VBG2000 Ribeye Tolerance Analysis

E+V Technology

03-27-2023

Introduction

Rib eye area contour analysis is one of the, if not the, most complicate part of beef rib eye grading 

instruments. Especially when muscles are connected to the longissimus dorsi or when fat “cuts” the 

entire REA. Some of the competitive grading instruments compensate this with manual corrections 

of the REA segmentation. 

It should be known what different line graders are able to reach on up to 400 head per hour.

The biggest challenge is operator placement performance what can easily cause significant variation 

in REA measurements. That’s the main reason for the developed VBG 7L to flag and improve camera 

placement over time and the current new development of the VBG robot, a fully automatic solution.

The aim of this document is to investigate the role of the Ribeye area (REA) tolerance given by the 

USDA draft.

When a certain acceptable tolerance of the REA is given, we want to calculate the amount of change 

in the Ribeye contour to reach this tolerance. This gives an idea of how accurate the contour detection 

algorithm and placement should be to achieve such a given REA tolerance.

One could imagen a perfect circle with radius r. Then the area of this circle is AA = ππrr2. To maintain a 

certain tolerance (±∆AA iiiiiih2) of the measured area of the circle, it’s easy to determine the maximum 

and minimum tolerance of the radius rrmmmmmm = �AA−∆AA

ππ and rrmmmmmm = �AA+∆AAππ . 

As an example, on a 15-inch2 circle a +1inch2 tolerance would equal only approx. 0.07inch radius 

difference. Since the ribeye contour is not a circle and is longer, this tolerance could be smaller. 

We propose a tolerance in % since it is a big difference if a fixed tolerance is applied for small or big rib 

eyes.

Methodology

We erode/dilate the ribeye contour and calculate the REA using VBG2000 until we reach the 

designated REA limit. Erosion makes the REA smaller, and the dilation makes the REA larger (Figure 1).
Figure 1 Erosion and dilation of the Ribeye

For example, erosion of the ribeye mask by 1 pixel, means that one pixel is removed from all around 

the contour, leaving it thinner by 1 pixel from all directions. Dilation works exactly in the opposite way.

The amount of the pixels eroded/dilated is then converted to mm using the image scale of VBG. We 

interpret this difference in mm to be the equivalent of the change of radius when dealing with perfect 

circles. There is of course no unique value for this difference since it depends on the size of the ribeye 

and how uniform/irregular the contour of the ribeye is.

We did this for 20 images of ribeye’s ranging in areas from 9 inch2 to 17.8 inch2

. In Figure 2 there are 

two examples of these images. 

Figure 2 Examples of the used ribeyes

Results

In this section we investigate two REA limits (±1 inch2 and ±2 inch2). 

The results of all 20 images can be found in Table 1 :
ID REA (inch2

) 

1 inch2

erode 

(pixel)

1 inch2

erode 

(mm)

2 inch2

erode 

(pixel)

2 inch2

erode 

(mm)

1 inch2

dilate 

(pixel)

1 inch2

dilate 

(mm)

2 inch2

dilate 

(pixel)

2 inch2

dilate 

(mm)

11 11.13 8 2.2 17 4.8 9 2.5 20 5.6 

16 11.77 7 2.0 15 4.2 8 2.2 18 5.1

18 11.39 7 2.0 15 4.2 9 2.5 18 5.1

40 12.07 5 1.4 11 3.1 7 2.0 14 3.9

41 17.57 5 1.4 11 3.1 6 1.7 14 3.9

42 15.9 6 1.7 12 3.4 7 2.0 14 3.9

45 14.12 7 2.0 14 3.9 8 2.2 17 4.8

102 12.07 6 1.7 13 3.7 8 2.2 17 4.8

104 12.28 7 2.0 16 4.5 9 2.5 19 5.3

109 9.14 7 2.0 14 3.9 9 2.5 20 5.6

120 15.14 6 1.7 13 3.7 8 2.2 18 5.1

131 11.18 6 1.7 13 3.7 8 2.2 18 5.1

201 9.5 8 2.2 16 4.5 9 2.5 20 5.6

250 10.38 6 1.7 14 3.9 9 2.5 19 5.3

281 9.55 6 1.7 13 3.7 6 1.7 15 4.2

301 16.54 5 1.4 11 3.1 6 1.7 14 3.9

311 17.81 5 1.4 11 3.1 7 2.0 14 3.9

325 14.86 6 1.7 13 3.7 8 2.2 16 4.5

377 13.59 5 1.4 10 2.8 5 1.4 12 3.4

384 14.89 5 1.4 11 3.1 7 2.0 14 3.9

Table 1 Results of the REA Tolerance try. 
Table 2 summarizes the observed change in the ribeye mask in mm in all directions, when 

considering different REA limits.

REA Limit Min change Max change Mean change

-1 inch2 -1.4 mm -2.3 mm -1.7 mm

+1 inch2 +1.4 mm +2.5 mm +2.2 mm

-2 inch2 -2.8 mm -4.8 mm -3.7 mm

+2 inch2 +3.4 mm +5.6 mm +4.7 mm

Table 2 Difference in mm of the ribeye contour corresponding to different REA limits. 

Conclusion

Considering the limit (±1 inch2) we see that it can correspond to min. ±1.4mm or 0,055inch “radius”, 

which is a very small value and it’s hard to achieve robustly for most of the analyzed rib eyes and 

camera operators.

Considering the limit (±2 inch2

) we see that it can correspond to -2.8mm or 0,11inch “radius”, which 

is still a small value given camera operator variations.

Recommendation

We recommend REA measuring tolerances in percentages as follows:

70% of all measured rib eyes within +-10% tolerance

80% of all measured rib eyes within +-13% tolerance

90% of all measured rib eyes within +-16% tolerance

95% of all measured rib eyes within +-18% tolerance