Stem calyx recognition of an apple using shape descriptors

Signal & Image Processing : An International Journal (SIPIJ) Vol.5, No.6, December 2014
DOI : 10.5121/sipij.2014.5602 17
STEM - CALYX RECOGNITION OF AN APPLE
USING SHAPE DESCRIPTORS
Mohana S.H., Prabhakar C.J
Department of P.G. Studies and Research in Computer Science, Kuvempu University
Shankaraghatta-577451, Shimoga, Karnataka, India
ABSTRACT
This paper presents a novel method to recognize stem - calyx of an apple using shape descriptors. The main
drawback of existing apple grading techniques is that stem - calyx part of an apple is treated as defects,
this leads to poor grading of apples. In order to overcome this drawback, we proposed an approach to
recognize stem-calyx and differentiated from true defects based on shape features. Our method comprises
of steps such as segmentation of apple using grow-cut method, candidate objects such as stem-calyx and
small defects are detected using multi-threshold segmentation. The shape features are extracted from
detected objects using Multifractal, Fourier and Radon descriptor and finally stem-calyx regions are
recognized and differentiated from true defects using SVM classifier. The proposed algorithm is evaluated
using experiments conducted on apple image dataset and results exhibit considerable improvement in
recognition of stem-calyx region compared to other techniques.
KEYWORDS
Stem-calyx recognition, Grow-cut, Multithreshold segmentation, Multifractal dimension, Radon transform,
Fourier transform, SVM
1. INTRODUCTION
Surface defect detection for inspection of quality of apples has been gaining importance in the
area of machine vision. Color, size and amount of defects are important aspects for inspection and
grading of fresh apples. Surface defects are of great concern to farmers and vendors to grade the
apples. The defect or damage is usually occurred in apples due to various factors. Apples with rot,
bruising, scab, fungal growth, injury, disease and other defects must be removed to prevent cross-
contamination and reduce subsequent processing cost. There are two important stages involved in
grading the apples such as surface defect detection and grading the apples based on identified
defects. The researchers have adopted image processing and computer vision based techniques to
detect the surface defects of apples, and apples are graded based on quantity of surface defects
detected using either RGB images (B.S Bennedsen et al., 2005; Prabhakar C.J et al., 2013) or
multispectral images (J.A Throop et al., 2005; V Leemans et al., 2002; Xianfeng Li et al., 2011).
The main drawback of these techniques is that while identifying the defects, stem-calyxes are
identified as defects because after applying image processing techniques, stem and calyx region
appears to be similar to defect spots. Due to similarity in appearance between stem-calyx and
defects, the defect detection algorithms wrongly identify the stem-calyx parts as defects, which
reduce the grading accuracy. Some researchers have proposed techniques to differentiate actual
defects and stem-calyx, but these techniques are not able to give the promising results. In this
paper, we proposed a technique to recognize stem-calyx and differentiated from true defects using

18
RGB image of an apple. The motivation to use RGB images is that unlike the MIR camera, digital
cameras are inexpensive and easy to afford. Another advantage of digital data is that they can be
readily processed using digital computers.
The techniques for stem-calyx recognition of apples can be classified into two categories. The
first category of techniques differentiates stem-calyx from true defects based on the threshold
employed on segmented apple image. Whereas the second categories of techniques make the
system to learn shape of stem-calyx part and true defects by extracting shape features and
recognizes stem-calyx part using classifier.
Threshold-Based Techniques
The X.Cheng et al. (2003) have proposed an approach for stem-calyx recognition in multispectral
images of apples. Brightness effect is eliminated using normalization and adaptive spherical
transform is used to distinguish the low- intensity defective portions from the actual stem-calyx.
The global threshold is used to extract the stem-calyx. V. Leemans et al. (2002) developed apple
grading technique according to their external quality using machine vision. Color grading is done
by Fisher’s linear discriminant analysis and stem-calyx is detected by using correlation pattern
recognition technique. The main drawback of the threshold based segmentation is that
misclassification may occur if the threshold of stem-calyx and true defects are similar.
Features-Based Techniques
D.Unay et al. (2007) have proposed an approach to recognize stem-calyx of apples using
monochrome images. Fruit area is separated from background using threshold based
segmentation. Object segmentation technique is used for stem-calyx detection and it is done by
thresholding. Statistical, shape and texture features are extracted. They conclude that SVM
classifier gives best performance in recognizing stem-calyx. J Xing et al. (2007) proposed an
approach for stem-calyx identification for multispectral images. In order to identify the
stem/calyx on apples, the technique is developed based on contour features in the PCA image
scores. The main drawback of these techniques is that they used MIR camera to capture
multispectral images, which are too expensive to use, and it is very difficult to process the huge
amount of data.
Dong Zhang et al. (2013) developed an automated apple stem-calyx detection using evolution
constructed features for Gala apples. Series of transforms were employed and AdaBoost classifier
is used to differentiate stem-calyx from true defects. L Jiang et al. (2009) developed a 3D surface
reconstruction of apple image and analyzed the depth information of apple surface to identify
stem-calyx part. Qingzhong Li et al. (2002) proposed an approach to detect the defects in the
surface of an apple. Stem-calyx part is identified using fractal features, which are fed into ANN
classifier. They considered mono fractal features to classify the stem-calyx part assuming that
concave surface. However, this is not true in case where apples are oriented along in any direction
and the concave surface may not exist. Another drawback of this technique is that they used
fractal features alone to distinguish the stem-calyx from true defects.
In order to overcome the drawback of mono fractal features where these features failed to
represent the stem-calyx part exists in the apple image with non-concave surface. We proposed an
approach to recognize the stem-calyx based on multifractal features. The recognition accuracy of
our technique is increased by combining multifractal descriptor with other two shape descriptors
such as Fourier and Radon transform based descriptors.

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The organization of remaining sections of the paper is as follows: In section 2, theoretical
description of proposed shape descriptors are given. The proposed approach for stem-calyx
recognition is discussed in the section 3. The experimental results are demonstrated in Section 4.
Finally, Section 5 draws the conclusion.
2. SHAPE DESCRIPTORS
In many applications, like stem-calyx recognition, the internal content of the shape is not an
important compared to the boundary of an object. The boundary-based techniques tend to be more
efficient for handling shapes that are describable by their object contours. The simplified
representation of an object is often called the shape descriptors or signatures. These simplified
representations are easier to store, compare and handle. The descriptors for irregular shapes like
stem-calyx should be different enough that the shapes can be discriminated.
2.1. Multifractal Descriptor
The fractal dimension is a very popular concept in mathematics due to its wide range of
applications. The fractal dimension was developed by Benoit Mandelbrot in 1967 (Benoit M,
1967). Fractals are generally self-similar and independent of scale. A fractal is a fragmented
geometrical object that can be divided into parts, and each part is a copy of the original in reduced
size. The important characteristic of fractal geometry is that ability to represent an irregular or
fragmented shape of complex objects, where as traditional Euclidean geometry fails to analyze. A
multifractal is a set of intertwined fractals. A multifractal object is more complex in the sense that
it is always invariant by translation. The multifractal dimensions were defined based on partition
function.
In our approach, we used Box Counting method to compute the multifractal dimension. Consider
the mass dimension α at a point x, the box Bε(x) is a box of radius ε centered at x. The probability
measure of mass in the box is defined as µ ൫Bε (x)൯. It can be shown that µ ൫Bε (x)൯ ∝ ε
α
. The
mass dimension specifies how fast the mass in the box Bε(x) decreases as the radius approaches
to zero. In the first step, we compute the total number of boxes required to cover the input image.
The total number of boxes can be calculated using below equation
்ܰ =
(௪௜ௗ௧௛)
(ఌ)మ
ଶ
, (1)
where, width size of the input image and ε is size of the box. It is necessary to eliminate the boxes
which are having zero elements. Therefore, we select the boxes with non-zero elements and are
defined as
ܰௌ = ∑ ܰ௜
ே೅
௜ୀଵ = ݊‫ݐ݋‬ ݊‫݈݈ݑ‬ , (2)
where Nୗ represents total number of boxes with non-zero elements. The total sum or mass of
pixels in all boxes can be obtained using the following equation
‫ܯ‬ఌ = ∑ ݉[௜,ఌ]
ேೄ
௜ୀଵ , (3)
where m[୧,ε] represents the mass of ith box with size ε. The probability P of the mass at ith box, is
relative to the total mass Mε and is defined as
ܲ[௜,ఌ] =
௠[೔,ഄ]
ெഄ
, (4)

20
the qth order normalized probability measures of a variable, µ(q , ε ) vary with the box size ε and
it is defined as
ߤ௜(‫ݍ‬ , ߝ ) =
[௣೔ (ఌ)]೜
∑ [௣೔ (ఌ)]೜
೔
, (5)
where p୧ (ε) is the probability of a measure in the ith box of size ε. It can be shown that P[୧,ε] ∝
εα
, the exponent α is called the Holder exponent at the point x, which is defined as
હ (‫ܙ‬ , ઽ ) = ∑ ૄܑ(‫ܙ‬ , ઽ ) ‫܏ܗܔ‬ ‫ܘ‬ܑ(ઽ )ܑ , for i=1, 2, 3, . . . , ‫ۼ‬‫܁‬ . (6)
For each q value, multifractal dimension is calculated as
܎ (‫ܙ‬ , ઽ ) = ∑ ૄܑ(‫ܙ‬ , ઽ ) ‫܏ܗܔ‬ ૄܑ(‫ܙ‬ , ઽ ),ܑ for i=1, 2, 3, . . . , ‫ۼ‬‫܁‬ . (7)
2.2. Fourier Descriptor
Fourier descriptor is commonly used in popular areas such as pattern recognition, computer
vision and image analysis. Fourier transformation on shape signatures is widely used for shape
analysis, and also some researchers are used for shape retrieval. In the Fourier descriptor (Charles
T Zhan et al., 1972), Fourier transformation and Fourier inverse transformation pairs were used to
extract shape features from candidate objects. In general, Fourier descriptor (FD) is obtained by
applying Fourier transform on a shape signature that is a one-dimensional function which is
derived from the shape boundary coordinates. The normalized Fourier transformed coefficients
are called the Fourier descriptor of the shape in that sample image. The boundary of an object is
plotted on the XY plane. Starting at a arbitrary point (x0 , y0), coordinate pairs (x0 , y0), (x1 ,
y1), (x2 , y2), . . . , (xN-1 , yN-1) traversing the boundary. Each coordinate pair can be treated as
a complex number, it can be represented as s(k) = x(k) + iy(k). The x-axis is treated as the real
axis and the y axis is treated as the imaginary axis of a sequence of complex numbers. The
advantage of this representation is that it reduces a 2-D problem into 1-D problem.
The Discrete Fourier Transform (DFT) of ‫)݇(ݏ‬ is
ࢇ(࢛) =
૚
ࡺ
∑ ࢙(࢑)ࡺି૚
࢑ୀ૙ ࢋି࢐૛࢛࣊࢑/ࡺ
, for u=0,1,2, . . . , N-1. (8)
The complex coefficients a(u) are called the Fourier Descriptors of the boundary. The Fourier
Descriptors are a frequency based description of the boundary of an image. The inverse Fourier
transform of ࢇ(࢛) restores ‫ݏ‬(݇). That is,
࢙(࢑) = ∑ ࢇ(࢛)ࡺି૚
࢛ୀ૙ ࢋ࢐૛࢛࣊࢑/ࡺ
, for k=0,1,2,…..,N-1. (9)
2.3. Radon Descriptor
The Radon transform (RT) was introduced by the Austrian mathematician Johann Radon in 1917.
The integral transform is consisting of the integral of a function over straight lines. The Radon
Transformation is a fundamental tool which is used in different applications such as radar
imaging, geophysical imaging and medical imaging. Sambhunath Biswas et al. (2012) developed
an efficient face recognition algorithm based on transformed shape features. By definition the
Radon transform of an image is determined by a set of projections of the image along lines taken
at different angles. For discrete binary image data, each non-zero image point is projected into a
Radon matrix. Let f(x, y) be an image. Its Radon transform is defined by
ܴ(ߩ, ߠ) = ‫׬‬ ‫׬‬ ݂(‫,ݔ‬ ‫)ݕ‬ ߜ
ା∞
ି∞
ା∞
ି∞
( ߩ − ‫ݔ‬ cos ߠ − ‫ݕ‬ sin ߠ)݀‫,ݕ݀ݔ‬ (10)

21
where δ (. ) is the Dirac function, θ ∈ [0, π] and ρ ∈ [−∞, +∞] . The Radon transform has
several useful properties. Some of them are relevant for shape representation: A translation of f
result in the shift of its transform in the variable ρ by a distance equal to the projection of the
translation vector on the line ρ = x cos θ + y sin θ. A rotation of the image by an angle
θ଴ implies a shift of the RT in variable θ. The Radon Transform is robust to noise, provided with
fast algorithms, and it projects a two-dimensional function into one-dimensional function.
Figure 1. Parallel–beam projection at rotation angle theta
Radon transform is based on the parameterization of straight lines and the evaluation of integrals
of an image along these lines. To represent an image, the radon function takes more than one
parallel-beam projections of the image from different angles by rotating the source around the
center of the image. The line integral of f(x,y) in the vertical direction is the projection of f(x,y)
onto the x-axis. The line integral in the horizontal direction is the projection of f (x,y) onto the y-
axis.
3. OUR APPROACH
In the training phase, we detect candidate objects such as stem part, calyx part and defected part
from training samples and shape features are extracted from the detected candidate objects. As we
described in the previous section, we extract and store the description of shape features using
Multifractal, Fourier and Radon descriptors. The feature extraction step for each candidate object
yields three feature vectors. The extracted feature vectors from stem part, calyx part and defected
part of various training samples captured in different viewpoint are stored independently in the
database and these stored feature vectors are treated as reference in order to recognize the stem-
calyx part. In the testing phase, we recognize the stem-calyx by extracting the feature vectors
from detected candidate objects of testing sample and compared with stored feature vectors using
classifier.
3.1 Candidate Objects Detection
In order to detect the candidate objects such as stem part, calyx part and defected part in an apple
image, we used the following steps. Pre-processing using a median filter, grow-cut approach for
background subtraction, it is followed by multi-threshold segmentation approach to segment the
candidate objects. Finally, the results of grow-cut and multi-threshold segmentations are
combined to detect the candidate objects.
A. Image pre-processing
In order to improve the quality of an image, operations need to be performed on it to remove or
decrease degradations suffered by the image during its acquisition. The captured apple images are
suffered from illumination variations due to specular reflection. The specular reflection leads to

22
poor performance during candidate objects detection process because the specular reflected part is
treated as the candidate object due to its white color compared to its surroundings.
We employ median filtering to normalize the uneven distribution of light and to suppress noise.
The median is much less sensitive than the mean to extreme values, i.e., they are the outliers. So,
here median filtering is used to remove these outliers without reducing the sharpness of the
image. The median filter technique allowed the edges to be preserved while filtering out the peak
noise. For this reason, the median filter is often used before applying candidate object detection
technique to preserve the shape of the candidate objects as much as possible.
B. Background Subtraction
The apple images were captured on a uniform color background. It is necessary to extract the ROI
i.e. fruit area from the apple image. We used grow-cut approach for background subtraction. It
removes background and gives fruit part separately. Vladimir Vezhnevets et al. (2005) from the
Media Laboratory at Moscow State University first came up with this algorithm. The unique
feature of the grow cut algorithm is in its ability to incorporate both “Von Neumann
neighborhood” theory and the “region growing/region merging” approach.
Multi-Threshold Segmentation
After extracting the apple fruit part from the image, we segment the candidate objects from fruit
area using multi-threshold segmentation. In multi-threshold segmentation, the images were
segmented several times at different threshold levels. We experimentally observed that the
candidate objects of various types of apples can be segmented accurately using threshold values
30, 50 and 65. The resulting binary images were added to form a so called multi layer image. This
in turn was then subjected to threshold segmentation. This segmentation aimed at identifying and
separates the healthy skin of an apple from the stem-calyx and defected areas in the original
image. The resulting binary image was referred to as a marker image. The final step consists of
constructing a binary image based on the marker image and the multi-layer image. With the
position of the candidate objects, a simple thresholding routine i.e. a gradient segmentation is
employed to determine the area of these candidate objects. The results obtained from the
background subtraction and multi-threshold segmentation methods are overlapped to each other.
In the resultant image, we observe that the candidate objects are appeared on the surface of the
apples.
Figure 2: Candidate object detection process: First row: The pre-processed Jonagold apple images with
stem part in view, Second row: fruit area extracted from images shown in first row, Third row: Detected
stem part using multi-threshold segmentation.

3.2 Shape Features Extraction from Candidate Objects
In order to recognize stem-calyx part, we extract shape features because of its discriminative
characteristics to distinguish stem
detected stem-calyx part and defect parts of training sample where the stem
parts are captured in different views with variation in scale and vie
features represent stem-calyx part and defect parts and invariant to variation in views and scale.
We used three shape descriptors such as Multi
descriptor to extract and store the s
Figure 3: First row: the apple images with
Multifractal Descriptor
We extract multifractal dimension features of detected candidate objects using
approach with the box size 2 x 2
After fitting the boxes to the candidate
pixel (mass distribution) in the box
processing. We calculate the mass distribution of
box. The exponent હ is called the Holder exponent is calculated
Finally, Multi-fractal dimension is calculated using
the plotted multifractal dimension graph for
the multifractal dimension exhibit discrimination power for stem, calyx and defect
Fourier Descriptor
The Fourier descriptors of the
coefficients. The general features of the candidate object
frequency descriptors and finer details of the
frequency descriptor. High-frequency information is ignored because it is not helpful in shape
discrimination. The complete number
large, a subset of the total coefficients is enough to capture the overall features of the sha
Fourier descriptor is clear representation of detected candidate objects, which can be observed in
the Figure 5, where the reconstructed candidate object
appear to be as like original candidate object
Image Processing : An International Journal (SIPIJ) Vol.5, No.6, December 2014
Features Extraction from Candidate Objects
calyx part, we extract shape features because of its discriminative
eristics to distinguish stem-calyx part from defects. We extract the shape features from
calyx part and defect parts of training sample where the stem-calyx part and defect
parts are captured in different views with variation in scale and views. The extracted shape
calyx part and defect parts and invariant to variation in views and scale.
We used three shape descriptors such as Multi-fractal descriptor, Fourier descriptor and Radon
descriptor to extract and store the shape features independently for each detected candidate object.
the apple images with stem/calyx and defected part in view. Second row:
stem-calyx part with defects.
We extract multifractal dimension features of detected candidate objects using box
2 (4 pixels). Here we varied the q value from -1 to +1
candidate image, we select the boxes which are having non
in the box, and the empty boxes are not considered for further
the mass distribution of all selected boxes and the probability of each
is called the Holder exponent is calculated using the probability
fractal dimension is calculated using normalized probability. In the Figure
plotted multifractal dimension graph for stem-calyx part and defected part, it is observed that
the multifractal dimension exhibit discrimination power for stem, calyx and defected
The Fourier descriptors of the detected candidate objects are formed by Fourier transformed
features of the candidate object shape are contained in the lower
frequency descriptors and finer details of the candidate shape are contained in the higher
frequency information is ignored because it is not helpful in shape
numbers of coefficients are generated from the transform is very
large, a subset of the total coefficients is enough to capture the overall features of the sha
reconstructed candidate object using the small set of Fourier coefficients
like original candidate object.
Image Processing : An International Journal (SIPIJ) Vol.5, No.6, December 2014
23
calyx part, we extract shape features because of its discriminative
calyx part from defects. We extract the shape features from
calyx part and defect
ws. The extracted shape
calyx part and defect parts and invariant to variation in views and scale.
fractal descriptor, Fourier descriptor and Radon
hape features independently for each detected candidate object.
row: detected
box counting
1 to +1 (21 points).
having non-zero
and the empty boxes are not considered for further
he probability of each
probability measure.
In the Figure 4, from
, it is observed that
ed part.
formed by Fourier transformed
shape are contained in the lower
ontained in the higher-
frequency information is ignored because it is not helpful in shape
of coefficients are generated from the transform is very
large, a subset of the total coefficients is enough to capture the overall features of the shape. The
small set of Fourier coefficients

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Figure 4: Results of multifractal descriptors: First column- Detected candidate objects, Second column-
Cropped image of candidate object, Third column-Schematic diagram of box counting method, Last
column- Corresponding graph of multifractal dimension.
Figure 5: Results of Fourier descriptor: First column – Candidate objects, Second column – Coordinate
values for boundary of candidate objects shown in first column, Third column – Reconstructed candidate
objects using small set of Fourier descriptors

25
Radon Descriptor
The Radon transform is a projection of the image intensity along a radial line oriented at a
specific angle. Radon transform is applied to the detected candidate objects region. In general, the
Radon transform of an image gives the projection of the candidate objects from 1 degree to 180
degrees. The experimentally it is observed that the Radon transform employed on candidate
object region with a projection angle 30 degrees give accurate representation of the detected
objects shape. The Radon transform is scale and rotation invariant, which can be observed in the
Figure 6 and Figure 7 respectively, where the behavior of Radon Transform is constant for
variation in rotation and scaling of candidate objects.
Figure 6: Behavior of Radon transform for scaling: First row - candidate object with different scale,
Second row – Corresponding result of Radon transform.
Figure 7: Behavior of Radon transform for orientation: First row - candidate object with different
orientation, Second row – Corresponding result of Radon transform.

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3.3 Stem - Calyx Recognition
In the training phase, we extracted the shape features of detected stem/calyx and defected parts
using three descriptors. The descriptors values or shape feature values are analyzed in order to
identify the discriminating power. It is observed that the extracted shape features of stem-calyx
parts are differing in nature compared to defect parts features. This motivated us to use the
combination of above mentioned descriptors to differentiate stem-calyx parts from true defects,
which increases the discrimination rate of stem-calyx from true defects. In order to differentiate
the stem-calyx from true defects, classifier is employed. We have conducted experiments to find
out suitable classifier, which yields highest recognition accuracy. We considered popular
supervised classification algorithms such as Support Vector Machine (SVM) (Vladimir N.
Vapnik, 1995), AdaBoost (Yoav Freund and Robert Schapire, 1995), Artificial Neural Network
(ANN) (Robert Hecht-Nielsen, 1986), Linear Discriminant Classifier (LDC) (R. A. Fisher, 1936)
and k-Nearest Neighbor classifier (k-NN) (Fix and Hodges, 1967).
4. EXPERIMENTAL RESULTS
We have conducted the experiments to evaluate the proposed method for recognizing stem-calyx
part and differentiated from true defects of an apple. Since, there is no benchmark database of
apples is available, we have created a Jonagold apple database for experimentation purpose.
Image acquisition device is composed of a resolution 2.0 mega pixel (1240 x 1600). The camera
is capable of acquiring only one-view of an apple. The healthy and small defected Jonagold
apples were selected for experimentation purpose based on visual inspection. The images of the
selected 200 Jonagold apples were captured in indoor environment with variation in lighting
condition. Each apple was captured in three views such as stem part in view, calyx part in view
and defected part in view.
The database contains 600 sample images of each image size 256 x 256 and 200 apple image
samples for each view. Among the above-said data samples, we selected randomly 75% (from
each view 150 samples) of the apple samples for training purpose, and the remaining 25% (from
each view 50) samples are used for testing purpose. In order to eliminate the intersection
(duplication) of training and testing sets, drop-one-out approach is used in this work. That is, an
apple used for training is excluded from the testing set. In order to find out the optimal parameter
for classifier, we have conducted several experiments using training and test sample. We
considered only multifractal dimension descriptor to represent stem-calyx and defected parts.
After conducting several experiments, it is observed that for SVM, polynomial kernel with a
degree 3 yields highest recognition rate. A two-layer ANN is used to recognize stem-calyx. It is a
feed-forward, error back-propagation network with adaptive learning rate. Several models of
ANN is tested, however the one with 10 hidden nodes perform better than others. 3 inputs, 10
hidden with 2 output nodes are used and similarly k=4 for k-NN classifier. In the following
experiments, classification algorithms with these best parameters are used.
Number of Fourier Descriptors
The experiments are conducted to identify the small subset of Fourier descriptors required to
represent overall features of the stem, calyx and defects. In these experiments, we used only
Fourier descriptor to represent the stem, calyx and defects and k-NN classifier is used for
classification. The Figure 8 shows that a small number of Fourier descriptors are sufficient for
shape representation of stem, calyx and defected part. In our experiments, as can be seen in
Figure 8, using more than 40 descriptors generally does not increase the recognition rate any
further for defected parts. The shape of the stem, calyx and defected parts may undergo a lot of
variation such as scaling and rotation. Therefore, in order to reflect such changes, we have limited

27
the number of descriptors to 95 for stem, 130 for calyx and 40 for defected parts in all the
experiments.
Figure 8. The Classification rate graph of the Fourier descriptors for stem, calyx and defects
Fusion of descriptors
The literature survey reveals that fusion of descriptors yields highest classification accuracy
compared to an individual descriptor alone. We selected feature concatenation as the fusion
approach. Three feature vectors mi (Multifractal descriptor), fi (Fourier descriptor) and ri (Radon
descriptor) are concatenated into a single feature vector vi = (mi , fi , ri) that is used for
classification. The distance in the concatenated feature vector is defined as
dt (vi , vj) = d(mi, mj) + d(fi, fj) + d(ri, rj). (11)
In order to verify the effectiveness of fusion of descriptors, we conducted experiments on fusion
of descriptors. The Table 1 shows that there is an increase in the recognition rate when descriptors
are fused. We fused the multifractal descriptor with Radon descriptor, which increases the
recognition accuracy than multifractal descriptor alone. Similar effect was found for all the
classifiers when we fused all three descriptors. Particularly, SVM classifier with the polynomial
degree 3 yields highest recognition rate compared to other classifier when all three descriptors are
combined and the results are shown in the Table 1. This concludes that the fusion of three
descriptors helps to improve the classification rate compared to individual descriptor alone.
Figure 9 describes, different levels of training datasets are used and classification rate is improved
with increase in training dataset.
Table 1. Demonstration of increase in recognition rate (%) for fusion of shape descriptors
(MD – Multifractal Descriptor, RD – Radon Descriptor, FD – Fourier Descriptor)
Descriptors
Classifiers
MD
MD +
RD
MD + RD +
FD
SVM
(Polynomial
degree 3)
92.40 93.60 96.00
LDC 91.20 92.40 94.80
AdaBoost 90.80 91.60 93.20
ANN 90.40 91.20 92.80
k-NN (k=4) 88.40 89.60 91.60

28
Figure 9. Classification accuracy of different classifiers for varying training samples
Evaluation of results
Table 2 shows the evaluation of experimental results using True Positive Rate (TPR) and False
Positive Rate (FPR) obtained using SVM classifier with polynomial degree 3. We used 50
samples for each view such as stem, calyx, defects, stem with small defects and calyx with small
defects. The TPR indicates the correct classification i.e., stem-calyx is classified as stem-calyx
and defect is classified as defect. The FPR indicates the false classification i.e, stem-calyx is
classified as defect and defect is classified as stem-calyx. From the results shown in the Table 2
indicates that proposed shape descriptors have shown high discrimination between stem-calyx
and defects. The TPR for stem is approximately near to 100% classification accuracy and only
2% of classification error. This is not true in case of calyx recognition, only 47 calyx regions
were correctly classified and remaining 03 regions were misclassified. This is due to the fact that
shape features of small defects and calyx appear to be similar. Therefore, the classifier failed to
distinguish these regions. Out of 100 test samples of stem and calyx regions, 04 regions were
misclassified and classification accuracy of our method is 96% for Jonagold apples. Out of 50
defects samples, only 01 defect is misclassified as stem-calyx. The literature survey reveals that
most of the stem-calyx recognition techniques uses apple with either stem-calyx or defects view.
There may be possibility that both stem-calyx and defects lie on the same view. Therefore, our
testing sample set consists of apple image including both stem-calyx and defects. The
classification accuracy for this test set is promising. These rates show significant improvement
with respect to the stem-calyx recognition results available in the literature.
Table 2. TPR and FPR for stem-calyx classification using SVM classifier
Different views of an apple TPR FPR
Stems (n=50) 49 (98%) 01
Calyxes (n=50) 47 (94%) 03
Defects (n=50) 49 (98%) 01
Stem with small defects (n=50) 48 (96%) 02
Calyx with small defects (n=50) 47 (94%) 03

29
Figure 10. Classification performances of classifiers using TPR and FPR
The Figure 10 displays the performance of the classifiers using the results of True Positive Rate
(TPR) and False Positive Rate (FPR). The diagonal line indicates the separation between the
perfect recognition and perfect rejection, because in the graph left-top most part is the best part
i.e., the best classification rate yields under this location and it presents the highest TPR and low
FPR. Here, SVM yields the high TPR and low FPR among the classifiers, so we can easily say
that SVM is the best classifier for our technique.
Discussion
The results of pre-processing showed that detection of candidate objects such as stem-calyx and
small defects is visually true. A promising observation is that none of the stem-calyx and defects
in the images is missed by proposed object segmentation step. The Jonagold was chosen for study
because its mixed colors on the surface made it a more challenging and hence convincing
example to demonstrate our algorithms performance. Other varieties such as red delicious, golden
delicious and granny smith that other studies used in the past, all have uniform colors on the
surface, which makes stem-calyx and defects detection an easier task.
The experimental results on stem-calyx recognition showed that proposed method yields highest
classification accuracy for classification of stem-calyx regions and distinguished from true defects
with small error rate for the Jonagold apple images captured in different orientation and scaling.
The final classification rate of about 98% for stem ends and 94% for calyxes were achieved on
the selected test samples. The average classification accuracy for both defective apples with stem
end view and defective apples with calyx end view were 95%. The increase in the classification
accuracy is due to the fact that discriminating shape features are extracted using scale and rotation
invariant feature descriptors. We observed that fusion of descriptors improves the classification
rate compared to individual shape descriptors. The proposed algorithm failed to distinguish stem-
calyx from true defects when, i) the apple images are captured in very high specular reflection
(non-uniformity of color), ii) the stem end or calyx appeared near the edge of the observed apple
surface, iii) small defects appeared very near the stem-ends or calyxes and iv) the apples are
having many defects with the big size.

30
5. CONCLUSION
In this paper, we proposed an approach to recognize the stem-calyx of Jonagold apples and
distinguished from the true defects. The grow-cut and multi-threshold techniques results are
combined to detect the candidate objects. We extracted the shape features from detected
candidate objects using three shape descriptors such as Multifractal, Fourier and Radon
descriptors. The extracted shape features are concatenated and used to discriminate stem-calyx
from true defects. We tested different classifiers such as SVM, ANN, k-NN, LDC and AdaBoost
to discriminate stem-calyx from true defects. The SVM classifier with polynomial kernel function
yields highest best recognition rate. The proposed method can be incorporated in apple grading
technique as one of the steps in order to increase the apple grading accuracy.
ACKNOWLEDGEMENTS
We would like to thank the anonymous reviewers for their critical comments and suggestions,
which helped to improve the previous version of this paper.
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