We implement an algorithm for compressing an image of a GMRF texture
to approximately 1 bit/pixel from the original 8 bits/pixel image.
The procedure is to find the MLE of the given image, (e.g. this
results in a total of eleven 32-bit floating point numbers for the 4th
order model). We then use a Max Quantizer, with characteristics given
in [33], to quantize the residual to 1-bit. The quantized
structure has a total of 
bits. To reconstruct the image from
its texture parameters and 1-bit Max quantization, we use an algorithm
similar to Algorithm 2. Instead of synthesizing a
texture from Gaussian noise, we begin with the 1-bit quantized array.
Compressed textures for a 4th order model are shown in
Figures 6 and 7. A result using the higher order model
is shown in Figure 8.
The noise sequence 
is generated as follows:
where
and the 
is given in (13).
We estimate the residual as:
and 
is the sequence which is Max quantized.
The image reconstruction from parameters and quantization 
is as follows:
where
and 
is given in (13); 
is
given in (14).
The texture compression algorithm has the same time complexity and scalability characteristics as Algorithm 4. The image reconstruction algorithm has the same complexities as Algorithm 2. Hence these algorithms scale with image size n and number of processors p.
This algorithm could be used to compress the textures regions in natural images as part of segmentation based compression schemes discussed in [27]. Compression factors of 35 have been obtained for the standard Lena and F-16 images, with no visible degradations. Compression factors of 80 have been shown to be feasible when small degradations are permitted in image reconstruction.
