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...fit measure is sufficient to eliminate the problems that traditionally plague directional operators, such as false responses to highly curved edges and extension of edges beyond corners; see Hildreth =-=[12]-=-. This particular form of projection function, that is a Authorized licensed use limited to: Peking University. Downloaded on April 8, 2009 at 08:11 from IEEE Xplore. Restrictions apply.696 IEEE TRAN...

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...= l3 are constants, minimizing the energy functional of equation (1) gives rise to the following two independent Euler equations: dE ext - 0 ass + Px,,,, + __ - ax UYSS + PYSSSS + ___ aE ext _ - 0 ay =-=(10)-=- (11) When a(s) and /3(s) are not constant, it is simpler to go directly to a discrete formulation of the energy functional in equation (2). Then we can write Es*nake = $I Edi) + %X0 (12) Approximatin...

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...et and Jepson [20, 23]. Waxman, Wu and Bergholm Waxman, Wu and Bergholm [61] apply spatiotemporal lters to binary edge maps to track edges in real-time. Edge maps E(x� t), based on DOG zero-crossings =-=[42]-=-, are smoothed with a Gaussian lter to create a convected activation pro le A(x� t): A(x� t) = G(x�t� x� y� t) E(x� t) : (2.29) Level contours of A(x� t) are then tracked using di erential methods. Ho...

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...he energy between 4 and 8 cycles/deg. (On a two-dimensional plot the area covered by an octave band is proportional to f 2.) This falloff in power can also be related to the fractal nature of the lumi=-=(7)-=- (9) U ei7 03 4.() 3.() 2.0 1.0 0.0 0.0 1.0 2.0 Loglo spatial frequency (cycles/picture) Fig. 8. Amplitude spectra for the six images A-F, averaged across all orientations. The spectra have been shift...

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...al imaging. Line correspondence is usually expressed by pairs of line ends or middle points. Standard edge detection methods, like Canny detector [28] or a detector based on the Laplacian of Gaussian =-=[126]-=-, are employed for the line feature detection. The survey of existing edge detection method together with their evaluation can be found in [222]. Li et al. [112] proposed to exploit the already detect...

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... to characterize the different singularities but no effective method has been derived yet. In computer vision, it is extremely important to detect the edges that appear in images and many researchers =-=[6, 16, 17, 21, 22]-=- have developed techniques based on multiscale transforms. These multiscale transforms are equivalent to a wavelet transform but have been studied before the development of the wavelet formalism. Let ...

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...n in Figure 9 was digitized from the output of an inexpensive vidicon television camera. This image was convolved with a Laplacian of Gaussian function ( =1:8pixels) as suggested by the Marr-Hildreth =-=[23]-=- theory of edge detection. Edges in the image should give rise to zero-crossings in this convolution, but where the intensity gradient is low there will also be many other zerocrossings that do not co...

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...ir maximum F-measure ( with respect to human ground-truth boundaries. Iso-F curves are shown in green. Our gP b detector [3] performs significantly better than other algorithms [2], [17], [18], [19], =-=[20]-=-, [21], [22], [23], [24], [25], [26], [27], [28] across almost the entire operating regime. Average agreement between human subjects is indicated by the green dot. Fig. 2. Evaluation of segmentation a...

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...ge, each node of Lt can be obtained directly by convolving Wt - Wt+l with the image. This difference of Gaussian-like functions resembles the Laplacian operators commonly used in the image processing =-=[5]-=-, so we refer to the sequence Lo, L~ .... , LN as the Laplacian pyramid. 2 2.3 Summation Property The steps used to construct the Laplacian pyramid may be reversed to recover the original image Go exa...