The multiresolution Fourier transform : a general purpose tool for image analysis

The extraction of meaningful features from an image forms an important area of image analysis. It enables the task of understanding visual information to be implemented in a coherent and well defined manner. However, although many of the traditional approaches to feature extraction have proved to be successful in specific areas, recent work has suggested that they do not provide sufficient generality when dealing with complex analysis problems such as those presented by natural images. This thesis considers the problem of deriving an image description which could form the basis of a more general approach to feature extraction. It is argued that an essential property of such a description is that it should have locality in both the spatial domain and in some classification space over a range of scales. Using the 2-d Fourier domain as a classification space, a number of image transforms that might provide the required description are investigated. These include combined representations such as a 2-d version of the short-time Fourier transform (STFT), and multiscale or pyramid representations such as the wavelet transform. However, it is shown that these are limited in their ability to provide sufficient locality in both domains and as such do not fulfill the requirement for generality. To overcome this limitation, an alternative approach is proposed in the form of the multiresolution Fourier transform (MFT). This has a hierarchical structure in which the outermost levels are the image and its discrete Fourier transform (DFT), whilst the intermediate levels are combined representations in space and spatial frequency. These levels are defined to be optimal in terms of locality and their resolution is such that within the transform as a whole there is a uniform variation in resolution between the spatial domain and the spatial frequency domain. This ensures that locality is provided in both domains over a range of scales. The MFT is also invertible and amenable to efficient computation via familiar signal processing techniques. Examples and experiments illustrating its properties are presented. The problem of extracting local image features such as lines and edges is then considered. A multiresolution image model based on these features is defined and it is shown that the MET provides an effective tool for estimating its parameters.. The model is also suitable for representing curves and a curve extraction algorithm is described. The results presented for synthetic and natural images compare favourably with existing methods. Furthermore, when coupled with the previous work in this area, they demonstrate that the MFT has the potential to provide a basis for the solution of general image analysis problems

Multiresolution estimation of 2-d disparity using a frequency domain approach

An efficient algorithm for the estimation of the 2-d disparity between a pair of stereo images is presented. Phase based methods are extended to the case of 2-d disparities and shown to correspond to computing local correlation fields. These are derived at multiple scales via the frequency domain and a coarse-to-fine 'focusing' strategy determines the final disparity estimate. Fast implementation is achieved by using a generalised form of wavelet transform, the multiresolution Fourier transform (MFT), which enables efficient calculation of the local correlations. Results from initial experiments on random noise stereo pairs containing both 1-d and 2-d disparities, illustrate the potential of the approach

Hierarchical descriptors for nonstationary 1 and 2 dimensional signal processing

The representation of signals with important local properties is considered. These signals have a degree of nonstationarity which is dependent upon the amount of localisation. Signal descriptors which seek to represent such signals must correspond in scale to the local properties in order to provide an efficient representation. A review is given of various methods that have been adopted. Although some of these have been used in specific applications, a general and computationally efficient representation is not available. A new descriptor is presented which seeks to fulfil this requirement. It combines the time and frequency representations of a signal in an optimal way by using basis functions which are maximally concentrated in both domains. This corresponds to representing the local properties of the signal. The descriptor adopts a hierarchical structure which incorporates multi-resolution in both domains so that the required amount of localisation can be determined for a given signal. This enables the descriptor to be generally applied since it is consistent with the concept of a nonstationary signal. Results of initial experiments on the descriptor are presented and the report concludes with a discussion of future investigations

Stabilitet i fosterhjem. Internasjonal forskning om barnets behov for trygghet og forutsigbarhet

Formålet med rapporten har vært å beskrive hva som skyldes ustabilitet under fosterhjemsplasseringer, for dernest å foreslå ulike tiltak som kan bøte på denne ustabiliteten. Rapporten har tre ulike deler som tematiserer fosterhjem og stabilitet. Den første delen er introduksjonen, og forklarer hvilken rolle stabilitet har for barn under plassering. Stabilitet og arbeid med å etablere en familieliknende situasjon for barna blir argumentert for at er og har vært et grunnleggende siktemål for fosterhjemstjenesten i norsk barnevern i mange år. Den andre delen avdekker de ulike mekanismene som gjør seg gjeldende, og som medfører ustabilitet. Den tredje delen presenterer en serie med tiltak som man kan tenke seg at kan avhjelpe de situasjoner som leder fram til ustabilitet under plasseringen, og som ble utledet under del to

Motion Segmentation Based on Integrated Region Layering and Motion Assignment

We describe a novel algorithm for segmenting image sequence frames into regions of pixels moving with coherent motion. It is based on fusing local grey level segmentations with motion estimates obtained using block and partial correlations. The key innovation is the method employed to assign motion labels to the grey level regions. This uses an explicit model of motion occlusion and uncovering based on boundary ownership which predicts the location of motioncompensated difference energy for a given labelling and depth ordering of adjacent regions. A significant advantage of the approach is that region layering is automatically generated with the best assignment. We incorporate the scheme into a global segmentation algorithm in which the local motion assignments are combined using a consistency criterion, leading to layered sets of connected sub-regions representing the segmented motion regions within the frame. Experiments demonstrate the approach is effective

Integrated segmentation and depth ordering of motion layers in image sequences

We describe a method to segment and depth order motion layers simultaneously in an image sequence. Previous approaches have tended to ignore the depth ordering issue or treat it as a post-processing operation. We argue here that motion estimation and segmentation are crucially dependent on depth order and hence that the latter should form an integral part of any layering scheme. Using an explicit model of boundary ownership allowing simultaneous assignment of motions to regions and extraction of depth order, the method fuses colour region segmentations with motion estimates obtained via block correlation. The motion estimates are then updated using a depthdependent partial correlation. Experiments show the approach is effective.

Tracking multiple animals in wildlife footage

We describe a method for tracking animals in wildlife footage. It uses a CONDENSATION particle filtering framework driven by learnt characteristics of specific animals. The key contribution is a periodic model of animal motion based on the relative positions over time of trackable features at significant body points. We also introduce techniques for maintaining a multimodal state density within the particle filter over time to enable consistent tracking of multiple animals. Initial experiments show that the approach has considerable potential. 1

Analysis of structured texture using the multiresolution Fourier transform

A multiresolution approach to the analysis of structural texture is presented. The multiresolution Fourier transform (MFT) is utilized as a framework to derive a robust algorithm which estimates textural features over a range of spatial scales based on local frequency domain properties. A pair of centroids of local spectra are extracted to represent the dominant frequencies of underlying spatial regions which are equivariant to rotation and scaling. Based on these centroids, the relationship between two different local spectra is characterized by an affine transformation. Assessment of the estimated affine transform is made by normalized correlation, which also provides local phase shift information. Analysis and synthesis of both artificial and natural images demonstrate the capability of the algorithm