A MULTIRESOLUTION SPLINE WITH APPLICATION TO IMAGE MOSAICS PDF

Burt and Edward H. Permission to copy without fee all or part of this material is granted provided that the copies are not made or distributed for direct commercial advantage, the ACM copyright notice and the title of the publication and its date appear, and notice is given that copying is by permission of the Association for Computing Machinery. Burt and E. Adelson Fig. A pair of images may be represented as a pair of surfaces above the x, y plane. The problem of image splining is to join these surfaces with a smooth seam, with as little distortion of each surface as possible.

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Burt and E. Graphics 2 , , These images vary from an actual image to a computer-generated image of an actual image. This technique of Splining is quite interesting to me because it seems to have many practical uses.

This is illustrated in figure 8 , with the eye in the hand also in figure 1 with the merging of the two halves of the planet surface. This method for films could reduce the cost of film producing, since it is technically using some of the methods of film production.

For instance figure 8 again with the eye in the hand is done in the same way that it is done in a film. The process occurs by filming parts you want, then creating areas to store the picture and then finally just merging the two with a few adjustments.

There was one problem that arose for me: What would happen if two images were not of the same size and they were merged? This was somewhat solved with the splining nonoverlapped images.

Even with this technique, to escape from creating double exposure an area has to be designated in advance for an image to create a smoother merging, for example again figure 8 the eye in the hand.

The Laplacian Pyramid which is very useful in Splining, reminds me of a tree structure or rather a linked list with the root node being the original image and each pointer is a filter. You may only traverse the list from the right to the left or left to the right. Traversing through the tree or the images gives the different pictures at each level.

Like a list you have to go from one to get the other. Bin Chen In image encoding, we need a technique, which is both easy to implement and requires a relatively simple computations, to provide greater data compression. Paper[1] proposed a compressed image representation called Laplacian-pyramid. Laplacian-pyramid combined the advantages of predictive and transform methods. It is implemented by first do a low-pass filter blur on the original image to get a reduced version, and repeat this to get a series of further reduced images, which together is called Gaussian pyramid.

The Laplacian pyramid is a sequence of error images which are the difference between two levels of the Gaussian pyramid. The weight w and the equivalent weighting function play important role in pyramid gneration. By choosing different values of a, we will obtain different effects to meet the actual situations. The Laplacian pyramid is something like a complement of the Gaussian pyramid, it can be decoded and recovered to the original image by expanding, then summing all the levels of the pyramid.

Quantization can be used to reduce the entropy, in the meantime, the proper choice of the number and distribution of quantization levels should be wisely chosen to made the degradation imperceptible to human. So, knowlege of human vision is needed in this case. Laplacian-pyarmid is a versatile data structure with many attactive features for image processing. It has many applications such as progressive image transmission.

A more interesting applications of Laplacian-pyamid is discussed in Paper[2] - Multiresolution spline with application to image mosaics. In many situations, we may want to combine two or more images into a larger image mosaic.

A common technical problem in image mosaics is joining two images so that the edge between them is invisible. Pyramid structure is found ideally suited for performing the splining steps. The multiresolution spline algorithm is defined in terms of the basic pyramid operations and can be generalized for constructing mosaics on overlapped and nonoverlapped square images as well as arbitrary shape images.

The images to be splined are first decomposed into a set of band-pass filtered images, then those images in the same spatial frequency band are assembled into a band-pass mosaic, finally those band-pass mosaic images are summed to abtain the desired image mosaic.

Thus, the multiresolution spline can eliminate visible seams between component images. Jeffrey Considine "The Laplacian pyramid as a compact image code" Burt and Adelson present the Laplacian pyramid used in the previous article. The idea behind it is that the value of a pixel is related to that of those around it.

In constructing it, the image is iteratively Gaussian blurred and decreased in resolution. The Laplacian pyramid is the series of differences between these images starting from the smallest image with the least detail.

Without compression of any sort, the Laplacian pyramid would be about double the size of the original image sum of powers of 2 but since each level has so little information only the difference with the previous it can be greatly compressed. Use of the Laplacian pyramid takes a simple representation of an image and shows its usefulness. Besides image compression, this technique could aid in speeding progressive transmission of images using the Laplacian pyramid.

They start presenting the use of weighted averages along the edge and show how it has disadvantages with pictures having details over a wide variety of frequencies.

As an alternative, they suggest breaking the images up by bands of frequencies and splining each subimage separately before splining and recombining them. This avoids problems from blending the images at too high or low a frequency. To me this sounded like blending the components of each images Fourier Transform separately but they used a Laplacian pyramid to subdivide the images which seems much more computationally efficient.

They also discuss using this method for irregularly shaped edges not straight but they seem vague about the use of a Gaussian weighting when apparently the method does not need to change.

Except for the section on irregular shapes, this paper is easy to follow. The math is simplified but not overly and appears correct for the most part I believe the sumation on p. Overall, this article is clear and to the point and presents a clean and efficient algorithm. Cameron Fordyce The authors present an efficient method for the compression of images that minimizes the loss of image information. An algorithm is also presented that appears to be relatively fast and not very computationally expensive.

The method is compared to other methods of compression both causal and noncausal methods. The operations of the Laplacian Pyramid have the advantage of being local and applicable iteratively over the image and over the successive images produced at each stage of the process.

The authors also propose other uses for their method such as progressive image transmission. It is difficult to judge the contributions of this paper given my lack of knowledge in this field and the age of the paper. However, I will try. The method in and of itself appeals to me because of its simplicity and repeatability. The convolution and subtraction cycle occurs at each level of compression and the reverse of these steps is used in the expansion of the image.

Also, in each intermediate image some information that is recognizeable is kept so that the use proposed by the authors, progressive image transmission, becomes possible. As Prof.

Sclaroff noted in class, there might be other uses for intermediate images such as segmentation of an image based on an image at the top of the 'pyramid' into useful and non useful subimages. Processing could then continue only on the subimage judged to be important. I wonder if how much any method that relies on the prediction of the value of a pixel given its surrounding pixels will perform badly in images that have areas of great differences in intensity in adjacent areas such as in binary images.

Unfortunately, the quality of the copying impeded evaluation of the examples provided by the authors. This paper describes a process of merging or combining two images together using a process called multiresolution splining.

It uses a filtering scheme to separate the image into a series of low-pass images. This process is carried out by producing a Gausssian Pyramid images. This process is carried out by producing a Gausssian Pyramid After the creation of this pyramid these low-pass images are converted to band-pass images by a process of constructing a Laplacian Pyramid.

Now that the various levels of the image have been separated out into there elementary parts they can be splined together on this lower level. At this point the splining algorithm is used on each on these levels to create a smooth transition between the combined images. This process has multiple benefits.

Intuitively, one is breaking up the image into all of its component parts. Only after each of these levels have been connected together are they integrated to get the resulting image. So, this process of multiresolution splining has the effect of making a image without any distortion. That is it will solve the problems of boundary lines being created in the resulting image and the double exposure effect. It also makes calculation of the image efficient because, all of the commutation is being done on the lower level images.

This paper discuses a technique for using the Laplacian Pyramid as a data structure to encode information about a image. This idea of encoding is based on the assumption that pixels are highly correlated to neighboring pixels and that a average or a summation of areas of pixels would be a more efficient way of storing images.

First a Gaussiam Pyramid is created by convolving the weighting function or averaging function with the image. The prediction error is then computed by subtracting the low-pass imaged by the original image.

The result of this process is a low-pass image and a prediction error that can be used to store the information about the correlated pixels and differences between the levels of the Gaussian Pyramid.

These differences between the levels of the Gaussian Pyramid are in fact the various levels of the Laplacian Pyramid. By repeating this process you get various different levels of the image and an effective way to store and compress an image. Jason Golubock A Multiresolution Spline With Application to Image Mosaics This article tells about a new technique that has been developed for joining two or more images into one image, or splining. The main problem with splining is that if two images are simply glued together over an edge, there is a visible seam, due to differences in shading and texture along the edges.

The techinique described in the article involves smoothing the edge over between the two images by taking a weighted average of the two images along the edge which smooths out the seam. The width of the strip over which the images are smoothed is variable, of course, and has a big effect on the outcome of the process.

Instead of just splining the whole image at once, the images are first decomposed into a series of band-pass filtered component images, which are splined individually using the weighted average. The width of the smoothing zone varies depending on which wave lengths are represented in the band, which tends to give optimal results. The individual splined images are then added together to get the final result.

The author seems rather pleased with this procedure, although he mentions that no really good splining technique has yet been found. Obviously I'm not exactly qualified to critique this technique or comment on its usefulness It is based on the fact that neighboring pixels in any image are usually highly correlated, and that storing the value of each pixel separately is rather redundant.

The procedure described here uses a Gaussian weighting function, and convolves this weighting function with the image to obtain a low-pass filtered image, which is then subtracted from the original. So rather than storing the original image, the band-pass filtered image is stored, along with the difference image between that and the original. This results in a net reduction in necessary storage space.

To make storage even more efficient, this process is repeated on the low-pass filtered image which was obtained from the original, and then repeated again, and so on. The result is the Laplacian Pyramid structure. The article also describes the process of decoding the image based on the pyramid to obtain the original image.

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A multiresolution spline with application to image mosaics

Burt and E. Graphics 2 , , These images vary from an actual image to a computer-generated image of an actual image. This technique of Splining is quite interesting to me because it seems to have many practical uses.

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