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1 Introduction

Information theory has long had applications to image compression. So far there have been few attempts to use information theoretic concepts related to the interpretation of images. This is in contrast to physics, where in the eighties the combination of computer simulations and information theoretic analysis of complex systems got much attention [1].

We believe in the application of information theory to AI, and particularly to vision. In this report a scale decomposition of an information measure in images is presented. Its usefulness as a step in early vision is discussed, and the theory is supported by an efficient implementation. We present experimental results from a wide range of images.

The importance of scale-space processing was acknowledged in the eighties in vision beginning with Witkin's early paper [4], and much of the work in this decade is nicely brought together by Lindeberg [2]. To our knowledge nobody has made an information theoretic treatment of how information (in the Shannon sense) is distributed in different scales in the image. We want to relate a measure of information to the interpretation of images, rather than to the efficient coding for transmission.

A measure of information in an image indexed by spatial location and spatial scale, is of obvious importance to image processing and interpretation. It allows us to save effort and reduce the chance of false positives by focusing attention on relevant data.

A scale related measure also gives us information about which operator sizes are appropriate, to minimize spurious (noise) responses without losing the information we are trying to extract.

1.1 Some Possible Applications

In a vision system, knowing the spatial scale of the information is just as important as knowing where it is. Traditionally the problem of choosing the relevant scale has been tackled by considering all possible scales. This has been done in for instance matching [10, 11], edge detection and segmentation [2]. This can require considerable extra time in an already complex algorithm, and we propose that in many cases is not necessary.

Another approach is to integrate the process of determining the relevant scale range into another (later) processing step, typically iteratively changing the scale window of the input that the other algorithm considers while it is running, and thus trying to solve the two problems simultaneously. An example of this is the validation gate of [8, 9]. It uses a time varying (scale) window, but still needs an initial estimate of the relevant scale.

The scale-space studies we have done, as well as other studies of the fractal dimension of man-made objects, or settings, indicate that most information is only in a small set of scale ranges gif. As an example consider a typical indoor setting. There is the scale of the room itself, which is around the ten meter range. Furniture in the room would typically be in the one to two meter range, and other objects, say the typical household items in a kitchen or items occupying an office desktop, are mostly in the one decimeter scale range.

Knowing those scales can for instance help select the best operator sizes to minimize spurious responses while not missing important details. In the Tinytown example shown in Fig. 6 we have two peaks in the scale-information diagram (Fig. 7). The first (representing the shortest resolution lengths) corresponds to the information in the texture patterns. The second peak corresponds to the information in the physical objects on a much larger scale. We want to select an operator size according to the second peak when segmenting objects, and to the first one when analyzing texture.

Another application is for matching segments of the image with some kind of deformable/scalable models, using an iterative optimization technique. For this we benefit from an initial approximation of the scale of the model to match. From the scale-space expansion we can get a good idea of what start sizes we should consider.

1.2 Attention Selection

The recent trend in active vision avoids processing the whole image, and instead selects and processes (or attends to) only parts of the image which are of special interest. Attention selection can be data-driven bottom-up, model-driven top-down or both [14, 16]. Attention selection allows us to focus attention on relevant data, not only saving effort, but also reducing the chance of false positive responses [12]. Much of the work in attention selection has been based on perceptual grouping and structural saliency [15]. More recently, appealing linear filter based approaches have proven successful [13], which looks promising in that it allows simpler, low level explanation of the human pre-attentive process.

These data-driven attention mechanisms work in two steps:

  1. Pre-attentive processing Compute some measure of saliency or conspicuousness globally over the whole image.
  2. Attention selection Invoke some ad hoc search method over the saliency map directing attention to areas of importance.

We propose the following two changes:

Much of the previous work on attention selection applies to the method we propose. If the pre-attentive saliency maps are transformed into probability distributions in scale and spatial coordinates our information measure can be computed, and used as a well-grounded base for selecting regions to attend.


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