Intensity Discontinuity Location to SubPixel Precision

Introduction

As has recently been pointed out in the literature (Nevatia & Babu 1978), the effectiveness of many machine vision systems is often limit.ed by the low level processing that constitutes the first stage of the system. Typically, this stage consists of operations such as edge detection, thinning, thresholding, & linking · in other words · line finding .

Given this current state of the art and the inspira­ tion of earlier MIT work (Binford 1970, Herskovitz & Biuford 1970), we have implemented an intermediate level vision system that is a marked improvement to this stage of vision systems. An earlier report on this system has been presented elsewhere (Mac Vicar-Whelan & Binford 81) where further details may be found . We present here im­ provements in the structure (noise) filter, results for 9 x 9 and 17 x 17 inhibition masks and the hardcopy output was also improved.

Most edge operators use the maximum gradient which requires a thinning operation. Both processes can intro­ duce uncertainties in the resulting edge. The laterally in­ hibited image, also used in the MIT systems (e.g. Crimson 80 and references therein), is equivalent to a second deriva­ tive operation and provides a more precise result due to e!Tective use of more of the information in the grey level image. We have chosen to illustrate our technique with an image that has already been discussed in the literature.

· This work was performed while P .. J. Mac Vicar-Whelan was on a leave of absence from Grand Valley State Collegoa, Michig!'D· Additional funding Wall provided by ARPA under contract No. MDA903-80-C-0102.

Discontinuity Point Linking

The zero points or zero crossings of the laterally in­ hibited image were linked together over a mesh of dimen­ sions equal to a single pixel separation. Decisions on the linking were based upon the intensity values of the corners of a mesh which were iour pixel values and a central value equal to the average of the four corner values.

A zero crossing was deemed to occur along the edge of a mesh if one corner of the mesh edge was above zero and the other corner was either equal to or below the zero value. Linear interpolation of these 2 corner values was taken as the subpixellocation of the zero crossing. Intramesh points were established using the corner values and the value at the center of the mesh.

Furthermore the central value can be used to disam­ biguate two trajectories that pass through a single mesh if it is assumed that the calculated value for the center of the mesh is accurate at least in so far as to whether or not it is above or below the zero value. This information can be used to separate two trajectories that pass through a single pixel.

Results

The · results of locating intensity discontinuities using our method is illustrated in the Figure for the image of a Lockheed L1011 on a runway- an image that has been used by our group in diverse contexts and reported upon else­ where in the literature. All results using our method were obtained using a threshold of 2 intensity units . Measured noise was 1.5 units.

The top row of the figure (left to right,) illustrates the result of applying the the Nevatia-Babu line finder (ACRONYM's current linefindcr) to the entire image, a 128 x 128 window centred about the plane's nose, and the result of applying 9 x 9 lateral inhibition operator to the digitized image.

The second row illustrates similar results found using a 5 x 5 mask. In addition a second window (18 x 18) about the nose presents details of the high precision obtaainable. Individual pixel structure is represented by the square grid.

An identical sequence of illustrations is presented in the next two rows for 9 x 9 and 17 x 17 masks respectively.

In addition to greater precision our new discontinuity locator, as demonstrated in the figure, does not need to be followed by the customary thinning stage. It is also very accurate since different models of the L 1011 can be distinguished on the the basis of the ratio of wing to tail span.

Increasing the size of the inhibition mask provides a cleaner (less small structure) but is accompanied by the undersirable result of broadening fine structure (eg the 2 pixel wide lines in the 128 x 128 windows).

Brooks (1981) presents further results using the Neva~ia­ Babu technique in the context of ACRONYM. Arnold (1978) presents the edges obtained using a Heuckel operator on this image.

As these results show, our processing produces rather improved results over those that are currently obtainable using other techniques.

We are currently extending this work to provide im­ proved 'real picture' data for some of the other image processing projects being studied in our laboratory.