main application of color moments. Images can be indexed, and the index will contain the computed color moments. Then, if someone has a particular image and wants to find similar images in the database, the color moments of the image of interest will also be computed. After that the following function will be used in order to compute a similarity score between the image of interest and all the images in the database:

where:

• H and I are the color distributions of the two images that are being compared
• i is the channel index and r is the total number of channels
•  and  are the first order moments computed for the image distributions.
•  and  are the second order moments computed for the image distributions.
• s_i^1 and s_i^2 are the third order moments computed for the image distributions.
• , , and  are weights, specified by the user, for each of the three color moments used.

Finally, the images in the database will be ranked according to the computed similarity score with the image of interest, and the database images with the lowest  value should be retrieved. "A retrieval based on  may produce false positives because the index contains no information about the correlation between the color channels". ^[3]

References[edit]

1. Jump up^ Hui Yu, Mingjing Li, Hong-Jiang Zhang, Jufu Feng. "Color Texture Moments for Content-Based Image Retrieval". Proc. IEEE Intl Conf. on Image Processing, pp. 929-932, Sep. 2002
2. Jump up^ Xiaoyin Duanmu. "Image Retrieval Using Color Moment Invariant". Seventh International Conference on Information Technology, pp. 200-203, 2010.
3. ^ Jump up to:^a b M. Stricker and M. Orengo. "Similarity of Color Images". In SPIE Conference on Storage and Retrieval for Image and Video Databases III, volume 2420, pp. 381-392, Feb. 1995.
4. Jump up^ V. Chitkara, M.A. Nascimento, and C. Mastaller. "Content-Based Image Retrieval Using Binary Signatures". In Technical Report TR-00-18, Department of Computing Science, University of Alberta, 2000
5. Jump up^ Noah Keen. "Color Moments". Feb. 2005

Sample