texture matching between patches of an image
The mean and standard deviation are two measurements of a distribution. Others you could also use are higher order moments like 'skewness' (how skewed the distribution is) and 'kurtosis' (how 'peaky' the distribution is).

However, what I would try is a histogram of the values for each of the channels. For example, if you used a histogram with 16 bins, you would get a feature vector with 48 values. The histogram bin values can be thought of as a descriptor of the distribution.

To account for changes in brightness, you need to introduce some illumination invariance. Already the LAB colour-space splits the image into luminance (L) and color (AB) channels. To achieve illumination invariance I would normalise the L channel histogram values using the norm of whatever measure you are using (in this case, euclidean distance, it would be the l2 norm). Normalising the A or B channels is probably not necessary. The normalisation accounts for any linear changes in luminance.

Depending on the images, you could also add vectors like:


histogram of oriented gradients (HOG)
histogram of connected components (make B/W then count how many pixels are white in the 8 connected neighbours)
k-means clustering of LAB values to get k centre LAB values which you can compare to other images.


and so on.