Training Bayesian networks for image segmentation

We are concerned with the problem of image segmentation in which each pixel is assigned to one of a predefined finite number of classes. In Bayesian image analysis, this requires fusing together local predictions for the class labels with a prior model of segmentations. Markov Random Fields (MRFs) have been used to incorporate some of this prior knowledge, but this not entirely satisfactory as inference in MRFs is NP-hard. The multiscale quadtree model of Bouman and Shapiro (1994) is an attractive alternative, as this is a tree-structured belief network in which inference can be carried out in linear time (Pearl 1988). It is an hierarchical model where the bottom-level nodes are pixels, and higher levels correspond to downsampled versions of the image. The conditional-probability tables (CPTs) in the belief network encode the knowledge of how the levels interact. In this paper we discuss two methods of learning the CPTs given training data, using (a) maximum likelihood and the EM algorithm and (b) emphconditional maximum likelihood (CML). Segmentations obtained using networks trained by CML show a statistically-significant improvement in performance on synthetic images. We also demonstrate the methods on a real-world outdoor-scene segmentation task.

Dynamical local models for segmentation and prediction of financial time series

In the analysis and prediction of many real-world time series, the assumption of stationarity is not valid. A special form of non-stationarity, where the underlying generator switches between (approximately) stationary regimes, seems particularly appropriate for financial markets. We introduce a new model which combines a dynamic switching (controlled by a hidden Markov model) and a non-linear dynamical system. We show how to train this hybrid model in a maximum likelihood approach and evaluate its performance on both synthetic and financial data.

The role of oscillatory brain activity in object processing and figure-ground segmentation in human vision

The perception of an object as a single entity within a visual scene requires that its features are bound together and segregated from the background and/or other objects. Here, we used magnetoencephalography (MEG) to assess the hypothesis that coherent percepts may arise from the synchronized high frequency (gamma) activity between neurons that code features of the same object. We also assessed the role of low frequency (alpha, beta) activity in object processing. The target stimulus (i.e. object) was a small patch of a concentric grating of 3c/°, viewed eccentrically. The background stimulus was either a blank field or a concentric grating of 3c/° periodicity, viewed centrally. With patterned backgrounds, the target stimulus emerged--through rotation about its own centre--as a circular subsection of the background. Data were acquired using a 275-channel whole-head MEG system and analyzed using Synthetic Aperture Magnetometry (SAM), which allows one to generate images of task-related cortical oscillatory power changes within specific frequency bands. Significant oscillatory activity across a broad range of frequencies was evident at the V1/V2 border, and subsequent analyses were based on a virtual electrode at this location. When the target was presented in isolation, we observed that: (i) contralateral stimulation yielded a sustained power increase in gamma activity; and (ii) both contra- and ipsilateral stimulation yielded near identical transient power changes in alpha (and beta) activity. When the target was presented against a patterned background, we observed that: (i) contralateral stimulation yielded an increase in high-gamma (>55 Hz) power together with a decrease in low-gamma (40-55 Hz) power; and (ii) both contra- and ipsilateral stimulation yielded a transient decrease in alpha (and beta) activity, though the reduction tended to be greatest for contralateral stimulation. The opposing power changes across different regions of the gamma spectrum with 'figure/ground' stimulation suggest a possible dual role for gamma rhythms in visual object coding, and provide general support of the binding-by-synchronization hypothesis. As the power changes in alpha and beta activity were largely independent of the spatial location of the target, however, we conclude that their role in object processing may relate principally to changes in visual attention.

Testing for market segmentation in the A and B share markets of China

Recent research has suggested that the A and B share markets of China may be informationally segmented. In this paper volatility patterns in the A and B share market are studied to establish whether volatility changes to the A and B share markets are synchronous. A consequence of new information, when investors act upon it is that volatility rises. This means that if the A and B markets are perfectly integrated volatility changes to each market would be expected to occur at the same time. However, if they are segmented there is no reason for volatility changes to occur on the same day. Using the iterative cumulative sum of squares across the different markets. Evidence is found of integration between the two A share markets but not between the A and B markets. © 2005 Taylor & Francis Group Ltd.

Applications of the behavioural homogeneity evaluation framework: the predictive ability of consumer involvement for international food market segmentation

This article proposes a framework of alternative international marketing strategies, based on the evaluation of intra- and inter-cultural behavioural homogeneity for market segmentation. The framework developed in this study provides a generic structure to behavioural homogeneity, proposing consumer involvement as a construct with unique predictive ability for international marketing strategy decisions. A model-based segmentation process, using structural equation models, is implemented to illustrate the application of the framework.

The behavioural homogeneity evaluation framework:Multi-level evaluations of consumer involvement in international segmentation

This paper presents a generic strategic framework of alternative international marketing strategies and market segmentation based on intra- and inter-cultural behavioural homogeneity. Consumer involvement (CI) is proposed as a pivotal construct to capture behavioural homogeneity, for the identification of market segments. Results from a five-country study demonstrate how the strategic framework can be valuable in managerial decision-making. First, there is evidence for the cultural invariance of the measurement of CI, allowing a true comparison of inter- and intra-cultural behavioural homogeneity. Second, CI influences purchase behaviour, and its evaluation provides a rich source of information for responsive market segmentation. Finally, a decomposition of behavioural variance suggests that national-cultural environment and nationally transcendent variables explain differences in behaviour. The Behavioural Homogeneity Evaluation Framework therefore suggests appropriate international marketing strategies, providing practical guidance for implementing involvement-contingent strategies. © 2007 Academy of International Business. All rights reserved.

Response-based segmentation using Finite Mixture Partial Least Squares: theoretical foundations and an application to American Customer Satisfaction Index Data

When applying multivariate analysis techniques in information systems and social science disciplines, such as management information systems (MIS) and marketing, the assumption that the empirical data originate from a single homogeneous population is often unrealistic. When applying a causal modeling approach, such as partial least squares (PLS) path modeling, segmentation is a key issue in coping with the problem of heterogeneity in estimated cause-and-effect relationships. This chapter presents a new PLS path modeling approach which classifies units on the basis of the heterogeneity of the estimates in the inner model. If unobserved heterogeneity significantly affects the estimated path model relationships on the aggregate data level, the methodology will allow homogenous groups of observations to be created that exhibit distinctive path model estimates. The approach will, thus, provide differentiated analytical outcomes that permit more precise interpretations of each segment formed. An application on a large data set in an example of the American customer satisfaction index (ACSI) substantiates the methodology’s effectiveness in evaluating PLS path modeling results.

The role of texture amplitude in shape from shading: evidence from a haptic matching task

The pattern of illumination on an undulating surface can be used to infer its 3-D form (shape from shading). But the recovery of shape would be invalid if the shading actually arose from reflectance variation. When a corrugated surface is painted with an albedo texture, the variation in local mean luminance (LM) due to shading is accompanied by a similar modulation in texture amplitude (AM). This is not so for reflectance variation, nor for roughly textured surfaces. We used a haptic matching technique to show that modulations of texture amplitude play a role in the interpretation of shape from shading. Observers were shown plaid stimuli comprising LM and AM combined in-phase (LM+AM) on one oblique and in anti-phase (LM-AM) on the other. Stimuli were presented via a modified ReachIN workstation allowing the co-registration of visual and haptic stimuli. In the first experiment, observers were asked to adjust the phase of a haptic surface, which had the same orientation as the LM+AM combination, until its peak in depth aligned with the visually perceived peak. The resulting alignments were consistent with the use of a lighting-from-above prior. In the second experiment, observers were asked to adjust the amplitude of the haptic surface to match that of the visually perceived surface. Observers chose relatively large amplitude settings when the haptic surface was oriented and phase-aligned with the LM+AM cue. When the haptic surface was aligned with the LM-AM cue, amplitude settings were close to zero. Thus the LM/AM phase relation is a significant visual depth cue, and is used to discriminate between shading and reflectance variations. [Supported by the Engineering and Physical Sciences Research Council, EPSRC].

The role of texture in shape from shading: are humans biased towards seeing relief textures?

When a textured surface is modulated in depth and illuminated, the level of illumination varies across the surface, producing coarse-scale luminance modulations (LM) and amplitude modulation (AM) of the fine-scale texture. If the surface has an albedo texture (reflectance variation) then the LM and AM components are always in-phase, but if the surface has a relief texture the phase relation between LM and AM varies with the direction and nature of the illuminant. We showed observers sinusoidal luminance and amplitude modulations of a binary noise texture, in various phase relationships, in a paired-comparisons design. In the first experiment, the combinations under test were presented in different temporal intervals. Observers indicated which interval contained the more depthy stimulus. LM and AM in-phase were seen as more depthy than LM alone which was in turn more depthy than LM and AM in anti-phase, but the differences were weak. In the second experiment the combinations under test were presented in a single interval on opposite obliques of a plaid pattern. Observers were asked to indicate the more depthy oblique. Observers produced the same depth rankings as before, but now the effects were more robust and significant. Intermediate LM/AM phase relationships were also tested: phase differences less than 90 deg were seen as more depthy than LM-only, while those greater than 90 deg were seen as less depthy. We conjecture that the visual system construes phase offsets between LM and AM as indicating relief texture and thus perceives these combinations as depthy even when their phase relationship is other than zero. However, when different LM/AM pairs are combined in a plaid, the signals on the obliques are unlikely to indicate corrugations of the same texture, and in this case the out-of-phase pairing is seen as flat. [Supported by the Engineering and Physical Sciences Research Council (EPSRC)].

The role of texture amplitude in shape from shading

When a textured surface is modulated in depth and illuminated, parts of the surface receive different levels of illumination; the resulting variations in luminance can be used to infer the shape of the depth modulations-shape from shading. The changes in illumination also produce changes in the amplitude of the texture, although local contrast remains constant. We investigated the role of texture amplitude in supporting shape from shading. If a luminance plaid is added to a binary noise texture (LM), shape from shading produces perception of corrugations in two directions. If the amplitude of the noise is also modulated (AM) such that it is in-phase with one of the luminance sinusoids and out-of-phase with the other, the resulting surface is seen as corrugated in only one directionöthat supported by the in-phase pairing. We confirmed this subjective report experimentally, using a depth-mapping technique. Further, we asked naïve observers to indicate the direction of corrugations in plaids made up of various combinations of LM and AM. LM+AM was seen as having most depth, then LM-only, then LM-AM, and then AM-only. Our results suggest that while LM is required to see depth from shading, its phase relative to any AM component is also important.

The interaction of luminance and texture amplitude in surface depth perception

Previous studies have suggested separate channels for detection of first-order luminance modulations (LM) and second-order modulations of the local amplitude (AM) of a texture. Mixtures of LM and AM with different phase relationships appear very different: in-phase compounds (LM + AM) look like 3-D corrugated surfaces, while out-of-phase compounds (LM - AM) appear flat and/or transparent. This difference may arise because the in-phase compounds are consistent with multiplicative shading, while the out-of-phase compounds are not. We investigated the role of these modulation components in surface depth perception. We used a textured background with thin bars formed by local changes in luminance and/or texture amplitude. These stimuli appear as embossed surfaces with wide and narrow regions. Keeping the AM modulation depth fixed at a suprathreshold level, we determined the amount of luminance contrast required for observers to correctly indicate the width (narrow or wide) of 'raised' regions in the display. Performance (compared to the LM-only case) was facilitated by the presence of AM, but, unexpectedly, performance for LM - AM was as good as for LM + AM. Thus, these results suggest that there is an interaction between first-order and second-order mechanisms during depth perception based on shading cues, but the phase dependence is not yet understood.