Multi-scale representation of an input image is employed in many visual processing applications such as feature detection (e.g. edge, blob, junction or ridge), feature classification, object recognition, object classification, image classification, shape analysis, and the like. A plurality of images, each of the images is at a different scale, are generated by smoothing the input image with ascending Gaussian kernels.
Optical blurring of an input image, resulting from the input image being out-of-focus, is modeled as a convolution of an input focused image with a Gaussian kernel of certain variance value. The value of the variance of the convolving Gaussian kernel corresponds to the blur level of the input image. Image convolution with a Gaussian kernel is described by equation (1):f*g(σ3)=(f*g(σ1))*g(σ2); σ3=√{square root over ((σ12+σ22))}  (1)    f—A focused image    g—A Gaussian kernel of certain variance    *—A convolution operator.When the input image is blurred (i.e., out-of-focus input image), generating a multi-scale representation of the input image, might result in a removal of important details from the image (i.e., over smoothing the input image). One way of overcoming the over-smoothing problem of a blurred input image, is to reconstruct a focused image from the blurred image by estimating the Gaussian kernel corresponding to the blur level of the image, de-convolving the input image with the estimated Gaussian kernel, and generating a multi-scale representation of the de-convolved image.
Reference is now made to FIG. 1, which is a schematic illustration of a method for generating a multi-scale representation of a blurred input image, operative as known in the art. In procedure 100, a Gaussian kernel, corresponding to the blur level of the input image, is estimated. The Gaussian kernel estimation is achieved by any of the blur level estimation techniques known in the art. In procedure 102, the blurred input image is de-convolved in order to reconstruct a focused image. The blurred image is de-convolved according to the Gaussian kernel, corresponding to the blur level of the image, estimated in procedure 100. In procedure 104, a multi-scale representation of the de-convolved image is generated by convolving the de-convolved image with a plurality of Gaussian kernels of ascending values of variance. In procedure 106, a visual processing is performed on the multi-scale representation of the input image.
Reference is now made to “Scale space theory in computer vision” by Tony Lindeberg, a book published by Springer (1994). This publication is directed at a formal framework, scale-space representation, for handling the notion of scale in image data. The book gives an introduction to the general foundations of the scale space theory and shows how it applies to essential problems in computer vision such as computation of image features.
Reference is now made to an article entitled “Estimating Image Blur in The Wavelet Domain”, by Filip Rooms et al. This reference is directed to a method for estimating the blur level of an input image, according to information contained in the input image. A blurred image is modeled as the corresponding focused image convolved with a Point Spread Function (PSF). The method includes the procedures of: calculating the Lipschitz exponent; generating a histogram; and estimating the blur of the image according to the center of gravity of the histogram and according to the maximum of the histogram. The Lipschitz exponent is calculated in all points, where there is a change in intensity in either the horizontal or the vertical direction. The histogram of the Lipschitz exponents, of the blurred image, is a single peak histogram with a certain distribution around that peak. The blur level of the image is estimated according to the center of gravity of the distribution around the peak and according to the maximum of the peak.
Reference is now made to an article entitled “Pyramid Method in Image Processing” written by E. H. Adelson et al. This reference is directed to a method for constructing an image pyramid of different resolutions. The image pyramid is employed for a variety of visual processing applications such as pattern recognition. The image pyramid consists of a sequence of copies of an original image in which both sample density and resolution are decreased. The method includes the procedures of convolving the original image with a set of Gaussian-like weighing functions, subtracting each Gaussian pyramid level from the next lower level in the pyramid, and interpolating sample values between those in a given level before that level is subtracted from the next lower level.
A zero level of the pyramid is the original image. The convolution procedure acts as a low-pass filter with the band limit reduced by one octave, with each level, correspondingly. The procedures of subtracting and interpolating act as a band-pass filter. The procedure of interpolating is necessary since the subtraction is between levels of different sample densities.