Mach edges: a critical test of the nonlinear 3rd derivative model for edge-detection

Feature detection is a crucial stage of visual processing. In previous feature-marking experiments we found that peaks in the 3rd derivative of the luminance profile can signify edges where there are no 1st derivative peaks nor 2nd derivative zero-crossings (Wallis and George 'Mach edges' (the edges of Mach bands) were nicely predicted by a new nonlinear model based on 3rd derivative filtering. As a critical test of the model, we now use a new class of stimuli, formed by adding a linear luminance ramp to the blurred triangle waves used previously. The ramp has no effect on the second or higher derivatives, but the nonlinear model predicts a shift from seeing two edges to seeing only one edge as the added ramp gradient increases. In experiment 1, subjects judged whether one or two edges were visible on each trial. In experiment 2, subjects used a cursor to mark perceived edges and bars. The position and polarity of the marked edges were close to model predictions. Both experiments produced the predicted shift from two to one Mach edge, but the shift was less complete than predicted. We conclude that the model is a useful predictor of edge perception, but needs some modification.

Third-derivative filters predict edge locations in spatial vision

Edge detection is crucial in visual processing. Previous computational and psychophysical models have often used peaks in the gradient or zero-crossings in the 2nd derivative to signal edges. We tested these approaches using a stimulus that has no such features. Its luminance profile was a triangle wave, blurred by a rectangular function. Subjects marked the position and polarity of perceived edges. For all blur widths tested, observers marked edges at or near 3rd derivative maxima, even though these were not 1st derivative maxima or 2nd derivative zero-crossings, at any scale. These results are predicted by a new nonlinear model based on 3rd derivative filtering. As a critical test, we added a ramp of variable slope to the blurred triangle-wave luminance profile. The ramp has no effect on the (linear) 2nd or higher derivatives, but the nonlinear model predicts a shift from seeing two edges to seeing one edge as the ramp gradient increases. Results of two experiments confirmed such a shift, thus supporting the new model. [Supported by the Engineering and Physical Sciences Research Council].

Seeing edge blur: receptive fields as multiscale neural templates

Edge blur is an important perceptual cue, but how does the visual system encode the degree of blur at edges? Blur could be measured by the width of the luminance gradient profile, peak ^ trough separation in the 2nd derivative profile, or the ratio of 1st-to-3rd derivative magnitudes. In template models, the system would store a set of templates of different sizes and find which one best fits the `signature' of the edge. The signature could be the luminance profile itself, or one of its spatial derivatives. I tested these possibilities in blur-matching experiments. In a 2AFC staircase procedure, observers adjusted the blur of Gaussian edges (30% contrast) to match the perceived blur of various non-Gaussian test edges. In experiment 1, test stimuli were mixtures of 2 Gaussian edges (eg 10 and 30 min of arc blur) at the same location, while in experiment 2, test stimuli were formed from a blurred edge sharpened to different extents by a compressive transformation. Predictions of the various models were tested against the blur-matching data, but only one model was strongly supported. This was the template model, in which the input signature is the 2nd derivative of the luminance profile, and the templates are applied to this signature at the zero-crossings. The templates are Gaussian derivative receptive fields that covary in width and length to form a self-similar set (ie same shape, different sizes). This naturally predicts that shorter edges should look sharper. As edge length gets shorter, responses of longer templates drop more than shorter ones, and so the response distribution shifts towards shorter (smaller) templates, signalling a sharper edge. The data confirmed this, including the scale-invariance implied by self-similarity, and a good fit was obtained from templates with a length-to-width ratio of about 1. The simultaneous analysis of edge blur and edge location may offer a new solution to the multiscale problem in edge detection.

Low level feature detection in human vision

Influential models of edge detection have generally supposed that an edge is detected at peaks in the 1st derivative of the luminance profile, or at zero-crossings in the 2nd derivative. However, when presented with blurred triangle-wave images, observers consistently marked edges not at these locations, but at peaks in the 3rd derivative. This new phenomenon, termed ‘Mach edges’ persisted when a luminance ramp was added to the blurred triangle-wave. Modelling of these Mach edge detection data required the addition of a physiologically plausible filter, prior to the 3rd derivative computation. A viable alternative model was examined, on the basis of data obtained with short-duration, high spatial-frequency stimuli. Detection and feature-making methods were used to examine the perception of Mach bands in an image set that spanned a range of Mach band detectabilities. A scale-space model that computed edge and bar features in parallel provided a better fit to the data than 4 competing models that combined information across scale in a different manner, or computed edge or bar features at a single scale. The perception of luminance bars was examined in 2 experiments. Data for one image-set suggested a simple rule for perception of a small Gaussian bar on a larger inverted Gaussian bar background. In previous research, discriminability (d’) has typically been reported to be a power function of contrast, where the exponent (p) is 2 to 3. However, using bar, grating, and Gaussian edge stimuli, with several methodologies, values of p were obtained that ranged from 1 to 1.7 across 6 experiments. This novel finding was explained by appealing to low stimulus uncertainty, or a near-linear transducer.

Normative contrast sensitivity values for the back-lit Melbourne Edge Test and the effect of visual impairment

Background: The Melbourne Edge Test (MET) is a portable forced-choice edge detection contrast sensitivity (CS) test. The original externally illuminated paper test has been superseded by a backlit version. The aim of this study was to establish normative values for age and to assess change with visual impairment. Method: The MET was administered to 168 people with normal vision (18-93 years old) and 93 patients with visual impairment (39-97 years old). Distance visual acuity (VA) was measured with a log MAR chart. Results: In those eyes without disease, MET CS was stable until the age of 50 years (23.8 ± .7 dB) after which it decreased at a rate of ≈1.5 dB per decade. Compared with normative values, people with low vision were found to have significantly reduced CS, which could not be totally accounted for by reduced VA. Conclusions: The MET provides a quick and easy measure of CS, which highlights a reduction in visual function that may not be detectable using VA measurements. © 2004 The College of Optometrists.

Objective grading of the anterior eye

Purpose. To convert objective image analysis of anterior ocular surfaces into recognisable clinical grades, in order to provide a more sensitive and reliable equivalent to current subjective grading methods; a prospective, randomized study correlating clinical grading with digital image assessment. Methods. The possible range of clinical presentations Of bulbar and palpebral hyperaemia, palpebral roughness and corneal staining were represented by 4 sets of 10 images. The images were displayed in random order and graded by 50 clinicians using both subjective CCLRU and Efron grading scales. Previously validated objective image analysis was performed 3 times oil each of the 40 images. Digital measures included edge-detection and relative-coloration components. Step-wise regression analysis determined correlations between the average subjective grade and the objective image analysis measures. Results. Average subjective grades Could be predicted by a combination of the objective image analysis components. These digital ``grades'' accounted for between 69%, (for Efron scale-graded palpebral redness) and 98% (for Efron scale-graded bulbar hyperaemia) of the subjective variance. Conclusions. The results indicate that clinicians may use a combination of vessel areas and overall hue in their judgment of clinical severity for certain conditions. Objective grading call take these aspects into account, and be used to predict an average ``objective grade'' to be used by a clinician in describing the anterior eye. These measures are more sensitive and reliable than subjective grading while still utilizing familiar terminology, and can be applied in research or practice to improve the detection, and monitoring of ocular surface changes.

Mach edges: local features predicted by 3rd derivative spatial filtering

Edges are key points of information in visual scenes. One important class of models supposes that edges correspond to the steepest parts of the luminance profile, implying that they can be found as peaks and troughs in the response of a gradient (1st derivative) filter, or as zero-crossings in the 2nd derivative (ZCs). We tested those ideas using a stimulus that has no local peaks of gradient and no ZCs, at any scale. The stimulus profile is analogous to the Mach ramp, but it is the luminance gradient (not the absolute luminance) that increases as a linear ramp between two plateaux; the luminance profile is a blurred triangle-wave. For all image-blurs tested, observers marked edges at or close to the corner points in the gradient profile, even though these were not gradient maxima. These Mach edges correspond to peaks and troughs in the 3rd derivative. Thus Mach edges are inconsistent with many standard edge-detection schemes, but are nicely predicted by a recent model that finds edge points with a 2-stage sequence of 1st then 2nd derivative operators, each followed by a half-wave rectifier.

Mach Bands: multi-scale spatial filtering and co-operative coding of edges and bars

Perception of Mach bands may be explained by spatial filtering ('lateral inhibition') that can be approximated by 2nd derivative computation, and several alternative models have been proposed. To distinguish between them, we used a novel set of ‘generalised Gaussian’ images, in which the sharp ramp-plateau junction of the Mach ramp was replaced by smoother transitions. The images ranged from a slightly blurred Mach ramp to a Gaussian edge and beyond, and also included a sine-wave edge. The probability of seeing Mach Bands increased with the (relative) sharpness of the junction, but was largely independent of absolute spatial scale. These data did not fit the predictions of MIRAGE, nor 2nd derivative computation at a single fine scale. In experiment 2, observers used a cursor to mark features on the same set of images. Data on perceived position of Mach bands did not support the local energy model. Perceived width of Mach bands was poorly explained by a single-scale edge detection model, despite its previous success with Mach edges (Wallis & Georgeson, 2009, Vision Research, 49, 1886-1893). A more successful model used separate (odd and even) scale-space filtering for edges and bars, local peak detection to find candidate features, and the MAX operator to compare odd- and even-filter response maps (Georgeson, VSS 2006, Journal of Vision 6(6), 191a). Mach bands are seen when there is a local peak in the even-filter (bar) response map, AND that peak value exceeds corresponding responses in the odd-filter (edge) maps.

Mach bands and multiscale models of spatial vision:the role of first, second, and third derivative operators in encoding bars and edges

Ernst Mach observed that light or dark bands could be seen at abrupt changes of luminance gradient in the absence of peaks or troughs in luminance. Many models of feature detection share the idea that bars, lines, and Mach bands are found at peaks and troughs in the output of even-symmetric spatial filters. Our experiments assessed the appearance of Mach bands (position and width) and the probability of seeing them on a novel set of generalized Gaussian edges. Mach band probability was mainly determined by the shape of the luminance profile and increased with the sharpness of its corners, controlled by a single parameter (n). Doubling or halving the size of the images had no significant effect. Variations in contrast (20%-80%) and duration (50-300 ms) had relatively minor effects. These results rule out the idea that Mach bands depend simply on the amplitude of the second derivative, but a multiscale model, based on Gaussian-smoothed first- and second-derivative filtering, can account accurately for the probability and perceived spatial layout of the bands. A key idea is that Mach band visibility depends on the ratio of second- to first-derivative responses at peaks in the second-derivative scale-space map. This ratio is approximately scale-invariant and increases with the sharpness of the corners of the luminance ramp, as observed. The edges of Mach bands pose a surprisingly difficult challenge for models of edge detection, but a nonlinear third-derivative operation is shown to predict the locations of Mach band edges strikingly well. Mach bands thus shed new light on the role of multiscale filtering systems in feature coding. © 2012 ARVO.

Image enhancement of real-time television to benefit the visually impaired

Purpose: To examine the use of real-time, generic edge detection, image processing techniques to enhance the television viewing of the visually impaired. Design: Prospective, clinical experimental study. Method: One hundred and two sequential visually impaired (average age 73.8 ± 14.8 years; 59% female) in a single center optimized a dynamic television image with respect to edge detection filter (Prewitt, Sobel, or the two combined), color (red, green, blue, or white), and intensity (one to 15 times) of the overlaid edges. They then rated the original television footage compared with a black-and-white image displaying the edges detected and the original television image with the detected edges overlaid in the chosen color and at the intensity selected. Footage of news, an advertisement, and the end of program credits were subjectively assessed in a random order. Results: A Prewitt filter was preferred (44%) compared with the Sobel filter (27%) or a combination of the two (28%). Green and white were equally popular for displaying the detected edges (32%), with blue (22%) and red (14%) less so. The average preferred edge intensity was 3.5 ± 1.7 times. The image-enhanced television was significantly preferred to the original (P < .001), which in turn was preferred to viewing the detected edges alone (P < .001) for each of the footage clips. Preference was not dependent on the condition causing visual impairment. Seventy percent were definitely willing to buy a set-top box that could achieve these effects for a reasonable price. Conclusions: Simple generic edge detection image enhancement options can be performed on television in real-time and significantly enhance the viewing of the visually impaired. © 2007 Elsevier Inc. All rights reserved.

Sensitivity and reliability of objective image analysis compared to subjective grading of bulbar hyperaemia

Aims: To establish the sensitivity and reliability of objective image analysis in direct comparison with subjective grading of bulbar hyperaemia. Methods: Images of the same eyes were captured with a range of bulbar hyperaemia caused by vasodilation. The progression was recorded and 45 images extracted. The images were objectively analysed on 14 occasions using previously validated edge-detection and colour-extraction techniques. They were also graded by 14 eye-care practitioners (ECPs) and 14 non-clinicians (NCb) using the Efron scale. Six ECPs repeated the grading on three separate occasions Results: Subjective grading was only able to differentiate images with differences in grade of 0.70-1.03 Efron units (sensitivity of 0.30-0.53), compared to 0,02-0.09 Efron units with objective techniques (sensitivity of 0.94-0.99). Significant differences were found between ECPs and individual repeats were also inconsistent (p<0.001). Objective analysis was 16x more reliable than subjective analysis. The NCLs used wider ranges of the scale but were more variable than ECPs, implying that training may have an effect on grading. Conclusions: Objective analysis may offer a new gold standard in anterior ocular examination, and should be developed further as a clinical research tool to allow more highly powered analysis, and to enhance the clinical monitoring of anterior eye disease.

Incremental nature of anterior eye grading scales determined by objective image analysis

Aim: To use previously validated image analysis techniques to determine the incremental nature of printed subjective anterior eye grading scales. Methods: A purpose designed computer program was written to detect edges using a 3 × 3 kernal and to extract colour planes in the selected area of an image. Annunziato and Efron pictorial, and CCLRU and Vistakon-Synoptik photographic grades of bulbar hyperaemia, palpebral hyperaemia roughness, and corneal staining were analysed. Results: The increments of the grading scales were best described by a quadratic rather than a linear function. Edge detection and colour extraction image analysis for bulbar hyperaemia (r2 = 0.35-0.99), palpebral hyperaemia (r2 = 0.71-0.99), palpebral roughness (r2 = 0.30-0.94), and corneal staining (r2 = 0.57-0.99) correlated well with scale grades, although the increments varied in magnitude and direction between different scales. Repeated image analysis measures had a 95% confidence interval of between 0.02 (colour extraction) and 0.10 (edge detection) scale units (on a 0-4 scale). Conclusion: The printed grading scales were more sensitive for grading features of low severity, but grades were not comparable between grading scales. Palpebral hyperaemia and staining grading is complicated by the variable presentations possible. Image analysis techniques are 6-35 times more repeatable than subjective grading, with a sensitivity of 1.2-2.8% of the scale.

Clinical monitoring of ocular physiology using digital image analysis

Aim: To examine the use of image analysis to quantify changes in ocular physiology. Method: A purpose designed computer program was written to objectively quantify bulbar hyperaemia, tarsal redness, corneal staining and tarsal staining. Thresholding, colour extraction and edge detection paradigms were investigated. The repeatability (stability) of each technique to changes in image luminance was assessed. A clinical pictorial grading scale was analysed to examine the repeatability and validity of the chosen image analysis technique. Results: Edge detection using a 3 × 3 kernel was found to be the most stable to changes in image luminance (2.6% over a +60 to -90% luminance range) and correlated well with the CCLRU scale images of bulbar hyperaemia (r = 0.96), corneal staining (r = 0.85) and the staining of palpebral roughness (r = 0.96). Extraction of the red colour plane demonstrated the best correlation-sensitivity combination for palpebral hyperaemia (r = 0.96). Repeatability variability was <0.5%. Conclusions: Digital imaging, in conjunction with computerised image analysis, allows objective, clinically valid and repeatable quantification of ocular features. It offers the possibility of improved diagnosis and monitoring of changes in ocular physiology in clinical practice. © 2003 British Contact Lens Association. Published by Elsevier Science Ltd. All rights reserved.

Spatial ecological complexity measures in GRASS GIS

Good estimates of ecosystem complexity are essential for a number of ecological tasks: from biodiversity estimation, to forest structure variable retrieval, to feature extraction by edge detection and generation of multifractal surface as neutral models for e.g. feature change assessment. Hence, measuring ecological complexity over space becomes crucial in macroecology and geography. Many geospatial tools have been advocated in spatial ecology to estimate ecosystem complexity and its changes over space and time. Among these tools, free and open source options especially offer opportunities to guarantee the robustness of algorithms and reproducibility. In this paper we will summarize the most straightforward measures of spatial complexity available in the Free and Open Source Software GRASS GIS, relating them to key ecological patterns and processes.

Adaptive edge analytics for distributed networked control of water systems

Over the last decade, there has been a trend where water utility companies aim to make water distribution networks more intelligent in order to improve their quality of service, reduce water waste, minimize maintenance costs etc., by incorporating IoT technologies. Current state of the art solutions use expensive power hungry deployments to monitor and transmit water network states periodically in order to detect anomalous behaviors such as water leakage and bursts. However, more than 97% of water network assets are remote away from power and are often in geographically remote underpopulated areas, facts that make current approaches unsuitable for next generation more dynamic adaptive water networks. Battery-driven wireless sensor/actuator based solutions are theoretically the perfect choice to support next generation water distribution. In this paper, we present an end-to-end water leak localization system, which exploits edge processing and enables the use of battery-driven sensor nodes. Our system combines a lightweight edge anomaly detection algorithm based on compression rates and an efficient localization algorithm based on graph theory. The edge anomaly detection and localization elements of the systems produce a timely and accurate localization result and reduce the communication by 99% compared to the traditional periodic communication. We evaluated our schemes by deploying non-intrusive sensors measuring vibrational data on a real-world water test rig that have had controlled leakage and burst scenarios implemented.