Autoregressive Models for Texture Images

Convolutional Autoregressive Model

The weights of a convolution kernel are optimized to best predict the center pixel of each window, $\mathbf{X}_i$. The weights of the kernel are constrained based on distance from the center, e.g. the first three weights, ${w_0, w_1, w_2}$, correspond to indices in the kernel with distances ${1, \sqrt{2}, 2}$ from the center pixel. Convolution is the Frobenius inner product between the image and kernel, optimized to best predict the center pixel, $c_i \in \mathbf{X}$.

Multiple convolution kernels are learned to account for various spatial scales in image. This is learned by dialating the kernel.

Datasets

Kylberg textures. Examples of each class:

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Results

The top row is for the model here. The additional rows (CNNs with millions of parameters) were described in Andrearczyk & Whelan, 2016.

	Kylberg	CUReT	DTD	kth-tips-2b	ImNet-T	ImNet-S1	ImNet-S2	ImageNet
ConvAR	99.6	93.06		60.36
T-CNN-1 (20.8)	89.5 ± 1.0	97.0 ± 1.0	20.6 ± 1.4	45.7 ± 1.2	42.7	34.9	42.1	13.2
T-CNN-2 (22.1)	99.2 ± 0.3	98.2 ± 0.6	24.6 ± 1.0	47.3 ± 2.0	62.9	59.6	70.2	39.7
T-CNN-3 (23.4)	99.2 ± 0.2	98.1 ± 1.0	27.8 ± 1.2	48.7 ± 1.3	71.1	69.4	78.6	51.2
T-CNN-4 (24.7)	98.8 ± 0.2	97.8 ± 0.9	25.4 ± 1.3	47.2 ± 1.4	71.1	69.4	76.9	28.6
T-CNN-5 (25.1)	98.1 ± 0.4	97.1 ± 1.2	19.1 ± 1.8	45.9 ± 1.5	65.8	54.7	72.1	24.6
AlexNet (60.9)	98.9 ± 0.3	98.7 ± 0.6	22.7 ± 1.3	47.6 ± 1.4	66.3	65.7	73.1	57.1

Citations

Mao, J., & Jain, A. K. (1992). Texture classification and segmentation using multiresolution simultaneous autoregressive models. Pattern recognition, 25(2), 173-188.

Kylberg, G. (2011). Kylberg texture dataset v. 1.0. Centre for Image Analysis, Swedish University of Agricultural Sciences and Uppsala University.

Andrearczyk, V., & Whelan, P. F. (2016). Using filter banks in Convolutional Neural Networks for texture classification. Pattern Recognition Letters, 84, 63–69. https://doi.org/10.1016/j.patrec.2016.08.016