{"title": "Extending Phase Mechanism to Differential Motion Opponency for Motion Pop-out", "book": "Advances in Neural Information Processing Systems", "page_first": 1267, "page_last": 1275, "abstract": "We extend the concept of phase tuning, a ubiquitous mechanism in sensory neurons including motion and disparity detection neurons, to the motion contrast detection.  We demonstrate that motion contrast can be detected by phase shifts between motion neuronal responses in different spatial regions. By constructing the differential motion opponency in response to motions in two different spatial regions, varying motion contrasts can be detected, where similar motion is detected by zero phase shifts and differences in motion by non-zero phase shifts.  The model can exhibit either enhancement or suppression of responses by either different or similar motion in the surrounding.  A primary advantage of the model is that the responses are selective to relative motion instead of absolute motion, which could model neurons found in neurophysiological experiments responsible for motion pop-out detection.", "full_text": " \n\n \n\nExtending Phase Mechanism to Differential \n\nMotion Opponency for Motion Pop-Out \n\nYicong Meng and Bertram E. Shi\n\nDepartment of Electronic and Computer Engineering \nHong Kong University of Science and Technology \n\nClear Water Bay, Kowloon, Hong Kong \n\n{eeyicong, eebert}@ust.hk\n\nAbstract \n\nWe extend the concept of phase tuning, a ubiquitous mechanism among \nsensory neurons including motion and disparity selective neurons, to the \nmotion contrast detection. We demonstrate that the motion contrast can be \ndetected by phase shifts between motion neuronal responses in different \nspatial regions. By constructing the differential motion opponency in \nresponse to motions in two different spatial regions, varying motion contrasts \ncan be detected, where similar motion is detected by zero phase shifts and \ndifferences in motion by non-zero phase shifts. The model can exhibit either \nenhancement or suppression of responses by either different or similar \nmotion in the surrounding. A primary advantage of the model is that the \nresponses are selective to relative motion instead of absolute motion, which \ncould model neurons found in neurophysiological experiments responsible \nfor motion pop-out detection. \n\nIntroduction \n\n1 \nMotion discontinuity or motion contrast is an important cue for the pop-out of salient moving \nobjects from contextual backgrounds. Although the neural mechanism underlying the motion \npop-out detection is still unknown, the center-surround receptive field (RF) organization is \nconsidered as a physiological basis responsible for the pop-out detection. \nThe center-surround RF structure is simple and ubiquitous in cortical cells especially in neurons \nprocessing motion and color information. Nakayama and Loomis [1] have predicted the existence \nof motion selective neurons with antagonistic center-surround receptive field organization in 1974. \nRecent physiological experiments [2][3] show that neurons with center-surround RFs have been \nfound in both middle temporal (MT) and medial superior temporal (MST) areas related to motion \nprocessing. This antagonistic mechanism has been suggested to detect motion segmentation [4], \nfigure/ground segregation [5] and the differentiation of object motion from ego-motion [6]. \nThere are many related works [7]-[12] on motion pop-out detection. Some works [7]-[9] are based \non spatio-temporal filtering outputs, but motion neurons are not fully interacted by either only \ninhibiting similar motion [7] or only enhancing opposite motion [8]. Heeger, et al. [7] proposed a \ncenter-surround operator to eliminate the response dependence upon rotational motions. But the \nHeeger's model only shows a complete center-surround interaction for moving directions. With \nrespect to the surrounding speed effects, the neuronal responses are suppressed by the same speed \nwith the center motion but not enhanced by other speeds. Similar problem existed in [8], which only \nmodeled the suppression of neuronal responses in the classical receptive field (CRF) by similar \nmotions in surrounding regions. Physiological experiments [10][11] show that many neurons in \nvisual cortex are sensitive to the motion contrast rather than depend upon the absolute direction and \nspeed of the object motion. Although pooling over motion neurons tuned to different velocities can \n\n\feliminate the dependence upon absolute velocities, it is computationally inefficient and still can't \ngive full interactions of both suppression and enhancement by similar and opposite surrounding \nmotions. The model proposed by Dellen, et al. [12] computed differential motion responses directly \nfrom complex cells in V1 and didn't utilize responses from direction selective neurons. \nIn this paper, we propose an opponency model which directly responds to differential motions by \nutilizing the phase shift mechanism. Phase tuning is a ubiquitous mechanism in sensory information \nprocessing, including motion, disparity and depth detection. Disparity selective neurons in the \nvisual cortex have been found to detect disparities by adjusting the phase shift between the receptive \nfield organizations in the left and right eyes [13][14]. Motion sensitive cells have been modeled in \nthe similar way as the disparity energy neurons and detect image motions by utilizing the phase shift \nbetween the real and imaginary parts of temporal complex valued responses, which are comparable \nto images to the left and right eyes [15]. Therefore, the differential motion can be modeled by \nexploring the similarity between images from different spatial regions and from different eyes. \nThe remainder of this paper is organized as following. Section 2 illustrates the phase shift motion \nenergy neurons which estimate image velocities by the phase tuning in the imaginary path of the \ntemporal receptive field responses. In section 3, we extend the concept of phase tuning to the \nconstruction of differential motion opponency. The phase difference determines the preferred \nvelocity difference between adjacent areas in retinal images. Section 4 investigates properties of \nmotion pop-out detection by the proposed motion opponency model. Finally, in section 5, we relate \nour proposed model to the neural mechanism of motion integration and motion segmentation in \nmotion related areas and suggest a possible interpretation for adaptive center-surround interactions \nobserved in biological experiments. \n\nPhase Shift Motion Energy Neurons \n\n2 \nAdelson and Bergen [16] proposed the motion energy model for visual motion perception by \nmeasuring spatio-temporal orientations of image sequences in space and time. The motion energy \nmodel posits that the responses of direction-selective V1 complex cells can be computed by a \ncombination of two linear spatio-temporal filtering stages, followed by squaring and summation. \nThe motion energy model was extended in [15] to be phase tuned by splitting the complex valued \ntemporal responses into real and imaginary paths and adding a phase shift on the imaginary path. \nFigure 1(a) demonstrates the schematic diagram of the phase shift motion energy model. Here we \nassume an input image sequence in two-dimensional space (x, y) and time t. The separable \nspatio-temporal receptive field ensures the cascade implementation of RF with spatial and temporal \nfilters. Due to the requirement of the causal temporal RF, the phase shift motion energy model \ndidn\u2019t adopt the Gabor filter like the spatial RF. The phase shift spatio-temporal RF is modeled with \n)\na complex valued function \n\u03a6 , where the spatial and temporal RFs are \n(\n,h t \u03a6 respectively, \ndenoted by \n\n(\ng x y and \n\n(\n(\ng x y h t\n\n(\nf x y t\n,\n\n=\n\n)\n\n)\n\n)\n\n,\n\n,\n\n,\n\n,\n\n\u22c5\n\n \n\n)\n)\n(\ng x y\n,\n=\n(\n)\nh t\n\u03a6 =\n\n,\n\n(\n\nN\nh\nreal\n\n)\nC\nx y\n,\n| 0,\n(\n( )\nt\nexp\n+\n\n\u03a9 + \u03a9\n\nj\n\nx\n\n(\nj\nexp\n)\nh\nj\n\u03a6\nimag\n\nx\n( )\nt\n\ny\n\n)\n\ny\n\n \n\n(1) \n\nand C is the covariance matrix of the spatial Gaussian envelope and \u03a6 is the phase tuning of the \nmotion energy neuron. The real and imaginary profiles of the temporal receptive field are Gamma \nmodulated sinusoidal functions with quadrature phases, \n)\n(\n,\ncos\n\u03a9\n\u03b1\u03c4\nt\n(\n)\n,\n|\nsin\n\u03a9\n\u03b1\u03c4\n\n(\n( )\nt\nt\n=\nG\n( )\n(\nt\n=\nG\n\nh\nreal\nh\nimag\n\n)\nt\n)\nt\n\n(2) \n\n|\nt\n\n \n\n \n\nt\n\nThe envelopes for complex exponentials are functions of Gaussian and Gamma distributions, \n\n \n\nN\n\n(\n\nx y\n,\n\n| 0,\n\nC\n\n)\n\n=\n\n1\n\n2\n\u03c0\u03c3\u03c3\ny\n\nx\n\nexp\n\n\u2212\n\n\u239b\n\u239c\n\u239c\n\u239d\n\n2\n\n2\n\ny\nx\n2\n2\n2\n\u03c3 \u03c3\ny\n\n\u2212\n\n2\nx\n\n \n\n\u239e\n\u239f\n\u239f\n\u23a0\n\n(3) \n\n\fh\nt\nreal( )\n\nh\nt\nimag( )\n\nrealV\n\ng x y\n( ,\n\n)\n\ng x y\n( ,\n\n)\n\nje \u03a6\n\nimagV\n\nV \u03a6\n\n(\n\n)\n\nM\n\nM\n\nM\n\nM\n\n(\u00b7)2\n(\u00b7)2\n\nM\n(\u00b7)2\n(\u00b7)2\n\nM\n(\u00b7)2\n(\u00b7)2\n\n(a) \n)max\n\nvE \u03a6\n\n(\n\nje \u03a6\n\nmin\n\ncw x y\n,\n\n(\n\n)\n\nsw x y\n,\n\n(\n\n)\n\nje \u03a6\n\nmin\n\nM\n( )0vE\ncw x y\n,\n\n(\n\n)\n\n0je\n\n\u222b\u222b\u222b\n\nx y \u03a6\n,\n\n,\n\nvE\u0394 \u0398\n\n(\n\n)\n\nje \u0398\n\ncK\n\nsK\n\n\u222b\u222b\u222b\n\nx y \u03a6\n,\n\n,\n\nM\n)\nsw x y\n,\n\n(\n\nvE \u03a6\n\n(\n\nM\n)min\n\ncw x y\n,\n\n(\n\n)\n\nje \u03a6\n\nmax\n\nsw x y\n,\n\n(\n\n)\n\n0je\n\nM\nje \u03a6\n\nmax\n\n(b) \n\n(\u00b7)2\n(\u00b7)2\n\nM\n(\u00b7)2\n(\u00b7)2\n\nM\n(\u00b7)2\n(\u00b7)2\n\nM\n\nM\n\nM\n\nM\n\n(c) \n\nFigure 1. (a) shows the diagram of the phase shift motion energy model adapted from [15]. (b) \ndraws the spatiotemporal representation of the phase shift motion energy neuron with the real\nand imaginary receptive field demonstrated by the two left pictures. (c) illustrates the \nconstruction of differential motion opponency with a phase difference \u0398 from two populations \nof phase shift motion energy neurons in two spatial areas c and s. To avoid clutter, the space \nlocation (x, y) is not explicitly shown in phase tuned motion energies. \n\n \n\n=\n\nG\n\nt\n( |\n\n, )\n\u03b1\u03c4\n\n1\n(\n)\n\u03b1\n\u0393\n\u03b1\u03c4\n( )u t\n(\n)\u03b1\u0393\n is the unit step function. The parameters \u03b1 and \u03c4 \nwhere \ndetermine the temporal RF size. As derived in [15], the motion energy at location (x, y) can be \ncomputed by \n \n\n is the gamma function and \n\n\u03a6 = +\n\nt\n\u239e\n\u239f\n\u03c4\n\u23a0\n\n\u239b\n\u2212\u239c\n\u239d\n\nS P\n\nu t\n( )\n\n(4) \n\n(5) \n\nexp\n\ncos\n\n1\n\u03b1\n\u2212\n\nE\n\nt\n\n \n\n,\n\n(\n\n)\n\u03a8 \u2212 \u03a6 \n\n(\nv x y\n,\n\n)\n\nwhere \n\n \n\nS\nP\n\n=\n\n=\n\n\u03a8 =\n\n2\n\n \n\n2\n\nV\n+\nreal\nV V\n*\n2\nreal\nimag\n(\nV V\nreal\n\narg\n\nV\nimag\n\n*\nimag\n\n)\n\nand complex valued responses in real and imaginary paths are obtained as, \n\nV\nreal\n\n(\n\nx y t\n,\n,\n\n)\n\n=\n\n \n\nV\nimag\n\n(\n\nx y t\n,\n,\n\n)\n\ng\n\n(\n)\n\u03be\u03b6\n\n,\n\nh\nreal\n\n(\n)\n\u03b7\n\n(\nI x\n\n\u2212\n\n\u03be \u03b6 \u03b7 \u03be \u03b6 \u03b7\n\nd d d\n\n\u2212\n\n\u2212\n\ny\n\nt\n\n,\n\n,\n\n)\n\ng\n\n(\n)\n\u03be\u03b6\n\n,\n\nh\nimag\n\n(\n)\n\u03b7\n\n(\nI x\n\n\u2212\n\n \n\u03be \u03b6 \u03b7 \u03be \u03b6 \u03b7\n\nd d d\n\n\u2212\n\n\u2212\n\ny\n\nt\n\n,\n\n,\n\n)\n\n,\n\n,\n\n\u222b\u222b\u222b\n\u222b\u222b\u222b\n\n\u03be\u03b6\u03b7\n=\n\n\u03be\u03b6\u03b7\n\n,\n\n,\n\n(6) \n\n(7) \n\nThe superscript * represents the complex conjugation and the phase shift parameter \u03a6 controls the \nspatio-temporal orientation tuning. To avoid clutter, the spatial location variables x and y for S, P, \n\u03a8, Vreal and Vimag are not explicitly shown in Eq. (5) and (6). Figure 1(b) demonstrates the even and \nodd profiles of the spatio-temporal RF tuned to a particular phase shift. \n\n\f\u0398(cid:3407)0 \n\n\u0398(cid:3408)0 \n\n \n\n(a) \n\n(b) \n\nFigure 2. Two types of differential motion opponency constructions of (a) center-surrounding \ninteraction and (b) left-right interaction. Among cells in area MT with surrounding \nmodulations, 25% of cells are with the antagonistic RF structure in the top row and another \n50% of cells have the integrative RF structure as shown in the bottom row. \n\n \n\n \n\n3 \n\nExtending Phase Mechanism \nOpponency \n\nto Differential Motion \n\nBased on the above phase shift motion energy model, the local image velocity at each spatial \nlocation can be represented by a phase shift which leads to the peak response across a population of \nmotion energy neurons. Across regions of different motions, there are clear discontinuities on the \nestimated velocity map. The motion discontinuities can be detected by edge detectors on the \nvelocity map to segment different motions. However, this algorithm for motion discontinuities \ndetection can\u2019t discriminate between the object motion and uniform motions in contextual \nbackgrounds. \nHere we propose a phase mechanism to detect differential motions inspired by the disparity energy \nmodel and adopt the center-surround inhibition mechanism to pop out the object motion from \ncontextual background motions. The motion differences between different spatial locations can be \nmodeled in the similar way as the disparity model. The motion energies from two neighboring \nlocations are considered as the retinal images to the left and right eyes. Thus, we can construct a \ndifferential motion opponency by placing two populations of phase shift motion energy neurons at \nvE\u0394 \u0398 of the opponency is the squared modulus of the \ndifferent spatial locations and the energy \naveraged phase shift motion energies over space and phase, \n\n(\n\n)\n\n \n\nE\n\n)\n\u0394 \u0398 =\nv\n\n(\n\n\u222b\u222b\u222b\n\nvE x y\n,\n\n(\n\n,\n\n)\n\u03a6 \u22c5\n\n(\nw x y\n,\n\n,\n\n\u03a6 \u0398\n\n|\n\n)\n\ndxdyd\n\n\u03a6\n\n2\n\n \n\n(8) \n\n,\n\n,\n\n)\n\n(\nw x y \u0398 is the profile for differential motion opponency and v\u0394 is the velocity difference \nwhere \n(\nw x y \u0398 is intended to \nbetween the two spatial regions defined by the kernel \nimplement the functional role of spatial interactions, it is desired to be a separable function in space \nand phase domain and can be modeled by phase tuned summation of two spatial kernels, \n \n\n(\nw x y \u0398 . Since \n\n(9) \n\n\u0398+ \u03a6\n\n)\n\n)\n\ne\n\n+\n\n \n\n,\n\n,\n\nj\n\n\u03a6\n\n,\n\n,\n\n,\n\n)\n\u03a6 \u0398 =\n\n|\n\n)\nw x y e\nc\n\n(\n\n,\n\nw x y\ns\n\n,\n\n(\n\n)\n\nj\n\nj\n\n(\n\n)\n\n,\n\ncw x y and \n\ns\u03c3 , and \u0398 is \nc\u03c3 and \nwhere \nthe phase difference representing velocity difference between two spatial regions c and s. \nSubstituting Eq. (9) into Eq. (8), the differential motion energy can be reformulated as \n\nsw x y are Gaussian kernels of different spatial sizes \n\n,\n\n(\n\n(\nw x y\n,\n)\n\n \n\nE\n\n)\n\u0394 \u0398 =\nv\n\n(\n\nK\n\nc\n\n+\n\ne K\u0398\nj\n\ns\n\n2\n\n \n\n(10) \n\n\fy\nt\ni\nc\no\ne\nV\n\nl\n\n \nt\n\nh\ng\nR\n\ni\n\n3\n\n2\n\n1\n\n0\n\n-1\n\n-2\n\n-3\n \n-3\n\n-2\n\n \n\n2\n\n3\n\n3\n\n2\n\n1\n\n0\n\n-1\n\n-2\n\n-3\n\ny\nt\ni\nc\no\ne\nV\n\nl\n\n \nt\nh\ng\nR\n\ni\n\n3\n\n2\n\n1\n\n0\n\n-1\n\n-2\n\n-3\n \n-3\n\n-2\n\n \n\n2\n\n3\n\n1\n\n0.98\n\n0.96\n\n0.94\n\n0.92\n\n0.9\n\n0.88\n\n0.86\n\n0.84\n\n0.82\n\n0.8\n\n0\n\n-1\n1\nLeft Velocity\n(a) \n\n0\n\n-1\n1\nLeft Velocity\n(b) \n\nFigure 3. (a) Phase map and (b) peak magnitude map are obtained from stimuli of two patches\nof random dots moving with different velocities. The two patches of stimuli are statistically \nindependent but share the same spatial properties: dot size of 2 pixels, dot density of 10% and\ndot coherence level of 100%. The phase tuned population of motion energy neurons are \n\napplied to each patch of random dots with RF parameters: \u2126t = 2\u03c0/8, \u2126t = 2\u03c0/16, \u03c3x = 5 and \u03c4\n\n= 5.5. For each combination of velocities from left and right patches, averaged phase shifts\nover space and time are computed and so do the magnitudes of peak responses. The unit for \nvelocities is pixels per frame. \n\nwhere \n\n \n\nK\n\nc\n\n=\n\nK\n\ns\n\n=\n\n\u03a6\n\nx y\n,\n\n,\n\n\u222b\u222b\u222b\n\u222b\u222b\u222b\n\nx y\n,\n\n,\n\n\u03a6\n\nE\nv c\n,\n\nE\nv s\n,\n\n(\n\n(\n\nx y\n,\n\n,\n\n\u03a6\n\nx y\n,\n\n,\n\n\u03a6\n\n)\n\n)\n\nexp\n\n(\n\nj\n\n\u03a6\n\n)\n\nexp\n\n(\n\nj\n\n\u03a6\n\n)\n\nw x y dxdyd\nc\n\n,\n\n)\n\n(\n\nw x y dxdyd\ns\n\n,\n\n)\n\n(\n\n\u03a6\n\n\u03a6\n\n \n\n (11) \n\n(\n\n)\n\n,\n\nx y \u03a6 and \n,\n\nv cE\n,\nshift \u03a6. Utilizing the results in Eq. (5) and (6), Eq. (10) and (11) generate similar results, \n\nx y \u03a6 are phase shift motion energies at location (x, y) and with phase \n,\n\nv sE\n,\n\n,\n\n(\n\n)\n\n \n\nwhere \n\nE\n\n)\n\u0394 \u0398 =\nv\n\n(\n\nS\n\nopp\n\n+\n\nP\nopp\n\ncos\n\n(\n\n)\n\u0398 \u2212 \u0398 \n\nopp\n\n(12) \n\n2\n\nK\n\ns\n\n=\n\nS\nopp\nP\nopp\n\u0398 =\n\n=\n\n2\n\nK\n+\nc\nK K\n2\n*\ns\n(\narg\n\nc\n\nc\n\n \n\n \n\n*\ns\n\n)\n\nopp\n\n, \n\noppS\n\nK K\n\n(13) \n\nopp\u0398 . \n\noppP and \n\nAccording to above derivations, by varying the phase shift \u0398 between \u2013\u03c0 and \u03c0, the relative motion \n\nenergy of the differential motion opponency can be modeled as population responses across a \npopulation of phase tuned motion opponencies. The response is completely specified by three \nparameters \nThe schematic diagram of this opponency is illustrated in Figure 1(c). The differential motion \nopponency is constituted by three stages. At the first stage, a population of phase shift motion \nenergy neurons is applied to be selective to different velocities. At the second stage, motion \nenergies from the first stage are weighted by kernels tuned to different spatial locations and phase \nshifts respectively for both spatial regions and two single differential motion signals in region c and \nregion s are achieved by integrating responses from these two regions over space and phase tuning. \nFinally, the differential motion energy is computed by the squared modulus of the summation of the \nintegrated motion signal in region c and phase shifted motion signal in region s. The subscripts c \nand s represent two interacted spatial regions which are not limited to the center and surround \nregions. The opponency could also be constructed by the neighboring left and right \n\n\fInhibitive interaction, \u0398 =(cid:3398)\u03c0/2 \n\nInhibitory\n\npi/2\n\nSurrouding Direction\n\n3pi/2\n\n2pi\n\nModel by Petkov et al. [8] \n\npi\n\n(a) \n\nInhibitory\n\ns\ne\ns\nn\no\np\ns\ne\nR\n\n2\n\n1.6\n\n1.2\n\n0.8\n\n0.4\n\n0\n0\n\n2\n\n1.6\n\n1.2\n\n0.8\n\n0.4\n\n0\n\ns\ne\ns\nn\no\np\ns\ne\nR\n\nExcitatory interaction, \u0398 =0 \n\nExcitatory\n\npi/2\n\npi\n\n3pi/2\n\n2pi\n\nSurrouding Direction\n\n(b) \n\nModel by Heeger et al. [7] \n\nInhibitory\n\npi/2\n\npi\n\nSurrouding Direction\n\n3pi/2\n\n2pi\n\ns\ne\ns\nn\no\np\ns\ne\nR\n\n2\n\n1.6\n\n1.2\n\n0.8\n\n0.4\n\n0\n0\n\n2\n\n1.6\n\n1.2\n\n0.8\n\ns\ne\ns\nn\no\np\ns\ne\nR\n\n0.4\n\n0\n0\n\n(d) \n\n0\n\npi/2\n\npi\n\nSurrouding Direction\n\n3pi/2\n\n2pi\n\n(c) \n\nFigure 4. Demonstrations of center-surround differential motion opponency, where (a) show \nthe excitation of opposite directions outside the CRF and (b) show the inhibition by \nsurrounding motions in same directions. The center-surround inhibition models by Petkov, et \nal. [8] and Heeger, et al. [7] are shown in (c) and (d). Responses above 1 indicate enhancement\nand responses below 1 indicate suppressions. \n\nspatial regions. Figure 2 shows two types of structures for the differential motion opponency. In \n[17], the authors demonstrates that among cells in area MT with surrounding modulations, 25% of \ncells are with the antagonistic RF structure as shown in Figure 2(a) and another 50% of cells have \nthe integrative RF structure as shown in Figure 2(b). \nThe velocity difference tuning of the opponency is determined by the phase shift parameter \u0398 \ncombined with parameters of spatial and temporal frequencies for motion energy neurons. The \nlarger phase shift magnitude prefers the bigger velocity difference. This phase tuning of velocity \ndifference is consistent with the phase tuning of motion energy neurons. Figure 3 shows the phase \nmap obtained by using random dots stimuli with different velocities on two spatial patches (left and \n\nright patches with sizes of 128 pixels (cid:3400) 128 pixels). Along the diagonal line, velocities from left and \n\nright patches are equal to each other and therefore phase estimates are zeros along this line. \nDeviated from the diagonal line to upper-left and lower-right, the phase magnitudes increase while \npositive phases indicate larger left velocities and negative phases indicate larger right velocities. \nThe phase tuning can give a good classification of velocity differences. \n\nValidation of Differential Motion Opponency \n\n4 \nOut derivation and analysis above show that the phase shift between two neighboring spatial regions \nis a good indicator for motion difference between these two regions. In this section, we validate the \nproposed differential motion opponency by two sets of experiments, which show effects of both \nsurrounding directions and speeds on the center motion. \n\n\f2\n\n1.6\n\n1.2\n\n0.8\n\ns\ne\ns\nn\no\np\ns\ne\nR\n\n0.4\n\n0\n-2\n\n-1.5\n\n-1\n\nInhibitory\n\n-0.5\n\n0\n\n0.5\n\nCenter Speed\n\n2\n\n1.6\n\n1.2\n\n0.8\n\ns\ne\ns\nn\no\np\ns\ne\nR\n\n0.4\n\n0\n-2\n\n-1.5\n\n-1\n\n1\n\n1.5\n\n2\n\nInhibitory\n\n-0.5\n\n0\n\n0.5\n\nCenter Speed\n\n1\n\n1.5\n\n2\n\n(a) \n\n(b) \n\nFigure 5. The insensitivity of the proposed opponency model to absolute center and\nsurrounding velocities is demonstrated in (a), where responses are enhanced for all center \nvelocities from -2 to 2 pixels per frame. In (b), the model by Heeger, et al. [7] only shows \nenhancement when the center speed matches the preferred speed of 1.2 pixel per frame. \nSimilarly, responses above 1 indicate enhancement and below 1 indicate suppressions. In both\ncurves, the velocity differences between center and surrounding regions are maintained as a\nconstant of 3 pixels per frame. \n\nPhysiological experiments [2][3] have demonstrated that the neuronal activities in the classical \nreceptive field are suppressed by responses outside the CRF to stimuli with similar motions \nincluding both directions and speeds on the center and surrounding regions. On the contrary, visual \nstimuli of opposite directions or quite different speeds outside the CRF enhance the responses in the \nCRF. In their experiments, they used a set of stimuli of random dots moving at different velocities, \nwhere there are small patches of moving random dots on the center. \nWe tested the properties of the proposed opponency model for motion difference measurement by \nusing similar random dots stimuli. The random dots on background move with different speeds and \nin different direction but have the same statistical parameters: dot size of 2 pixels, dot density of \n10% and motion coherence level of 100%. The small random dots patches are placed on the center \nof background stimuli to stimulate the neurons in the CRF. These small patches share the same \nstatistical parameters with background random dots but move with a constant velocity of 1 pixel per \nframe. \nFigure 4 shows results for the enhanced and suppressed responses in the CRF with varying \nsurrounding directions. The phase shift motion energy neurons had the same spatial and temporal \nfrequencies and the same receptive field sizes, and were selective to vertical orientations. The \n\npreferred spatial frequency was 2\u03c0/16 radian per pixel and the temporal frequency was 2\u03c0/16 radian \npixels, corresponding to a spatial bandwidth of 1.96 octaves. The time constant \u03c4 was 5.5 frames \n\nper frame. The sizes of RF in horizontal and vertical directions were respectively 5 pixels and 10 \n\nwhich resulted in a temporal bandwidth of 1.96 octaves. As shown in Figure 4 (a) and (b), the \nsurrounding motion of opposite direction gives the largest response to the motion in the CRF for the \ninhibitory interaction and the smallest response for the excitatory interaction. \nResults demonstrated in Figure 4 are consistent with physiological results reported in [3]. In Born\u2019s \npaper, inhibitory cells show response enhancement and excitatory cells show response suppression \nwhen surrounding motions are in opposite directions. The 3-dB bandwidth for the surrounding \nmoving direction is about 135 degrees for the physiological experiments while the bandwidth is \nabout 180 degrees for the simulation results in our proposed model. \nModels proposed by Petkov, et al. [8] and Heeger, et al. [7] also show clear inhibition between \nopposite motions. The Petkov\u2019s model achieves the surrounding suppression for each point in \n(\nx y t space by the subtraction between responses from that point and its surroundings and \n,\nfollowed by a half-wave rectification, \n)\n\n\u2212 \u22c5\n\u03b8\u03b1\nv\n,\n\nx y t\n,\n,\n\nx y t\n,\n,\n\nE\nv\n\n,\n\u03b8\n\n(\n\nx y t\n,\n,\n\nE\n%\nv\n\n,\n\u03b8\n\n(\n\n(14) \n\n+\n\n)\n\n \n\n,\n\n)\n\n=\n\nS\n\n(\n\n)\n\n \n\n\forientation \u03b8, \n\nwhere \n(\n\nvE\nx y t\n,\n,\n\n(\n)\n\n,\n\u03b8\n\n is the suppressed motion energy and the factor \u03b1 controls the inhibition strength. The \n\n is the motion energy at location (x,y) and time t for a given preferred speed v and \n(\n is the average motion energy in the surrounding of point (x, y, t), \nx y t\n,\n,\n\nx y t\n,\n,\nvS\n,\n\u03b8\n\n)\n\n)\n\nvE\n\u03b8%\n,\ninhibition term is computed by weighted motion energy \n)\n \n is the surround weighting function. \n\nx y t\n,\n,\n\nx y t\n,\n,\n\nE\nv\n\n=\n\nS\n\n)\n\n(\n\n(\n\n,\n\u03b8\n\n,\n\u03b8\n\nv\n\n(\n\nx y t w\n,\nv\n\n\u2217\n\n,\n\n(\n\n,\n\u03b8\n\nx y t\n,\n,\n\n)\n\n \n\n(15) \n\n)\n\n,\n\u03b8\n\nvw\n\nwhere \nThe Heeger\u2019s model constructs the center-surround motion opponent by computing the weighted \nsum of responses from motion selective cells, \n)\n\nx y E\n,\nv\n\nx y t\n,\n,\n\nx y t\n,\n,\n\n(16) \n\n(\n\u03b2\n\n( )\nt\n\nR\nv\n\nE\n\n=\n\n\u2212\n\n)\n\n(\n\n(\n\n)\n\n,\n\u03b8\n\n,\n\u03b8\n\n,\n\u03b8\n\n \n\n \n\n\u2212\n\nv\n\n\u23a4\n\u23a6\n\n\u2211\n\nx y\n,\n\n\u23a1\n\u23a3\n\n(\n\n)\n\n,x y\u03b2\n\n is a center-surround weighting function and the motion energy at each point should \n\nwhere \nbe normalized across all cells with different tuning properties. \nAs shown in Figure 4 (c) and (d) for results of Petkov\u2019s and Heeger\u2019s models, we replace the \nconventional frequency tuned motion energy neuron with our proposed phase tuned neuron. The \nmodel by Petkov, et al. [8] is generally suppressive and only reproduces less suppression for \nopposite motions, which is inconsistent with results from [3]. The model by Heeger, et al. [7] has \nsimilar properties with our proposed model with respect to both excitatory and inhibitory \ninteractions. \nTo evaluate the sensitivity of the proposed opponency model to velocity differences, we did \nsimulations by using similar stimuli with the above experiment in Figure 4 but maintaining a \nconstant velocity difference of 3 pixels per frame between the center and surrounding random dot \npatches. As shown in Figure 5, by varying the velocities of random dots on the center region, we \nfound that responses by the proposed model are always enhanced independent upon absolute \nvelocities of center stimuli, but responses by the Heeger\u2019s model achieve the enhancement at a \ncenter velocity of 1.2 pixels per frame and maintain suppressed at other speeds. \n\nDiscussion \n\n5 \nWe proposed a new biologically plausible model of the differential motion opponency to model the \nspatial interaction property of motion energy neurons. The proposed opponency model is motivated \nby the phase tuning mechanism of disparity energy neurons which infers the disparity information \nfrom the phase difference between complex valued responses to left and right retinal images. \nHence, the two neighboring spatial areas can be considered as left and right images and the motion \ndifference between these two spatial regions is detected by the phase difference between the \ncomplex valued responses at these two regions. Our experimental results demonstrate a consistent \nconclusion with physiological experiments that motions of opposite directions and different speeds \noutside the CRF can show both inhibitive and excitatory effects on the CRF responses. The \ninhibitive interaction helps to segment the moving object from backgrounds when fed back to \nlow-level features such as edges, orientations and color information. \nExcept providing a unifying phase mechanism in understanding neurons with different functional \nroles at different brain areas, the proposed opponency model could possibly provide a way to \nunderstand the motion integration and motion segmentation. Integration and segmentation are two \nopposite motion perception tasks but co-exist to constitute two fundamental types of motion \nprocessing. Segmentation is achieved by discriminating motion signals from different objects, \nwhich is thought to be due to the antagonistic interaction between center and surrounding RFs. \nIntegration is obtained by utilizing the enhancing function of surrounding areas to CRF areas. Both \ntypes of processing have been found in motion related areas including area MT and MST. Tadin, et \nal. 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