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.

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.

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.

Methods of Color Images Procession for Further Identification of the Object

The offered paper deals with the problems of color images preliminary procession. Among these are: interference control (local ones and noise) and extraction of the object from the background on the stage preceding the process of contours extraction. It was considered for a long time that execution of smoothing in segmentation through the boundary extraction is inadmissible, but the described methods and the obtained results evidence about expedience of using the noise control methods.

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.

Extended principal component analysis and its applications to image analysis

The objectives of this research are to analyze and develop a modified Principal Component Analysis (PCA) and to develop a two-dimensional PCA with applications in image processing. PCA is a classical multivariate technique where its mathematical treatment is purely based on the eigensystem of positive-definite symmetric matrices. Its main function is to statistically transform a set of correlated variables to a new set of uncorrelated variables over $\IR\sp{n}$ by retaining most of the variations present in the original variables.^ The variances of the Principal Components (PCs) obtained from the modified PCA form a correlation matrix of the original variables. The decomposition of this correlation matrix into a diagonal matrix produces a set of orthonormal basis that can be used to linearly transform the given PCs. It is this linear transformation that reproduces the original variables. The two-dimensional PCA can be devised as a two successive of one-dimensional PCA. It can be shown that, for an $m\times n$ matrix, the PCs obtained from the two-dimensional PCA are the singular values of that matrix.^ In this research, several applications for image analysis based on PCA are developed, i.e., edge detection, feature extraction, and multi-resolution PCA decomposition and reconstruction. ^

Constructive Synthesis of Memory-Intensive Accelerators for FPGA From Nested Loop Kernels

Field-programmable gate arrays are ideal hosts to custom accelerators for signal, image, and data processing but de- mand manual register transfer level design if high performance and low cost are desired. High-level synthesis reduces this design burden but requires manual design of complex on-chip and off-chip memory architectures, a major limitation in applications such as video processing. This paper presents an approach to resolve this shortcoming. A constructive process is described that can derive such accelerators, including on- and off-chip memory storage from a C description such that a user-defined throughput constraint is met. By employing a novel statement-oriented approach, dataflow intermediate models are derived and used to support simple ap- proaches for on-/off-chip buffer partitioning, derivation of custom on-chip memory hierarchies and architecture transformation to ensure user-defined throughput constraints are met with minimum cost. When applied to accelerators for full search motion estima- tion, matrix multiplication, Sobel edge detection, and fast Fourier transform, it is shown how real-time performance up to an order of magnitude in advance of existing commercial HLS tools is enabled whilst including all requisite memory infrastructure. Further, op- timizations are presented that reduce the on-chip buffer capacity and physical resource cost by up to 96% and 75%, respectively, whilst maintaining real-time performance.

Shock Train/Boundary-Layer Interaction in Rectangular Scramjet Isolators

Numerous studies of the dual-mode scramjet isolator, a critical component in preventing inlet unstart and/or vehicle loss by containing a collection of flow disturbances called a shock train, have been performed since the dual-mode propulsion cycle was introduced in the 1960s. Low momentum corner flow and other three-dimensional effects inherent to rectangular isolators have, however, been largely ignored in experimental studies of the boundary layer separation driven isolator shock train dynamics. Furthermore, the use of two dimensional diagnostic techniques in past works, be it single-perspective line-of-sight schlieren/shadowgraphy or single axis wall pressure measurements, have been unable to resolve the three-dimensional flow features inside the rectangular isolator. These flow characteristics need to be thoroughly understood if robust dual-mode scramjet designs are to be fielded. The work presented in this thesis is focused on experimentally analyzing shock train/boundary layer interactions from multiple perspectives in aspect ratio 1.0, 3.0, and 6.0 rectangular isolators with inflow Mach numbers ranging from 2.4 to 2.7. Secondary steady-state Computational Fluid Dynamics studies are performed to compare to the experimental results and to provide additional perspectives of the flow field. Specific issues that remain unresolved after decades of isolator shock train studies that are addressed in this work include the three-dimensional formation of the isolator shock train front, the spatial and temporal low momentum corner flow separation scales, the transient behavior of shock train/boundary layer interaction at specific coordinates along the isolator's lateral axis, and effects of the rectangular geometry on semi-empirical relations for shock train length prediction. A novel multiplane shadowgraph technique is developed to resolve the structure of the shock train along both the minor and major duct axis simultaneously. It is shown that the shock train front is of a hybrid oblique/normal nature. Initial low momentum corner flow separation spawns the formation of oblique shock planes which interact and proceed toward the center flow region, becoming more normal in the process. The hybrid structure becomes more two-dimensional as aspect ratio is increased but corner flow separation precedes center flow separation on the order of 1 duct height for all aspect ratios considered. Additional instantaneous oil flow surface visualization shows the symmetry of the three-dimensional shock train front around the lower wall centerline. Quantitative synthetic schlieren visualization shows the density gradient magnitude approximately double between the corner oblique and center flow normal structures. Fast response pressure measurements acquired near the corner region of the duct show preliminary separation in the outer regions preceding centerline separation on the order of 2 seconds. Non-intrusive Focusing Schlieren Deflectometry Velocimeter measurements reveal that both shock train oscillation frequency and velocity component decrease as measurements are taken away from centerline and towards the side-wall region, along with confirming the more two dimensional shock train front approximation for higher aspect ratios. An updated modification to Waltrup \& Billig's original semi-empirical shock train length relation for circular ducts based on centerline pressure measurements is introduced to account for rectangular isolator aspect ratio, upstream corner separation length scale, and major- and minor-axis boundary layer momentum thickness asymmetry. The latter is derived both experimentally and computationally and it is shown that the major-axis (side-wall) boundary layer has lower momentum thickness compared to the minor-axis (nozzle bounded) boundary layer, making it more separable. Furthermore, it is shown that the updated correlation drastically improves shock train length prediction capabilities in higher aspect ratio isolators. This thesis suggests that performance analysis of rectangular confined supersonic flow fields can no longer be based on observations and measurements obtained along a single axis alone. Knowledge gained by the work performed in this study will allow for the development of more robust shock train leading edge detection techniques and isolator designs which can greatly mitigate the risk of inlet unstart and/or vehicle loss in flight.

Detection of mesoscale thermal fronts from 4km data using smoothing techniques: Gradient-based fronts classification and basin scale application

In order to optimize frontal detection in sea surface temperature fields at 4 km resolution, a combined statistical and expert-based approach is applied to test different spatial smoothing of the data prior to the detection process. Fronts are usually detected at 1 km resolution using the histogram-based, single image edge detection (SIED) algorithm developed by Cayula and Cornillon in 1992, with a standard preliminary smoothing using a median filter and a 3 × 3 pixel kernel. Here, detections are performed in three study regions (off Morocco, the Mozambique Channel, and north-western Australia) and across the Indian Ocean basin using the combination of multiple windows (CMW) method developed by Nieto, Demarcq and McClatchie in 2012 which improves on the original Cayula and Cornillon algorithm. Detections at 4 km and 1 km of resolution are compared. Fronts are divided in two intensity classes (“weak” and “strong”) according to their thermal gradient. A preliminary smoothing is applied prior to the detection using different convolutions: three type of filters (median, average and Gaussian) combined with four kernel sizes (3 × 3, 5 × 5, 7 × 7, and 9 × 9 pixels) and three detection window sizes (16 × 16, 24 × 24 and 32 × 32 pixels) to test the effect of these smoothing combinations on reducing the background noise of the data and therefore on improving the frontal detection. The performance of the combinations on 4 km data are evaluated using two criteria: detection efficiency and front length. We find that the optimal combination of preliminary smoothing parameters in enhancing detection efficiency and preserving front length includes a median filter, a 16 × 16 pixel window size, and a 5 × 5 pixel kernel for strong fronts and a 7 × 7 pixel kernel for weak fronts. Results show an improvement in detection performance (from largest to smallest window size) of 71% for strong fronts and 120% for weak fronts. Despite the small window used (16 × 16 pixels), the length of the fronts has been preserved relative to that found with 1 km data. This optimal preliminary smoothing and the CMW detection algorithm on 4 km sea surface temperature data are then used to describe the spatial distribution of the monthly frequencies of occurrence for both strong and weak fronts across the Indian Ocean basin. In general strong fronts are observed in coastal areas whereas weak fronts, with some seasonal exceptions, are mainly located in the open ocean. This study shows that adequate noise reduction done by a preliminary smoothing of the data considerably improves the frontal detection efficiency as well as the global quality of the results. Consequently, the use of 4 km data enables frontal detections similar to 1 km data (using a standard median 3 × 3 convolution) in terms of detectability, length and location. This method, using 4 km data is easily applicable to large regions or at the global scale with far less constraints of data manipulation and processing time relative to 1 km data.

Automatic dynamic mask extraction for PIV images containing an unsteady interface, bubbles, and a moving structure

When performing Particle Image Velocimetry (PIV) measurements in complex fluid flows with moving interfaces and a two-phase flow, it is necessary to develop a mask to remove non-physical measurements. This is the case when studying, for example, the complex bubble sweep-down phenomenon observed in oceanographic research vessels. Indeed, in such a configuration, the presence of an unsteady free surface, of a solid–liquid interface and of bubbles in the PIV frame, leads to generate numerous laser reflections and therefore spurious velocity vectors. In this note, an image masking process is developed to successively identify the boundaries of the ship and the free surface interface. As the presence of the solid hull surface induces laser reflections, the hull edge contours are simply detected in the first PIV frame and dynamically estimated for consecutive ones. As for the unsteady surface determination, a specific process is implemented like the following: i) the edge detection of the gradient magnitude in the PIV frame, ii) the extraction of the particles by filtering high-intensity large areas related to the bubbles and/or hull reflections, iii) the extraction of the rough region containing these particles and their reflections, iv) the removal of these reflections. The unsteady surface is finally obtained with a fifth-order polynomial interpolation. The resulted free surface is successfully validated from the Fourier analysis and by visualizing selected PIV images containing numerous spurious high intensity areas. This paper demonstrates how this data analysis process leads to PIV images database without reflections and an automatic detection of both the free surface and the rigid body. An application of this new mask is finally detailed, allowing a preliminary analysis of the hydrodynamic flow.