Multiscale Structure Tensor for Improved Feature Extraction and Image Regularization


Regularization methods are used widely in image selective smoothing and edge preserving restoration of noisy images. Traditional methods utilize image gradients within regularization function for controlling the smoothing and can produce artifacts when noise levels are higher. In this paper, we consider a robust image adaptive exponent driven regularization for filtering noisy images with salient feature preservation. Our spatially adaptive variable exponent function depends on a continuous switch based on the eigenvalues of structure tensor which identifies noisy edges, and corners with higher accuracy. Structure tensor eigenvalues encode various image features and we consider a spatially varying continuous map which provides multiscale edge maps of natural images. By embedding the structure tensor-based exponent in a well-defined regularization model, we obtain denoising filters which are capable of obtaining good feature preserving image restoration. The GPU-based implementation computes the edge map in real time at 45–60 frames/s depending on the GPU card. Multiscale structure tensor-based spatially adaptive variable exponent provides reliable edge maps and compared with standard edge detectors it is robust under various noisy conditions. Moreover, filtering based on the multiscale variable exponent map method outperforms L0 sparse gradient-based image smoothing and related filters.

Parameters sensitivity:

Effect of contrast (k) parameter

The parameter k>0 in our SSTED controls the contrast/density of edges: higher values captures stronger edges and lower values include smaller edges




Example comparison edge detectors on BSDS500 dataset:

Between BSDS500 Ground-truth (GT), based on the summed boundaries drawn by five humans, Canny edge detector and our proposed:



BSDS500 GT (5 humans)



V. B. S. Prasath, R. Pelapur, G. Seetharaman, K. Palaniappan. Multiscale structure tensor for improved feature extraction and image regularization. IEEE Transactions on Image Processing, 28(12), 6198-6210, Dec 2019. doi:10.1109/TIP.2019.2924799 

See our related works in general vectorial p(x) map-based diffusion flows were analysis and experiments undertaken in image smoothing, restoration and edge detection:

V. B. S. Prasath, D. Vorotnikov. On time adaptive critical variable exponent vectorial diffusion flows and their applications in image processing I. Analysis. Nonlinear Analysis, 168, pp. 176-197, Mar 2018. doi:10.1016/ Preliminary version at arXiv, March 2016. doi:10.48550/arXiv.1603.06337. This part explains the theoretical analysis of the diffusion models.

V. B. S. Prasath, D. Vorotnikov. On time adaptive critical variable exponent vectorial diffusion flows and their applications in image processing II. Experiments. In Preparation, 2024. doi:10.48550/arXiv.24xx.abcde This part presents the image processing applications (smoothing, restoration, edge detection) of the VarEx diffusion models.