Iaetsd appearance based american sign language recognition

APPEARANCE BASED AMERICAN SIGN LANGUAGE RECOGNITION
USING GESTURE SEGMENTATION AND MODIFIED SIFT ALGORITHM
Author1 prof.P.Subba Rao Author2 Mallisetti Ravikumar
Professor of ECE M.E. (Communication Systems)
SRKR College of Engineering SRKR College of Engineering
Dept. of Electronic and communications Dept. of Electronic and communications
Bhimavaram, India Bhimavaram, India
Abstract— the work presented in this paper is to develop a system
for automatic Recognition of static gestures of alphabets in Ameri-
can Sign Language. In doing so three feature extraction methods
and neural network is used to recognize signs. The system recognizes
images of bare hands, which allows the user to interact with the sys-
tem in a natural way. An image is processed and converted to a fea-
ture vector that will be compared with the feature vectors of a train-
ing set of signs. Further work is to investigate the application of the
Scale-Invariant Feature Transform (SIFT) to the problem of hand
gesture recognition by using MATLAB.The algorithm uses modi-
fied SIFT approach to match key-points between the query image
and the original database of Bare Hand images taken. The extracted
features are highly distinctive as they are shift, scale and rotation
invariant. They are also partially invariant to illumination and af-
fine transformations. The system is implemented and tested using
data sets of number of samples of hand images for each signs. Three
feature extraction methods are tested and best one is suggested with
results obtained from ANN. The system is able to recognize selected
ASL signs with the accuracy of 92.33% using edge detection and
98.99 using sift algorithm.
Index Terms— ASL using MATLAB, Orientation Histogram, SIFT,
ASL Recognition, ASL using ANN, ASIFT Algorithm
——————————  ——————————
I.INTRODUCTION
A. American Sign language:
The sign language is the fundamental communication method be-
tween the people who suffer from hearing defects. In order for an
ordinary person to communicate with deaf people, a translator is
usually needed the sign language into natural language and vice
versa. International Journal of Language and Communication Disor-
ders, 2005) Sign language can be considered as a collection of ges-
tures, movements, posters, and facial expressions corresponding to
letters and words in natural languages.
American Sign Language (ASL) National Institute on Deafness &
Other communication Disorders, 2005) is a complete language that
employs signs made with the hands and other facial expressions and
postures of the body. According to the research by Ted Camp found
on the Web site www.silentworldministries.org, ASL is the fourth
most used language in the United States only behind English, Span-
ish and Italian (Comp). ASL is a visual language meaning it is not
expressed through sound but rather through combining hand shapes
through movement of hands, arms and facial expressions. Facial
expressions are extremely important in signing. (www.nidcd.nih.gov
(US government)). ASL also has its own grammar that is different
from other sign languages Such as English and Swedish. ASL con-
sists of approximately 6000 gestures of common words or proper
Nouns. Finger spelling used to communicate unclear Words or
proper nouns. Finger spelling uses one hand and 26 gestures to
communicate the 26 letters of the alphabet.
There are two types of gesture interaction, communicative gestures
work as symbolic language (Which is the focus in this project) and
manipulative gestures provide multi-dimensional control. Also, ges-
tures can be divided into static gestures (hand postures) and dynamic
gestures (Hong et al., 2000). The hand motion conveys as much
meaning as their posture does. A static sign is determined by a cer-
tain configuration of the hand, while a dynamic gesture is a moving
gesture determined by a sequence of hand movements and configura-
tions. Dynamic gestures are sometimes accompanied with body and
facial expressions.The aim of sign language alphabets recognition is
to provide an easy, efficient and accurate mechanism to transform
sign language into text or speech. With the help of computerized
digital image processing and neural network the system can interpret
ASL alphabets.
The 26 alphabets of ASL are shown in Fig.1.
Figure. 1. The American Sign Language finger spelling alphabet
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.
B. Related Work
Attempts to automatically recognize sign language began to appear
in the 90s. Research on hand gestures can be classified into two cate
Gories. First category relies on electromechanical devices that are
used to measure the different gesture parameters such as hand’s posi-
tion, angle, and the location of the fingertips. Systems that use such
devices are called glove-based systems. A major problem with such
systems is that they force the signer to wear cumbersome and incon-
venient devices. Hence the way by which the user interacts with the
system will be complicated and less natural. The second category
uses machine vision and image processing techniques to create vis-
ual based hand gesture recognition systems. Visual based gesture
recognition systems are further divided into two categories: The first
one relies on using specially designed gloves with visual markers
called “visual-based gesture with glove-markers (VBGwGM)” that
help in determining hand postures. But using gloves and markers do
not provide the naturalness required in humancomputer interaction
systems. Besides, if colored gloves are used, the processing com-
plexity is increased. The second one that is an alternative to the sec-
ond kind of visual based gesture recognition systems can be called
“pure visual-based gesture (PVBG)” means visual-based gesture
without glove-markers. And this type tries to achieve the ultimate
convenience naturalness by using images of bare hands to recognize
Types of algorithms can be used for image recognition
1. Learning algorithms.
a. Neural network (e.g. research work of Banarse, 1993).
b. Hidden Markov Models (e.g. research work of Charniak, 1993).
c. Instance-based learning(research work of Kadous,1995)
2. Miscellaneous techniques.
a. The linguistic approach (e.g. research work of Hand, Sexton, and
mullan, 1994)
b. Appearance-based motion analysis (e.g. research Work of Davis
and Shah, 1993).
c. Spatio-temporal vector analysis (e.g. research Work of Wuek,
1994
1. Feature extraction, statistics, and models
1. The placement and number of cameras used.
2. The visibility of the object (hand) to the camera for simpler ex-
traction of hand data/features.
5. The efficiency and effectiveness of the selectedalgorithms to pro-
vide maximum accuracy and robustness
3. The extraction of features from the stream of Streams of raw Im-
age data.
4. The ability of recognition algorithms to extracted features.
5. The efficiency and effectiveness of the selected algorithms to pro-
vide maximum accuracy and robustness.
II.SYSTEM DESIGN AND IMPLEMENTATION
The system is designed to visually recognize all static signs of the
American Sign Language (ASL), all signs of ASL alphabets using
bare hands. The user/signers are not required to wear any gloves or
to use any devices to interact with the system. But, since different
signers vary their hand shape size, body size, operation habit and so
on, which bring more difficulties in recognition. Therefore, it real-
izes the necessity for signer independent sign language recognition
to improve the system robustness and practicability in the future. The
system gives the comparison of the three feature extraction methods
used for ASL recognition and suggest a method based on recognition
Rate. It relies on presenting thegesture as a feature vector that is
translation, rotation and scale invariant. The combination of the fea-
ture extraction method with excellent image processing and neural
networks capabilities has led to the successful development of ASL
recognition system using MATLAB. The system has two phases: the
feature extraction phase and the classification as shown in Fig.2.
Images were prepared using portable document format (PDF) form
so the system will deal with the images that have a uniform back-
ground.
a. Template matching (e.g. research work Darrell and Pentland,
1993)
b. Feature extraction and analysis, (e.g. research work of Rbine,
1991)
c. Active shape models “Smart snakes” (e.g. research work of Heap
and Samaria, 1995)
d. Principal component analysis (e.g. research work of Birk, Moes-
lund and Madsen, 1997)
e. Linear fingertip models (Research work of Davis and shah, 1993)
f. Causal analysis (e.g. research work of Brand and Irfan, 1995).
Among many factors, five important factors must be considered for
the successful development of a visionbased solution to collecting
data for hand posture and gesture recognition
Fig 2. Designed System block diagram
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A. Feature Extraction Phase
Images of signs were resized to 80 by 64, by default “imresize” uses
nearest neighbor interpolation to determine the values of pixels in the
output image but other interpolation methods can be specified. Here
‘Bicubic’ method is used because if the specified output size is
smaller than the size of the input image, “imresize” applies a low
pass filter before interpolation to reduce aliasing. Therefore we get
default filter size 11- by11. To alleviate the problem of different
lighting conditions of signs taken and the HSV “(Hue, Saturation,
Brightness)” non-linearity by eliminating the HSV information while
retaining the luminance. The RGB color space (Red, Green and Blue
which considered the primary colors of the visible light spectrum) is
converted through grayscale image to a binary image. Binary images
are images whose pixels have only two possible intensity values.
They are normally displayed as black and white. Numerically, the
two values are often 0 for black and either 1 or 255 for white. Binary
images are often produced by thresholding a grayscale or color im-
age from the background. This conversion resulted in sharp and clear
details for the image. It is seen that the RGB color space conversion
to HSV color space then to a binary image produced images that lack
many features of the sign. So edge detection is used to identify the
Parameters of a curve that best fir a set of given edge points. Edges
are significant local changes of intensity in an image. Edges typically
occur on the boundary between two different regions in an image.
Various physical events cause intensity changes. Goal of edge detec-
tion is to produce a line drawing of a scene from an image of that
scene. Also important features can be extracted from the edges. And
these features can be used for recognition. Here canny edge detection
technique is used because it provides the optimal edge detection So-
lution. Canny edge detector results in a better edge detection co
pared to Sobel edge detector. The output of the edge detector defines
‘where’ features are in the image. Canny method is better, but in
some cases it provides extra details more than needed. To solve this
Problem a threshold of 0.25 is decided after testing different thresh-
old values and observing results on the overall recognition system.
1. Feature Extraction Methods Used.
a. Histogram Technique
b. Hough
c. OTSU’s segmentation algorithm
d. Segmentation and Extraction with edge detection
B.Classification Phase
The next important step is the application of proper feature extrac-
tion method and the next is the classification stage, a 3-layer, feed-
forward back propagation neural network is constructed.
The classification neural network is shown (see figure 3).
It has 256 instances as its input. Classification phase includes net-
work architecture, creating network and training the network. Net-
work of feed forward back propagation with supervised learning is
used.
Fig. 3: Classification network.
Figure. 4. System Overview.
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III.MODIFIED SIFT ALGORITHM
A complete description of SIFT can be found in [1].An overview of
the algorithm is presented here. The algorithm has the major stages
as mentioned below:
• Scale-space extrema detection: The first stage searches over scale
space using a Difference of Gaussian function to identify potential
interest points.
• Key point localization: The location and scale of each candidate
point is determined and key points are selected based on measures of
stability.
• Orientation assignment: One or more orientations are assigned to
each key point based on local image gradients.
• Key point descriptor: A descriptor is generated for each keypoint
from local image gradients information at the scale found in the sec-
ond stage.
Each one of the above-mentioned stages is elaborated further in the
following sections.
Rgb to gray con-
version
Edgedetetion
Feature
extraction
Feature vector
Classified sign
Neuralnework
Featureextraction
Classification
Prepared image
Image resizing
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The goal is to design a highly distinctive descriptor for each inter-
est point to facilitate meaningful matches, while simultaneously
ensuring that a given interest point will have the same descriptor
regardless of the hand position, the lighting in the environment,
etc. Thus both detection and description steps rely on invariance
of various properties for effective image matching. It attempts to
process static images of the subject considered, and then matches
them to a statistical database of preprocessed images to ultimately
recognize the specific set of signed letter.
A. FINDING KEYPOINTS
The SIFT feature algorithm is based upon finding locations
(called key points) within the scale space of an image which can
be reliably extracted. The first stage of computation searches over
all scales and image locations. It is implemented efficiently by
using a difference-of-Gaussian function to identify potential in-
terest points that are invariant to scale and orientation. Key points
are identified as local maxima or minima of the DoG images
across scales. Each pixel in a DoG image is compared to its 8
neighbours at the same scale, and the 9 corresponding neighbours
at neighbouring scales. If the pixel is a local maximum or mini-
mum, it is selected as a candidate key point.
We have a small image database, so we don't need a large number
of key points for each image. Also, the difference in scale be-
tween large and small bare hands is not so big.
Figure5: Detected key points for Image representing “Y” Character
B. KEYPOINT LOCALIZATION
In this step the key points are filtered so that only stable and more
localized key points are retained. First a 3D quadratic function is
fitted to the local sample points to determine the location of the
maximum. If it is found that the extremum lies closer to a differ-
ent sample point, the sample point is changed and the interpola-
tion performed instead about that point. The function value at the
extremum is used for rejecting unstable extrema with low con-
trast.The DoG operator has a strong response along edges present
in an image, which give rise to unstable key points. A poorly de-
fined peak in the DoG function will have a large principal curva-
ture across the edge but a small principal curvature in the perpen-
dicular direction.
C. ORIENTATION ASSIGNMENT
In order for the feature descriptors to be rotation invariant, an
orientation is assigned to each key point and all subsequent opera-
tions are done relative to the orientation of the key point. This
allows for matching even if the query image is rotated by any
angle. In order to simplify the algorithm, we tried to skip this part
and assume no orientation for all key points. When tested, it gave
wrong results with nearly all the images where the bare hand im-
age is rotated with an angle of 15º to 20º or more. We realized
that this step can't be elim nated. In this algorithm, the orientation
is in the range [- PI, PI] radians.
D. KEYPOINT DESCRIPTORS
First the image gradient magnitudes and orientations are calcu-
lated around the key point, using the scale of the key point to se-
lect the level of Gaussian blur for the image. The coordinates of
the descriptor and the gradient orientations are rotated relative to
the key point orientation. Note here that after the grid around the
key point is rotated, we need to interpolate the Gaussian blurred
image around the key point at non-integer pixel values. We found
that the 2D interpolation in MATLAB takes much time. So, for
simplicity, we always approximate the grid around the key point
after rotation to the next integer value. By experiment, we real-
ized that, this operation increased the speed much and still had
minor effect on the accuracy of the whole algorithm. The gradient
magnitude is weighted by a gaussian weighting function with σ,
equal to one half of the descriptor window width to give less
credit to gradients far from center of descriptor. Then, these mag-
nitude samples are accumulated into an orientation histogram
summarizing the content over 4x4 subregion. Fig. 4 describes the
whole operation. Trilinear interpolation is used to distribute the
value of each gradient sample into adjacent bins. The descriptor is
formed from a vector containing the values of all the orientation
histogram entries. The algorithm uses 4x4 array of histograms
with 8orientation bins in each resulting in a feature vector of 128
elements. The feature vector is then normalized to unit length to
reduce the effect of illumination change. The values in unit length
vector are thresholded to 0.2 and then renormalized to unit length.
This is done to take care of the effect of nonlinear illumination
changes.
Figure6: Gaussian & DoG pyramids (Source: Reference 1)
Figure 7: 2x2 descriptor array computed from 8x8 samples (Source: Ref-
erence 1)
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E. SIMPLIFICATIONS TO SIFT ALGORITHM
The distance of one feature point in first image and all feature
points in second image must be calculated when SIFT algorithm
is used to match image, every feature point is 128- dimensional
data, the complexity of the calculation can well be imagined.A
changed Comparability measurement method is introduced to
improve SIFT algorithm efficiency. First, Euclidean distance is
replaced by dot product of unit vector as it is less computational.
Then, Part characteristics of 128-dimensional feature point take
part in the calculation gradually. SIFT algorithm time reduced.
Euclidean Distance is distance between the end points of the two
vectors. Euclidean distance is a bad idea because Euclidean dis-
tance is large for vectors of different lengths. This measure suf-
fers from a drawback: two images with very similar content can
have a significant vector difference simply because one is much
longer than the other. Thus the relative distributions may be iden-
tical in the two images, but the absolute term frequencies of one
may be far larger. So the key idea is to rank images according to
angle with query images. To compensate for the effect of length,
the standard way of quantifying the similarity between two im-
ages d1 and d2 is to compute the cosine similarity of their vector
representations V (d1) and V (d2)
Sim (d1, d2) = V (d1). V (d2) / |V (d1) ||V (d2)|
Where the numerator represents the dot product (also known as
the inner product) of the vectors V (d1) and V (d2), while the
denominator is the product of their Euclidean lengths.
F. KEYPOINT MATCHING USING UNIT VECTORS
1. Match (image1, image2). This function reads two images, finds
their SIFT [1] [6] features. A match is accepted only if its dis-
tance is less than dist Ratio times the distance to the second clos-
est match. It returns the number of matches displayed. Where the
numerator represents the dot product (also known as the inner
product) of the vectors V (d1) and V (d2), while the denominator
is the product of their Euclidean lengths.
2. Find SIFT (Scale Invariant Fourier Transform) Key points for
each image. For finding the SIFT Key points specify what are its
locations and descriptors.
3. It is easier to compute dot products between unit vectors rather
than Euclidean distances. Note that the ratio of angles acos of dot
products of unit vectors is a close approximation to the ratio of
Euclidean distances for small angles.
4. Assume some distance ratio for example suppose distance ra-
tio=0.5 it means that it only keep matches in which the ratio of
vector angles from the nearest to second nearest neighbour is less
than distance Ratio.
5. Now for each descriptor in the first image, select its match
To second image.
6. Compute matrix transpose, Computes vector of dot
Products, Take inverse cosine and sort reproducts, Take inverse
cosine and sort results. Check if nearest neighbour has angle less
than dist Ratio times second.
7. Then create a new image showing the two images side by side.
Using this algorithm we read image and calculate key- points,
descriptors and locations by applying threshold. Descriptors given
as P-by-128 matrix where p is number of key-points and each row
gives an invariant descriptor for one of the p key-points. The de-
scriptor is a vector of 128 values normalized to unit length. Loca-
tions are P-by-4 matrix, in which each row has the 4 values for a
key-point location (row, column, scale, orientation). The orienta-
tion is in the range [-PI, PI] radians
Fig8. SIFT Key-points Extraction, Image showing matched
keypoints between input image and database image.
Now apply these steps in our previous image from which SIFT
features are extracted.
Algorithmblockdiagram
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IV. EXPERIMENTAL RESULTS AND ANALYSIS
The performance of the recognition system is evaluated by testing
its ability to classify signs for both training and testing set of data.
The effect of the number of inputs to the neural network is con-
sidered.
A.Data Set
The data set used for training and testing the recognition system
consists of grayscale images for all the ASL signs used in the
experiments are shown see fig. 4. Also 8 samples for each sign
will be taken from 8 different volunteers. For each sign 5 out of 8
samples will be used for training purpose while remaining five
signs were used for testing. The samples will be taken from dif-
ferent distances by WEB camera, and with different orientations.
In this way a data set will be obtained with cases that have differ-
ent sizes and orientations and hence can examine the capabilities
of the feature extraction scheme.
B.Recognition Rate
The system performance can be evaluated based on its ability to
correctly classify samples to their corresponding classes. The
recognition rate can be defined as the ratio of the number of cor-
rectly classified samples to the total number of samples and can
be given as
Recognition rate =
.
n
no ofcorrectlyclassifiedsigns
totaL oofsigns
C.Experimental Results
SIGN Recognized
samples
Misclassified
samples
Ecognition
rate
A 7 1 66.66
B 7 1 66.66
C 7 1 66.66
D 8 0 100
E 8 0 100
F 8 0 100
G 7 1 66.66
H 7 1 66.66
I 8 0 100
J 8 0 100
K 7 1 66.66
L 7 1 66.66
M 8 0 100
N 7 1 66.66
O 7 1 66.66
P 8 0 100
Q 8 0 100
R 7 1 66.66
S 7 1 66.66
T 8 0 100
U 8 0 100
V 8 0 100
W 8 0 100
X 6 2 33.33
Y 8 0 100
Z 6 2 33.33
TOTAL 193 15 92.78
Table 1 Results of training 8 samples for each sign with (0.25) Canny
Threshold
The network is trained on 8 samples of each sign. Samples of
same size and other features like distance rotation and lighting
effect and with uniform background are taken into consideration
while discarding the others.
Figure. 9 Training chart for a network trained on 8 samples for each sign,
(0.25) Canny threshold
Figure 10 Percentage error recognition chart of neural network
E. GUI Simulating Results (sign to text)
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For testing the unknown signs we have created a GUI as shown in
Fig. 5 which provides the user an easy way to select any sigh
He/She wants to test and then after clicking on the Apply
pushbutton it will display the meaning of the selected sign.
F. GUI SIMULATING RESULTS (TEXT TO SIGN)
A text to sign interpreter means if the user types any sign or sen-
tence corresponding signs are shown so that normal person to
deaf people communication can be done. Examples of showing
the sign to text converters are shown (See figure 6). Fig. 6 shows
when the user type the name ‘BOB’ in the text box its corre-
sponding signs are appear on the screen one by one above the text
or spelling.
The approach described above has been implemented using-
MATLAB. The implementation has two aspects: training and
inference. During the training phase locally invariant features
(key points, orientation, scales and descriptors) from all training
images are retrieved using the SIFT algorithm.During inference,
the objective is to recognize a test image. A set of local invariant
features are retrieved for the test image during the inference phase
and compared against the training feature-set using the metric
explained in section 4.The title of the closest match is returned as
the final output.
In order to prove the performance of our proposed system, we
Predefined the number of gestures from B, C, H, I, L, O, Y and
create a hand gesture database. Matching is performed between
images by unit vectors. The matching is accomplished for pro-
posed method and the result shows that it produces 98% accuracy.
In Figure 7, we can easily identify Database Images 1, 3, 7 have
more number of key-points matched with input image key-points
.So Distance Ratio
Parameter and threshold are adjusted.
Figure 11: comparison of key-points on given input with database For a
single input image for first cycle.
In Figure 8, we compare Database Images 1, 3, 7 with input im-
age key points. So Database Image 3 is closest match with input
image.
single input image after resetting threshold value and Distance ratio value
The problem now is how we can identify a 'No Match'. For this,
we saw that the 'No Match' query images are in many cases con-
fused with the database images that have a large number of fea-
ture vectors in the feature vectors database. We decided to com-
pare the highest vote (corresponding to the right image) and the
second highest vote (corresponding to the most conflicting im-
age). If the difference between them is larger than a threshold,
then there is a match and this match corresponds to the highest
vote. If the difference is smaller than a threshold, then we declare
a 'No Match'. The values of THRESHOLD were chosen by ex-
periment on training set images either with match or no match.
single input image (No Match Case)
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Figure14: Example of a “no match” Image not in training set for figure3
Gesture
Name
Testing Num-
ber
Success
Number
Correct Rate
B 150 149 99.3
C 150 148 98.7
H 150 148 98.7
I 150 149 99.3
L 150 148 98.7
O 150 148 98.7
Y 150 149 99.3
Table2. The results of classifier for the training set and Testing set
FIGURE15 RECOGNIZED STATIC SIGN USING PCA ALGORITHM
FIGURE 16 RECOGNIZED DYNAMIC SIGN USING PCA ALGRITHM
7. CONCLUSIONS:
IV. HARDWARE AND SOFTWARE
The system is implemented in MATALAB version R13.5. The
recognition training and tests were run on a modern standard PC
(1.5 GHz AMD processor, 128 MB of RAM running under win-
dows 2008.) WEB-CAM-1.3 is used for image capturing.
The system is proved robust against changes in gesture.Using
Histogram technique we get the misclassified results. Hence His-
togram technique is applicable to only small set of ASL alphabets
or gestures which are completely different from each other. It
does not work well for the large or all 26 number of set of ASL
signs. For more set of sign gestures segmentation method is sug-
gested. The main problem with this technique is how good differ-
entiation one can achieve. This is mainly dependent upon the
images but it comes down to the algorithm as well. It may be en-
hanced using other image
Processing technique like edge detection as done in the presenting
paper. We used the well known edge detector like Canny, Sobel
and Prewitt operators to detect the edges with different threshold.
We get good results with Canny with 0.25 threshold value. Using
edge detection along with segmentation method recognition rate
of 92.33% is achieved. Also the system is made background inde-
pendent. As we have implemented sign to text interpreter reverse
also implemented that is text to sign interpreter.
The Algorithm is based mainly on using SIFT features to match
the image to respective sign by hand gesture. Some modifications
were made to increase the simplicity of the SIFT algorithm. Ap-
plying the algorithm on the training set, we found that it was al-
ways able to identify the right sign by hand gesture or to declare
‘No Match’ in case of no match condition. The algorithm was
highly robust to scale
Difference, rotation by any angle and reflection from the test im-
age. SIFT is a state-of-the-art algorithm for extracting locally
invariant features and it gave me an opportunity to understand
several aspects of application in image recognition. I believe this
effort resulted in a robust image recognition implementation,
which should perform quite well with the final test images. In
future I would like to work on improving the performance of the
SIFT for Global Features.
The local invariant features of SIFT can be augmented by com-
puting global features of an image.
FUTURE SCOPE / CHALLENGES
The work presented in this project recognizes ASL static signs
only. The work can be extended to be able to recognize dynamic
signs of ASL. The system deals with images with uniform back-
ground, but it can be made background independent. It is over-
come and it is made Background independent. The network can
be trained to the other types of images. It is important to consider
increasing data size, so that it can have more accurate and highly
performance system.
ACKNOWLEDGMENT
The authors wish to thank to guide Prof.P.SUBBA RAO for his
valuable guidance for this work. And the volunteers who has
given gesture images in the required format no of times whenever
required till to the results.
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