Problem Definition

Resolution enhancement involves the problem of magnifying a small image to several times its size while avoiding blurring, ringing and other artifacts.  We tackle the problem of magnifying an image without incurring the edge enhancement effects and other structural distortions characteristic of classical  image magnification techniques. We propose an iterative algorithm based on a Projections onto Convex Sets (POCS) formalization.

Applications:

1. Image Magnification.
2. Phase Retrieval.

Details:

Classical image magnification  methods include bilinear, bicubic and FIR interpolation schemes followed by a sharpening method like unsharp masking. Such interpolation schemes tend to blur the images when applied indiscriminately. Unsharp masking, which involves subtracting a properly scaled Laplacian of the image from itself, produces artifacts and increases noise. More sophisticated schemes involving wavelet- or fractal-based techniques have also been proposed. Such methods perform extrapolation of the signal in either the wavelet or fractal domain, which leads to objectionable artifacts when the assumptions behind such extrapolation are violated. It may also be noted that such extrapolatory assumptions predict and actively enhance the high-frequency content within the image, thus increasing any noise present in the unmagnified image.

The proposed method starts with an initial magnified image obtained through selective interpolation followed by an iterative procedure which aims to avoid edge-related artifacts while retaining and enhancing sharpness. The initial image is a composite image formed from a base interpolation scheme in the smooth areas of the image and from a selective interpolation mechanism in the non-smooth (or edge) areas. The proposed iterative algorithm aims to find a magnified image satisfying two constraints: one of the constraints is derived from sampling theory while the other constraint reflects the confidence that we place on the initial iterate. Both the constraints are convex sets; thus, we seek a solution which is at the intersection of these two convex sets and  can be obtained using the projection on convex sets (POCS) method.  Starting with the initial iterate, we project alternately on the two constraints. Convergence is guaranteed since we operate within the POCS formalism.

The proposed algorithm consists of three basic steps: Finding edges
Edge locations are found using a multiscale segmentation algorithm. Obtaining the initial image
This is done using a bilinear interpolation scheme in the smooth regions and a selective interpolation mechanism in the non-smooth areas POCS based iterative algorithm
The first constraint set arises from sampling theory which suggests that the unmagnified image can be viewed as being  obtained by subsampling the magnified image without aliasing. The second constraint set arises by constraining the non-edge and edge location values to vary within limits from their initial estimate.

Results:

                                                                    

Fig 1a - Lena, 4x magnification using bilinear interpolation                      Fig 1b -  Segmentation of  Fig 1a

                                                                    

Fig 1c - Proposed method  with coarse segmentation                              Fig 1d - Proposed method with fine segmentation
 

Publications:

• POCS based adaptive image magnification
• Ratakonda, K.; Ahuja, N.

Image Processing, 1998. ICIP 98. Proceedings. 1998 International Conference on ,  1998
Page(s): 203 -207 vol.3

Contact Information:

Narendra Ahuja
2041 Beckman Institute
405 N. Mathews Avenue, Urbana IL 61801, USA.
Ph: (217) 333-1837
Fax: (217) 244-8371
Email: ahuja@vision.ai.uiuc.edu