Santhana Krishnamachari

Multiresolution Gauss-Markov random field models for texture segmentation

This paper presents multiresolution models for Gauss-Markov random fields (GMRFs) with applications to texture segmentation. Coarser resolution sample fields are obtained by subsampling the sample field at fine resolution. Although the Markov property is lost under such resolution transformation, coarse resolution non-Markov random fields can be effectively approximated by Markov fields. We present two techniques to estimate the GMRF parameters at coarser resolutions from the fine resolution parameters, one by minimizing the Kullback-Leibler distance and another based on local conditional distribution invariance. We also allude to the fact that different GMRF parameters at the fine resolution can result in the same probability measure after subsampling and present the results for first- and second-order cases. We apply this multiresolution model to texture segmentation. Different texture regions in an image are modeled by GMRFs and the associated parameters are assumed to be known. Parameters at lower resolutions are estimated from the fine resolution parameters. The coarsest resolution data is first segmented and the segmentation results are propagated upward to the finer resolution. We use the iterated conditional mode (ICM) minimization at all resolutions. Our experiments with synthetic, Brodatz texture, and real satellite images show that the multiresolution technique results in a better segmentation and requires lesser computation than the single resolution algorithm.

Delineating buildings by grouping lines with MRFs

Traditionally, Markov random field (MRF) models have been used in low-level image analysis. The article presents an MRF-based scheme to perform object delineation. The proposed edge-based approach involves extracting straight lines from the edge map of an image. Then, an MRF model is used to group these lines to delineate buildings in aerial images.

GMRF models and wavelet decomposition for texture segmentation

A multichannel scheme for texture segmentation using Gauss Markov random fields (GMRF) is presented. We present a family of filters called Markov filters with a property that, when a homogeneous GMRF is filtered with these filters, the resulting output is also a GMRF. We use these filters to decompose images in a fashion similar to the wavelet decomposition, such that the individual subbands are also GMRFs. However, in wavelet decomposition, after filtering, the individual subbands are subsampled and Markov fields lose the Markov property when subsampled. We have shown in [Krishnamachari and Chellappa, 1995] that subsampled GMRFs can be efficiently approximated by Markov fields using the local conditional distribution invariance approximation. Hence individual subbands can be modeled by GMRFs. We have used this multichannel model to classify remote sensed imagery and to perform texture segmentation.

Multiresolution GMRF models for texture segmentation

A multiresolution model for Gauss Markov random fields (GMRF) is presented. Coarser resolution sample fields are obtained by either subsampling or local averaging the sample field at the fine resolution. Although Markovianity is lost under such resolution transformation, coarser resolution non-Markov random fields can be effectively approximated by Markov fields. We use a local conditional distribution invariance approximation, to estimate the parameters of the coarser resolution processes from the fine resolution parameters. This multiresolution model is used to perform texture segmentation.

An energy minimization approach to building detection in aerial images

An energy function based approach is presented to detect rectangular shapes in images. The proposed edge-based approach involves extracting straight lines from an edge map of the image. Then a Markov Random Field (MRF) is built on these lines. The energy function associated with the MRF can be construed as a measure of the conditional probability of observing the lines given the rectangular shapes (the positions and number of which are unknown) in the image and the minimization results in a maximum likelihood estimate. This approach, supplemented with some qualitative information about shadows and gradients, is used to detect rectangular buildings in real aerial images. Due to poor quality of the real images, only partial shapes are extracted in some cases. A modified deformable contour (snakes) based approach is then presented for completion of the partial shapes.<<ETX>>