Dynamic Vision for Perception and Control of Motion - Ernst D. Dickmanns Part 6 ppt

5.2 Efficient Extraction of Oriented Edge Features 135 ference is largest in amplitude, the gradient over two consecutive mask elements is maximal. However, due to local perturbations, this need not corre- spond to an actual extreme gradient on the scale of interest. Experience with images from natural environments has shown that two additional parameters may considerably improve the results obtained: 1. By allowing a yet to be specified number n 0 of entries in the mask center to be dropped, the results achieved may be more robust. This can be immediately appreciated when taking into account that either the actual edge direction may deviate from the mask orientation used or the edge is not straight but curved; by setting central elements of the mask to zero, the extreme intensity gradient becomes more pronounced. The rest of Figure 5.10 shows typical mask parameters with n 0 = 1 for masks three and five pixels in depth (m d = 3 or 5), and with n 0 = 2 for m d = 8 as well as n 0 = 3 for m d = 17 (rows b, c). 2. Local perturbations are suppressed by assigning to the mask a significant depth n d , which designates the number of pixels along the search path in each row or column in each positive and negative field. The total mask depth m d then is m d = 2 n d + n 0 . Figure 5.10 shows the corresponding mask schemes. In line (b) a rather large mask for finding the transition between relatively large homogeneous areas with ragged boundaries is given (m d = 17 pixels wide and each field with seven elements, so that the correlation value is formed from large averages; for a mask width n w of 17 pixels, the correlation value is formed from 7·17 = 119 pixels). With the number of zero-values in between chosen as n 0 = 3, the total receptive field (= mask) size is 17·17 = 289 pixels. The sum formed from n d mask elements (vector values “ColSum”) divided by (n w · n d ) represents the average intensity value in the oblique image region adjacent to the edge. At the maximum correlation value found, this is the average gray value on one side of the edge. This information may be used for recognizing a specific edge feature in consecutive images or for grouping edges in a scene context. For larger mask depths, it is more efficient when shifting the mask along the search direction, to subtract the last mask element (ColSum-value) from the summed field intensities and add the next one at the front in the search direction, see line (c) in Figure 5.10); the number of operations needed is much lower than for summing all ColSum elements anew in each field. The optimal value of these additional mask parameters n d and n 0 as well as the mask width n w depend on the scene at hand and are considered knowledge gained Figure 5.10. Efficient mask evaluation with the “Colsum”-vector; the n d -values given are typical for sizes of “receptive fields” formed b) m d = 2; m d = 3; m d = 5; m d = 8 7 3 7 Masks characterized by: (n d n 0 n d ) m d = 17 (Total mask depth) (a) (b) (c) 5 Extraction of Visual Features 136 by experience in visually similar environments. From these considerations, generic edge extraction mask sets for specific problems have resulted. In Figure 5.11, some representative receptive fields for different tasks are given. The mask parameters can be changed from one video frame to the next, allowing easy adaptation to changing scenes observed continuously, like driving on a curved road. The large mask in the center top of Figure 5.11 may be used on dirt roads in the near region with ragged transitions from road to shoulder. For sharp, pronounced edges like well-kept lane markings, a receptive field like that in the upper right corner (probably with n d = 2, that is, m d = 5) will be most efficient. The further one looks ahead, the more the mask width n w should be reduced (9 or 5 pixels); part (c) in the lower center shows a typical mask for edges on the right-hand side of a straight road further away (smaller and oblique to the right). The 5 × 5 (2, 1, 2) mask at the left hand side of Figure 5.11 has been the standard mask for initial detection of other vehicles and obstacles on the road through horizontal edges; collections of horizontal edge elements are good indicators for objects torn by gravity to the road surface. Additional masks are then applied for checking object hypotheses formed. If narrow lines like lane markings have to be detected, there is an optimal mask width depending on the width of the line in the image: If the mask depth n d chosen is too large, the line will be low-pass-filtered and extreme gradients lose in magnitude; if mask depth is too small, sensitivity to noise increases. As an optional step, while adding up pixel values for mask elements “ColSum” or while forming the receptive fields, the extreme intensity values of pixels in Col- Sum and of each ColSum vector component (max. and min.) may be determined. The former gives an indication of the validity of averaging (when the extreme values are not too far apart), while the latter may be used for automatically adjusting threshold parameters. In natural environments, in addition, this gives an indication Figure 5.11. Examples of receptive fields and search paths for efficient edge feature extraction; mask parameters can be changed from one video-frame to the next, allowing easy adaptation to changing scenes observed continuously R e c e p tiv e fie l d o f mask : n w = 1 7 n = 17 n w = 17 Search direction horizontal Search path center Search direction vertical (Shift of mask by 1 pixel at a time) Search path center (vertical) Receptive field of size 5×5: n d =2; n 0 =1; edge orien- tation16 (horizontal) n w = 5 search region condensed to 1-dimensional (averaged) vector n 0 =3 E d g e o r i e nt a t i o n 5 + - 0 n d =1 E d g e o r i e n t a t i o n 5 m d = 2·n d + n 0 =14 + 3 = 17 m d = 3 For fuzzy large scale edge For sharp, pro - nounced edge total = 289 pixel (tot al = 51 p ix el) (a) (b) n w = 9 Search path horizontal or vertical for diagonal edge direction d) 25 pixels n 0 = 2; n w = 5 Receptive field total = 30 pixel (c) Edge orientation 4 n d =7 n d =7 + + 0 - - - + n 0 =2; m d = 6 : small base for localizing edges with larger curvature ++ - 0 0 - E d ge orientation 8 5.2 Efficient Extraction of Oriented Edge Features 137 of the contrasts in the scene. These are some of the general environmental parameters to be collected in parallel (right-hand part of Figure 5.1). 5.2.2 Search Paths and Subpixel Accuracy The masks defined in the previous section are applied to rectangular search ranges to find all possible candidates for an edge in these ranges. The smaller these search ranges can be kept, the more efficient the overall algorithm is going to be. If the high-level interpretation via recursive estimation is stable and good information on the variances is available, the search region for specific features may be confined to the 3 ı region around the predicted value, which is not very large, usually (ı = standard variation). It does not make sense first to perform the image processing part in a large search region fixed in advance and afterwards sort out the features according to the variance criterion. In order not to destabilize the tracking process, prediction errors > 3 ı are considered outliers and are usually removed when they appear for the first time in a sequence.] Figure 5.6 shows an example of edge localization with a ternary mask of size n w = 17, n d = 2, and n 0 = 1 (i.e., mask depth m d = 5). The mask response is close to zero when the region to which it is applied is close to homogeneously gray (irre- spective of the gray value); this is an important design factor for abating sensitivity to light levels. It means that the plus– and minus regions have to be the same size. The lower part of the figure shows the resulting correlation values (mask re- sponses) which form the basis for determining edge location. If the image areas within each field of the mask are homogeneous, the response is maximal at the location of the edge. With different light levels, only the magnitude of the extreme value changes but not its location. Highly discernible extreme values are obtained also for neighboring mask orientations. The larger the parameter n 0 , the less pronounced is the extreme value in the search direction, and the more tolerant it is to deviations in angle. These robustness aspects make the method well suited for natural outdoor scenes. Search directions (horizontal or vertical) are automatically chosen depending on the feature orientation specified. The horizontal search direction is used for mask orientations between 45 to 135° as well as between 225 and 315°; vertical search is applied for mask directions between 135 to 225° and 315 to 45°. To avoid too fre- quent switching between search directions, a hysteresis (dead zone of about one direction–increment for the larger mask widths) is often used that means switching is actually performed (automatically) 6 to 11° beyond the diagonal lines, depending on the direction from which these are approached. 5.2.2.1 Subpixel Accuracy by Second-Order Interpolation Experience with several interpolation schemes, taking up to two correlation values on each side of the extreme value into account, has shown that the simple second- order parabola interpolation is the most cost-effective and robust solution (Figure 5.12). Just the neighboring correlation values around a peak serve as a basis. 5 Extraction of Visual Features 138 If an extreme value of the magnitude of the mask response above the threshold level (see Figure 5.6) has been found by stating that the new value is smaller than the old one, the last three values are used to find the interpolating parabola of second order. Its extreme value yields the position y extr of the edge to subpixel accuracy and the corresponding magnitude C extr ; this position is obtained at the location where the derivative of the parabolic unction is zero. Designating the largest correlation value found as C 0 at pixel position 0, the previous one C m at í1, and the last correlation value C p at position +1 (which indicated that there is an extreme value by its magnitude C p < C 0 ), the following differences 00m 1m = ; = DCC DCC p (5.1) yield the location of the extreme value at distance 01 extr 0 extr 0 1 d 0.5/ (2 / 1) from pixel position 0, such that: y = y + d with the value = 0.25 d . y DD y CC Dy     (5.2) From the last expressions of Equation 5.1 and 5.2 it is seen that the interpolated value lies on the side of C 0 on which the neighboring correlation value measured is larger. Experience with real-world scenes has shown that subpixel accuracy in the range of 0.3 to 0.1 may be achieved. 5.2.2.2 Position and Direction of an Optimal Edge Determining precise edge direction by applying, additionally, the two neighboring mask orientations in the same search path and performing a bi–variant interpolation has been investigated, but the results were rather disappointing. Precise edge direction can be determined more reliably by exploiting results from three neighboring search paths with the same mask direction (see Figure 5.13). The central edge position to subpixel accuracy yields the position of the tangent point, while the tangent direction is determined from the straight line connecting the positions of the (equidistant) neighboring edge points; this is Figure 5.13. Determination of the tangent direction of a slightly curved edge by sub-pixel localization of edge points in three neighboring search paths and parabolic interpolation Figure 5.12. Subpixel edge localization by parabolic interpolation after passing a maximum in mask response 5.2 Efficient Extraction of Oriented Edge Features 139 the result of a parabolic interpolation for the three points. Once it is known that the edge is curved – because the edge point at the center does not lie on the straight line connecting the neighboring edge points – the ques- tion arises whether the amount of curvature can also be determined with little effort (at least approximately). This is the case. 5.2.2.3 Approximate Determination of Edge Curvature When applying a series of equidistant search stripes to an image region, the method of the previous section yields to each point on the edge also the corresponding edge direction that is its tangent. Two points and two slopes determine the coefficients of a third-order polynomial, dubbed Hermite-interpolation after a French mathema- tician. As a third-order curve, it can have at most one inflection point. Taking the connecting line (dash-dotted in Figure 5.14) between the two tangent points P -d and P +d as reference (chord line or secant), a simple linear relationship for a smooth curve with small angles ȥ relative to the chord line can be derived. Tangent directions are used in differential-geometry terms, yielding a linear curvature model; the reference is the slope of the straight line connecting the tangent points (secant). Let m íd and m +d be the slopes of the tangents at points P íd and P +d respectively; s be the running variable in the direction of the arc (edge line); and ȥ the angle between the local tangent and the chord direction (|ȥ| < 0.2 radian so that cos(ȥ) §1). The linear curvature model in differential-geometry terms with s as running variable along the arc s from x §íd to x § +d is: 0 1 + ; dȥ dCCCs Cs   1 Cs . (5.3) Since curvature is a second-order concept with respect to Cartesian coordinates, lateral position y results from a second integral of the curvature model. With the origin at the center of the chord, x in the direction of the chord, y normal to it, and ȥ íd = arctan(m -d ) § m íd as the angle between the tangent and chord directions at point P íd , the equation describing the curved arc then is given by Equation 5.4 below [with ȥ in the range ± 0.2 radian (~ 11°), the cosine can be approximated by 1 and the sine by the argument ȥ]: 0001 0 23 0000 0 x = + ; ȥ(s) ȥ + (ı) dıȥ+ /2 ; y(s) = + sin[ȥ(ı)] dı ȥ /2 /6. s 2 s ds C Cs+Cs yysCs     ³ ³ (5.4) At the tangent points at the ends of the chord (± d), there is 2 dd00 1 2 +d +d 0 0 1 ȥ = ȥ + /2; (a) ȥ = ȥ + + /2. (b) mCdCd mCdCd  | | (5.5) At the points of intersection of chord and curve, there is, by definition y(± d) = 0, 23 00 0 1 23 00 0 1 () ȥ /2 /6 0; (a) () ȥ /2 /6 0. (b) yd y dCd Cd yd y dCd Cd        (5.6) Equations 5.5 and 5.6 can be solved for the curvature parameters C 0 and C 1 as well as for the state values y 0 and m 0 (ȥ 0 ) at the origin x = 0 to yield 5 Extraction of Visual Features 140 0 2 1 0 0 ( )/(2 ), 1.5 ( )/ , ȥ 0.25 ( ), 0.25 ( ) . dd dd dd dd Cmm d Cmmd mm ymmd              (5.7) The linear curvature model can be computed easily from the tangent directions relative to the chord line and the distance (2·d) between the tangent points. Of course, this distance has to be chosen such that the angle con- straint (|ȥ| < 0.2 radian) is not violated. On smooth curves, this is always possible; however, for large curvatures, the distance d allowed becomes small and the scale for measuring edge locations and tangent directions probably has to be adapted. Very sharp curves have to be isolated and jumped over as “corners” having large directional changes over small arc lengths. In an idealized but simple scheme, they can be approximated by a Dirac impulse in curvature with a finite change in direction over zero arc length. Due to the differencing process unavoidable for curvature determination, the results tend to be noisy. When basic properties of objects recognized are known, a post–processing step for noise reduction exploiting this knowledge should be included. Remark: The special advantage of subscale resolution for dynamic vision lies in the fact that the onset of changes in motion behavior may be detected earlier, yielding better tracking performance, crucial for some applications. The aperture problem inherent in edge tracking will be revisited in Section 9.5 after the basic tracking problem has been discussed. 5.2.3 Edge Candidate Selection Usually, due to image noise there are many insignificant extreme values in the resulting correlation vector, as can be seen in Figure 5.6. Positioning the threshold properly (and selecting the mask parameters in general) depends very much on the scene at hand, as may be seen in Figure 5.15, due to shadow boundaries and scene noise, the largest gradient values may not be those looked for in the task context (road boundary). Colinearity conditions (or even edge elements on a smoothly Figure 5.14. Approximate determination of curvature of a slightly curved edge by sub-pixel localization of edge points and tangent directions: Hermite-interpolation of a third order parabola from two tangent points P -d P +d m -d m +d y 0 = 0.25 (m +d – m íd ) d Linear curvature model: C = C 0 + C 1 · s; í d < s < + d ·d s C 0 = (m +d – m íd )/(2·d) C 1 = 1.5·(m -d + m +d )/d 2 Ȍ íd = arctan(m íd ) § m íd Ȍ -d íd 0 y x Ȍ 0 = í 0.25·(m íd + m +d ) 0 5.2 Efficient Extraction of Oriented Edge Features 141 Figure 5.15. The challenge of edge feature selection in road scenes: Good decisions can be made only by resorting to higher level knowledge. Road scenes with shadows (and texture); extreme correlation values marking road boundaries may not be the absolutely largest ones. curved line) may be needed for proper feature selection; therefore, threshold selection in the feature extraction step should not eliminate these candidates. Depending on the situation, these parameters have to be specified by the user (now) or by a knowledge-based component on the higher system levels of a more mature version. Average intensity levels and intensity ranges resulting from region-based methods (see Section 5.3) will yield information for the latter case. As a service to the user, in the code CRONOS, the extreme values found in one function call may be listed according to their correlation values; the user can spec- ify how many candidates he wants presented at most in the function call. As an extreme value of the search either the pixel position with the largest mask response may be chosen (simplest case with large measurement noise), or several neighboring correspondence values may be taken into account allowing interpolation. 5.2.4 Template Scaling as a Function of the Overall “Gestalt” An additional degree of freedom available to the designer of a vision system is the focal length of the camera for scaling the image size of an object to its distance in the scene. To analyze as many details as possible of an object of interest, one tends to assume that a focal length, which lets the object (in its largest dimension) just fill the image would be optimal. This may be the case for a static scene being observed from a stationary camera. If either the object observed or the vehicle carry- 5 Extraction of Visual Features 142 ing the camera or both can move, there should be some room left for searching and tracking over time. Generously granting an additional space of the actual size of the object to each side results in the requirement that perspective mapping (focal length) should be adjusted so that the major object dimension in the image is about one third of the image. This leaves some regions in the image for recognizing the environment of the object, which again may be useful in a task context. To discover essential shape details of an object, the smallest edge element template should not be larger than about one-tenth of the largest object dimension. This yields the requirement that the size of an object in the image to be analyzed in some detail should be about 20 to 30 pixels. However, due to the poor angular resolution of masks with a size of three pixels, a factor of 2 (60 pixels) seems more comfortable. This leads to the requirement that objects in an image must be larger than about 150 pixels. Keep in mind that objects imaged with a size (region) of only about a half dozen pixels still can be noticed (discovered and roughly tracked), however, due to spurious details from discrete mapping (rectangular pixel size) into the sensor array, no meaningful shape analysis can be performed. This has been a heuristic discussion of the effects of object size on shape recognition. A more operational consideration based on straight edge template matching and coordinate-free differential geometry shape representation by piecewise func- tions with linear curvature models is to follow. A lower limit to the support region required for achieving accuracy of about one-tenth of a pixel in a tangent position and about 1° in the tangent direction (order of magnitude) by subpixel resolution is about eight to ten pixels. The efficient scheme given in [Dickmanns 1985] for accurately determining the curvature parameters is limited to a smooth change in the tangent direction of about 20 to 25°; for recovering a circle (360°). This means that about n elef § 15 to 18 elemental edge features have to be measured. Since the ratio of circumference to diameter is ʌ for a circle, the smallest circle satisfying these conditions for non–overlapping support regions is n elef times (mask size = 8 to 10 pixels) divided by ʌ. This yields a required size of about 40 to 60 pixels in linear extension of an object in an image. Since corners (points of finite direction change) can be included as curvature impulses measurable by adjacent tangent directions, the smallest (horizontally aligned) measurable square is ten pixels wide while the diagonal is about 14 pixels; more irregularly shaped objects with concavities require a larger number of tangent measurements. The convex hull and its dimensions give the smallest size measurable in units of the support region. Fine internal structures may be lost. From these considerations, for accurate shape analysis down to the percent range, the image of the object should be between 20 and 100 pixel in linear extension, in general. This fits well in the template size range from 3 (or 5) to 17 (or 33) pixels. Usual image sizes of several hundred lines allow the presence of several well-recognizable objects in each image; other scales of resolution may require different focal lengths for imaging (from microscopy to far ranging telescopes). Template scaling for line detection: Finally, choosing the right scale for detecting (thin) lines will be discussed using a real example [Hofmann 2004]. Figure 5.16 shows results for an obliquely imaged lane marking which appears 16 pixels wide in the search direction (top: image section searched, width n w = 9 pixel). Summing up the mask elements in the edge direction corresponds to rectifying the image 5.2 Efficient Extraction of Oriented Edge Features 143 stripe, as shown below in the figure; however, only one intensity value remains, so that for the rest of the pixel-operations with different mask sizes in the search direction, about one order of magnitude in efficiency is gained. All five masks investigated (a) to (e) rely on the same “ColSum”-vector; depending on the depth of the masks, the valid search ranges are reduced (see double-arrows at bottom). Figure 5.16. Optimal mask size for line recognition: For general scaling, mask size should be scaled by line width (= 16 pixels here) The averaged intensity profile of the mask elements is given in the vertical center (around 90 for the road, and ~130 for the lane marker); the lane marking clearly sticks out. Curve (e) shows the mask response for the mask of highest possible resolution (1, 0, 1); see legend. It can be seen that the edge is correctly detected with respect to location, but due to the smaller extreme value, sensitivity to noise is higher than that for the other masks. All other masks have been chosen with n 0 = 3 for reducing sensitivity to slightly different edge directions including curved edges. In practical terms, this means that the three central values under the mask shifted over the ColSum–vector need not be touched; only n d values to the left and to the right need be summed. Depth values for the two fields of the mask of n d = 4, 8, and 16 (curves a, b, c) yield the same gradient values and edge location; the mask response widens with increasing field width. By scaling the field depth n d of the mask by the width of the line l w to be detected, the curves can be generalized to scaled masks of depths n d /l w = ¼, ½, and 1. Case (d) shows with n d /l w = 21/16 = 1.3 that for field depths larger than line width, the maximal gradient decreases and the edge is localized at a wrong position. So, the field width selected should always be smaller than the line to be detected. The number of zeros at the center should be less than the field depth, probably less than half that value for larger masks; values between 1 and 3 have shown good results for n d up to 7. For the detection of dirt roads with jagged edges and homogeneous intensity values on and off the road, large n 0 are favorable. 5 Extraction of Visual Features 144 5.3 The Unified Blob-edge-corner Method (UBM) The approach discussed above for detecting edge features of single (sub-) objects based on receptive fields (masks) has been generalized to a feature extraction method for characterizing image regions and general image properties by oriented edges, homogeneously shaded areas, and nonhomogeneous areas with corners and texture. For characterizing textures by their statistical properties of image intensities in real time (certain types of textures), more computing power is needed; this has to be added in the future. In an even more general approach, stripe directions could be defined in any orientation, and color could be added as a new feature space. For efficiency reasons, here, only horizontal and vertical stripes in intensity images are considered, for which only one matrix index and the gray values vary at a time). To achieve reusability of intermediate results, stripe widths are confined to even numbers and are decomposed into two half-stripes. 5.3.1 Segmentation of Stripes through Corners, Edges, and Blobs In this image evaluation method, the goal is to start from as few assumptions on intensity distributions as possible. Since pixel noise is an important factor in outdoor environments, some kind of smoothing has to be taken into account, however. This is done by fitting models with planar intensity distribution to local pixel values if they exhibit some smoothness conditions; otherwise, the region will be characterized as nonhomogeneous. Surprisingly, it has turned out that the planarity check for local intensity distribution itself constitutes a nice feature for region segmentation. 5.3.1.1 Stripe Selection and Decomposition into Elementary Blocks The field size for the least-squares fit of a planar pixel-intensity model is (2·m) × (2·n), and is called the “model support region” or mask region. For reusability of intermediate results in computation, this support region is subdivided into basic (elementary) image regions (called mask elements or briefly “mels”) that can be defined by two numbers: The number of pixels in the row direction m, and the number of pixels in the column direction n. In Figure 5.17, m has been selected as 4 and n as 2; the total stripe width for row search thus is 4 pixels. For m = n = 1, the highest possible image resolution will be obtained; however, strong influence of noise on the pixel level may show up in the results in this case. When working with video fields (sub–images with only odd or even row– indices, as is often done in practical applications), it makes sense for horizontal stripes to choose m = 2n; this yields averaging of pixels at least in row direction for n = 1. Rendering these mels as squares, finally yields the original rectangular image shape with half the original full-frame resolution. By shifting stripe evaluation by only half the stripe width, all intermediate pixel results in one half-stripe can be reused directly in the next stripe by just changing sign (see below). The price to be paid for this convenience is that the results obtained have to be represented at the [...]... direction (Iwmax-st and Iwmin-st) and for each mel (Icmax-st and Icmin-st); dividing the maximal and minimal value within each mel by the average for the mel, these scaled values will allow monitoring the appropriateness of averaging A reasonable balance between computing statistical data and fast performance has to be found for each set of problems Table 5.1 summarizes the parameters for feature evaluation... left of blob 2 in Figure 5.32 are points in case However, all four edges of these two lane markings are strong features by themselves and will be detected independently of the blob analysis, usually (see lower bar in the figure with characterization of edges as DH for darkto-bright and HD for bright-to-dark transitions [Hofmann 2004]) The basic mathematical tool used for the least squares fit of a... stages) Note that the center of a pixel or of mels does not coincide with the origin O of the masks, which is for all masks at (0, 0) The mask origin is always defined as the point where all four quadrants (mels) meet The computation of the average inten-4 -3 -2 -1 0 1 2 3 4 -4 Mask with mask element mel = 4×4 Mask in stripe Ri -3 at index k–1 Mask with mask elements 3 × 3 -2 -1 0 Q2 = I11 3 4 Q3 = I21... Check conditions for an extreme value of intensity gradient: product [(last d.o.g.) × (actual d.o.g.*)] < 0]? yes Determine edge location and edge orientation to subpixel accuracy; store in list of ‘edge features’ Update description of candidates for homogeneous shading Are the conditions for corner candidates satisfied? (circularity > qmin) and (traceN > traceNmin) Store in list of ‘nonlinearly shaded’... threshold value ErrMax 5.3 The Unified Blob-edge-corner Method (UBM) 155 Absolute number of occurrences (thousands) Figure 5.23 shows a Absolute number of locations of nonplanarity summary of results for the 35 absolute number of masks 11.11 4.5 with nonplanar intensity 30 4 distribution as a function of a variety of cell and 3.5 25 mask parameters as well 3 as of the threshold value 20 2.5 ErrMax in... 5.3 The Unified Blob-edge-corner Method (UBM) 157 occurrence in % of ~ 25 000 mask locations (cells) occurrence in % of ~ 200 000 mask locations (pixels) from several sets of parameters (mc , nc , m, n) and with a payoff function yet to be defined Values in the range 2 ErrMax 5% are recommended as default for reducing computer load, on the one hand, and for keeping good candidates for corners, on the... representations For computing gradients, of course, the real mel centers shown in quadrant Q4 have to be used The reconstruction of image intensities from results of one stripe is done for the central part of the mask (± half the size of the width normal to the search direction of the mask element) This is shown in the right part (b) of the figure by different shading It shows (low-frequency) shifting of the... underneath vehicles, and sky are designated; some correspondences are shown by dotted lines In 5.3 The Unified Blob-edge-corner Method (UBM) AB675 -Cell21; Col xxx; VarLim7.5; ReductLR ; N>4 163 AB675-Cell21; Col 335 VarLim7.5; ReductLR; N>4 220 191 200 180 sky with clouds column 335 truck at right 160 lane marking 140 71 120 100 80 Col 44 60 110 175 180 237 265 335 40 0 AB675-Cell21; Col 175; VarLim7.5;... 160 50 column 265 road 100 shade underneath car 150 200 250 300 80 40 0 150 50 100 150 200 250 300 AB675-Cell21; Col 110; VarLim7.5; ReductLR; N>4 column 44 rear light of second car left 200 shade underneath car 60 AB675-Cell21; Col 44; VarLim7.5; ReductLR; N>4 250 300 120 road 100 250 sky with clouds 140 truck in front 60 40 0 200 AB675-Cell21; Col 265 ; VarLim7.5; ReductLR; N>4 140 100 150 220 160 ... of 1-D blobs; values for VarLim of up to 100 (ten intensity levels out of 2 56 typical for 8-bit intensity coding in video) yield acceptable results for many applications A good check for the usefulness of the blob concept is the image quality judged by humans, after the image has been reconstructed from its abstract blob representation by average gray values, shading parameters, and the locations of . d < s < + d d s C 0 = (m +d – m d )/(2 d) C 1 = 1.5·(m -d + m +d ) /d 2 Ȍ d = arctan(m d ) § m d Ȍ -d d 0 y x Ȍ 0 = í 0.25·(m d + m +d ) 0 5.2 Efficient Extraction of Oriented Edge. (b) mCdCd mCdCd  | | (5.5) At the points of intersection of chord and curve, there is, by definition y(± d) = 0, 23 00 0 1 23 00 0 1 () ȥ /2 /6 0; (a) () ȥ /2 /6 0. (b) yd y dCd Cd yd y dCd. list of ‘nonlinearly shaded’ segments Update description of candidates for homogeneous shading yes yes no Are the conditions for corner candidates satisfied? (circularity > q min ) and

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