JP2008508576A - Method for creating a symbol pattern, symbol pattern obtained thereby, method and system for locating in such a symbol pattern, and computer program product for performing the method - Google Patents

Abstract

  The present invention relates to a method for creating a two-dimensional symbol pattern that may be utilized to determine a position within a large area covered by a pattern for recording handwritten information, for example by a pen-like device. The present invention is useful for creating a symbol pattern having the desired characteristics, i.e., any sufficiently large observed portion is unique and allows unambiguous determination of position. The symbol pattern is based on a non-repeating sequence of symbol values Sk each corresponding to a fixed linear combination of monomial coefficients in xk modulo P (x), where P (x) is in field Fq An arbitrary polynomial of degree n. The symbol pattern is generated by folding the sequence according to a wrapping scheme. The present invention also relates to a method and system for finding the position of a group of observed symbol values in this symbol pattern, and a computer program product for performing the method.

Description

(Cross-reference of related applications)
This application claims the benefit of Swedish Patent Application No. 0401812-3 and US Provisional Patent Application No. 60 / 585,856, both filed July 8, 2004 and incorporated herein by reference.

  The present invention relates to a method for creating a two-dimensional symbol pattern that may be utilized to determine a position within a large area covered by a pattern for recording handwritten information, for example by a pen-like device. The present invention is useful for creating symbol patterns having the desired characteristics that allow unambiguous determination of position.

  The present invention also relates to a method and system for locating a group of symbol values observed in this symbol pattern, and a computer program product for performing the method.

  In this field, scanning into a pen-like instrument that incorporates memory and computer processing capabilities to calculate the pen position relative to a pattern printed on paper or displayed on a computer screen, for example. It is known to form patterns that may be applied.

It is also known to generate repetitive or non-repetitive sequences with a linear feedback shift register (LFSR). Non-repeating sequences have the property that each subsequence of a predetermined number of consecutive values occurs only once in the sequence. Thus, in non-repeating sequences, the location of each subsequence of a predetermined length is clearly determined. It is known to wrap or fold such repetitive sequences into a two-dimensional symbol pattern to locate in such a pattern. See published patent applications assigned to Microsoft Corporation, U.S. 2004/0085287, U.S. 2004/0085302, U.S. 2004/0086181, and U.S. 2004/0086191.
Swedish Patent Application No. 0401812-3 US Provisional Patent Application No. 60 / 585,856 Published patent application, US 2004/0085287 US 2004/0085302 US 2004/0086181 US 2004/0086191 US Pat. No. 6,674,427 US Pat. No. 6,667,695 R. Lidl and H.C. Niederreiter, “Introduction to finite fields and their applications”, Chapter 6—Linear Recurrence Sequences (revised 1994, University of Cambridge, University of Canada)

  The problem with wrapped sequences in the prior art is whether such a two-dimensional pattern obtained by wrapping a non-repeating sequence has the desired properties, i.e., any sufficiently large observed pattern. There is no way to tell that a part is unique. If it is not unique, it is impossible to determine its position clearly.

  The present invention provides a tool for creating conditions that determine the relationship between an observed group (mask) of symbol patterns and a valid non-repeating sequence. Furthermore, the present invention provides an efficient technique not only for recovering the position in the symbol pattern, but also for testing whether the wrapped sequence has the proper characteristics for position determination.

  The invention is defined in the appended claims.

  The present invention will be described in detail later with reference to the accompanying drawings.

  For further understanding, some of the mathematics behind the present invention are described, some of which also form the prior art. The following terms and definitions are used.

（Ｐ（ｘ）を法として）として定義される
Ｆｑ 典型的にはｑ＝２であるが、必ずしもｑ＝２ではない次数ｑの有限体
Ｇ（ｆ（ｘ））ｒ_ｋにおける単項式ｘ^ｎ−１の係数等の補助関数
Ｗ ラッピングシーケンス
ｗ ラップ長（行に関して、あるいは列に関してラッピングするとき）
Ｂ マスク＝幾何学的な走査パターン（＝球体）によって観察される要素の列ベクトル
Ｂ’ 同上、別の走査パターンを用いる
ＢＰ シンボルパターンの細分
ｍ Ｂのサイズ（＝“ｋｘ１”、矩形走査パターンの場合）；（ｍ≧ｎ）
Ｃ シーケンスＳにおける場所ｋに対応する剰余多項式ｒｋの（サイズｎの）係数の列ベクトル
Ｔ Ｂ＝ＴＣを履行する変換行列Ｔ、ＴはランクＮ＝ｎを有する
Ｔ’ Ｂ＝Ｔ’Ｃを履行する変換行列Ｔ’、ＴはランクＮ＝ｎ−ｊを有する
Ｘ、Ｙ 求められる位置（Ｂが不規則な形である場合、Ｂの左上隅、つまり「第1の」要素）
Ｂ_Ｘ，Ｙ 求められた位置（Ｘ、Ｙ）でのＢ（およびＢ’）の要素
Ｃ_Ｘ、Ｙ 求められた位置（Ｘ、Ｙ）に対応するＣの係数
ｋ Ｃの係数がＣＸ、Ｙに等しいシーケンスＳにおける場所
Ｈ ＨＴ＝０を履行し、一意のゼロ以外の列のあるチェックマトリックス
ｈ_ｉ Ｈの列ｉ、Ｂのビットｉで発生するビットエラーの一連の徴候
ＬＦＳＲ 線形フィードバックシフトレジスタ
第1のタスクは所望の特性を有するシンボルパターンＰ^Ｗを作成することである。これは、長い非反復シーケンスＳを形成し、ラッピングしてから、十分に大きな観察されたマスクとシーケンスとの間の変換行列Ｔによって表される変換関係が規定される条件を履行することを確認することによって行われてよい。シンボルパターンの例は図１に示されており、白のピクセルと黒のピクセルが各々シンボル値１と０を表している。このようにして、シンボルパターンは、各々が少なくとも一つのシンボル値またはシーケンスＳの要素を表すシンボルの並べられた集合から構成される。 Terms and definitions S Length of sequence L S of elements S _k (k = 0 to L−1)
In the remainder polynomial of PW sequence S and rank _{r k} of n degrees and LFSR size N T of the wrapping scheme W symbol pattern P formed by the (x) of n polynomials n polynomial P (x), Fq [x] Count with / P (x)

Although the Fq typically defined (P (a x) modulo) as a q = 2, the finite field G of necessarily q = a 2 not order q (f (x)) monomials in _{r k} ^{x n-} Auxiliary function such as coefficient ¹ W wrapping sequence w Wrap length (when wrapping with respect to rows or columns)
B mask = column vector B 'of elements observed by a geometric scanning pattern (= sphere) Same as above, BP using another scanning pattern size of mB of symbol pattern (= "kx1", rectangular scanning pattern Case); (m ≧ n)
C implements a transformation matrix T that implements a column vector T B = TC of coefficients (of size n) of the remainder polynomial rk corresponding to location k in sequence S, T implements T ′ B = T′C with rank N = n The transformation matrix T ′, T is X, Y with rank N = n−j The position to be obtained (if B is irregularly shaped, the upper left corner of B, ie the “first” element)
B _{X, Y} The element C _X of B (and B ′) at the determined position (X, Y), the coefficient of the C coefficient k C corresponding to the determined position (X, Y) is CX, Y A sequence of indications of bit errors occurring in column i, B bit i of check matrix h _i H, with location H HT = 0 in sequence S equal to and having a unique non-zero column LFSR Linear Feedback Shift Register One task is to create a symbol pattern P ^W having desired characteristics. This confirms that the long non-repeating sequence S is formed, wrapped, and then fulfills the conditions that define the transformation relationship represented by the transformation matrix T between the sufficiently large observed mask and sequence. It may be done by doing. An example symbol pattern is shown in FIG. 1, where white and black pixels represent symbol values 1 and 0, respectively. In this way, the symbol pattern consists of an ordered set of symbols, each representing at least one symbol value or an element of the sequence S.

  Although the following description is based on a sequence S composed of binary symbol values, the underlying principles of the present invention are generally applicable to symbol values at any base (ie, for any order q of field Fq). .

It is well known that the linear feedback shift register LFSR can be used to generate long non-repeating binary sequences such that any sufficiently large subsequence is unique within the sequence. n-size LFSRs are connected along r ₀ , r ₁ ,. . . , R _n−1, and a simple computing device consisting of at least one XOR-gate as shown, for example, in FIG. The device has discrete times t ₀ , t ₁ . . . It is updated with. At time t _k , k> 0 and every bit holder is updated simultaneously with the value calculated at the end of the arrow pointing to it. Contents _C k at time ^{_{t k = (c 0 (k}} ), c 1 (k), ..., c n-1 (k)) is called the LFSR state at time _{t k.} At time t ₀ , the state is for example {1, 0, 0,. . . , 0}. At each time t _k , the bits contained in r _n−1 are shifted out to generate the k th bit of the binary sequence S. There are many unique states and, in fact, for some LFSRs, the duration of the sequence is so long that the generated sequence S may have a duration of at most 2 ⁿ −1. Another property that is desirable for the purposes of the present invention is that any sequence of n consecutive bits during the period is unique.

In the example of FIG. 2, the LFSR includes five bit holders and one XOR gate. The depicted LFSR represents a polynomial P (x) = x ⁵ + x ² +1, and may generate a non-repeating sequence of a specific length depending on P (z) and the initial value of the bit holder. For details on LFSR and generation of repetitive and non-repetitive sequences, see i. a. R. Lidl and H.C. Niederreiter, “Introduction to finite fields and their applications”, Chapter 6—Linear Recurring Sequences (revised 1994, University of Cambridge, United Kingdom) Are listed.

  The LFSR is a practical device for generating a sequence. Fortunately, the LFSR also allows natural mathematical processing in terms of generators in the polynomial rings described next.

The F ₂ and binary field. Let F ₂ [x] be the field of all polynomials in x with coefficients from F ₂ . _{Finally, F} 2 in the case of a polynomial P (x) in [x] R in (x, P (x)) , F 2 [x] / P k = 0,1,2 in (x). . . Elements x ^k in the case ^of, i.e. not exhibit a ring consisting of x ^k P a (x) modulo where each monomial coefficients in F _2. The smallest positive o is called the order of the ring so that xo-1 can be divided by P (x) in F ₂ [x].

に従うことを観察する。別段に定めをした場合、ＬＦＳＲの状態はＲ（ｘ，Ｐ（ｘ））の要素で一意に識別できる。したがって、ＬＦＳＲで生成されるシーケンスの期間はＲ（ｘ、Ｐ（ｘ））の次数に等しい。特にＦ_２［ｘ］の度ｎの原始多項式に対応するＬＦＳＲは、全ゼロ文字列を除く長さｎのすべての考えられる０／１文字列が、シーケンスの中で一度（および一度だけ）発生するように期間２^ｎ−１の周期的なシーケンスを生成する。 Ring R (x, P (x)) is associated with the LFSR as follows. Let n be the degree of (Px), XOR gates Consider a LFSR of size n that is between the _{c L-1} and _{c L} for each monomial ^{x L} of p (x). Here, LFSR state C _k = (c ₀ ^(k) , c ₁ ^(k) ,..., C _n−1 ^(k) ) at time t _k , multiplication by x corresponds to shift of LFSR Since the subtraction for calculating the remainder after division by P (x) corresponds to the calculation of the XOR gate,

Observe to follow. When determined otherwise, the state of the LFSR can be uniquely identified by the element of R (x, P (x)). Therefore, the duration of the sequence generated by the LFSR is equal to the order of R (x, P (x)). In particular, an LFSR corresponding to a primitive polynomial of degree n of F ₂ [x] generates all possible 0/1 strings of length n except for all zero strings once (and only once) in the sequence. A periodic sequence of period 2 ⁿ −1 is generated.

とし、任意の多項式ｆ（ｘ）の場合、単項式ｘ^ｎ−１がＰ（ｘ）を法として剰余多項式ｆ（ｘ）の一部である場合には、Ｇ（ｆ（ｘ））を１とし、それ以外の場合を０とする。 For convenience, some auxiliary symbols are introduced.

In the case of an arbitrary polynomial f (x), G (f (x)) is set to 1 when the monomial x ⁿ⁻¹ is part of the remainder polynomial f (x) modulo P (x). Otherwise, 0 is assumed.

Based on previous observations, ready to establish a connection between the LFSR state at the k th point in the bit S _k and any past LFSR generated sequence S is completed.

について

に従う。 Fact 1: The kth bit S _k of the LFSR generation sequence S is arbitrary

about

Follow.

Given an n-size LFSR sequence S, the pattern P ^W obtained by wrapping S with respect to a row every w th symbol has the property that any sufficiently large submatrix is unique among P ^W. Hope to characterize when to get. Formally, the entry P ^W (X, Y) in the row Y and column X of the pattern is specified by P ^W (X, Y) = _{SYw + X.}

At the upper left corner of (X, Y) where k = Yx + X, associate the LFSR state Ck with the a x b-submatrix in ^PW . Fact 1 only makes the following happen.

Ｇ（ｆ（ｘ））は一次関数であるため、前記方程式を以下のように行列形式にすることができる。

Since G (f (x)) is a linear function, the equation can be in matrix form as follows.

簡潔にするため、この関係をＢ＝ＴＣとして書き、この場合、Ｇはパターン部分行列ベクトルであり、ＴはＬＦＳＲ状態からパターン部分行列への線形変換であり、ＣはＬＦＳＲ状態ベクトルである。我々の主要定理を前提とする。

For simplicity, this relationship is written as B = TC, where G is a pattern submatrix vector, T is a linear transformation from an LFSR state to a pattern submatrix, and C is an LFSR state vector. Assuming our main theorem.

Theorem: Let P (x) of F ₂ [x] be a polynomial of degree n. Let L be the order of R (x, P (x)). Thus, R (x, P (x )) patterns ^{P W} obtained from the sequence S of length L generated by the LFSR for, if the corresponding G has rank n of greater than _{F 2,} a in ^{P W} The x b− submatrix has a unique property. Further, it is also a necessary requirement when the order is maximum (L = 2 ⁿ −1).

The aforementioned pattern ^PW was obtained by wrapping the sequence S with respect to the row every wth symbol. Alternatively, other embedding or wrapping schemes of the sequence may be used, for example to wrap around the columns every wth symbol, or to form a two-dimensional pattern such as an oblique embedding of the sequence. Still other embeddings may help, but preferably the difference between the indices of the sequence elements at adjacent positions is constant. For the sake of clarity, for each position (X, Y) in the pattern, a sequence that can be represented by q (X, Y) = k, which means that the symbol value S _k is at position (X, Y) in the pattern Associated a unique location k in S. Where q (X + 1, Y) -q (X, Y) modulo L and q (X, Y + 1) -q (X, Y) modulo L is constant at position (X, Y Regardless of the choice of), clear advantages may be obtained by the present invention, as will be clarified further.

  Further, the technique of the present invention not only allows for a modified wrapping scheme, but also checks for uniqueness and handles position decoding of arbitrary shapes of groups of symbols / symbol values as opposed to just rectangles as described above. May be used. In the following, an example of a pattern in which the group of symbol values in the shape of a small sphere is unique and the wrapping scheme includes wrapping on a column is shown.

Ｆ_２［ｘ］／Ｐ（ｘ）でカウントし、ベクトル

を定義する。 Consider the following polynomial:

Count with F ₂ [x] / P (x), vector

Define

Since P (x) is a primitive _polynomial, the first k> 0 is r k = _{r 0} is ^{k = 2} 16 -1.

k = 0, 1, 2,. . . Consider the pattern obtained by wrapping the sequence G (r _k ) for 2 ¹⁶ −2 where G (f (x)) of any polynomial f (x) is P (x) The modulo is the (binary) coefficient of the monomial x ¹⁵ in f (x). In general, G (f (x)) may be any linear combination of monomial coefficients in f (x) modulo P (x).

An example of a symbol pattern ^PW is shown in FIG. 1 where white and black pixels represent the values 1 and 0, respectively. The sequence starts at the upper left corner, continues down, wraps each 187 bits, and starts again from the top in the next column to the right of the previous column. The selection of the sequence, that is, P (x) and the wrap length 187 are not arbitrary. In contrast, they are chosen with great care to obtain some desirable decoding characteristics.

  First, to ensure that each sufficiently large area of the pattern is unique within the pattern, allowing fast inversion, that is, a fast algorithm that locates coordinates in the pattern of the area being viewed. I hope.

  Second, it will also prefer the ability to compute the coordinates of the seen part of a bit even in the presence of error-prone embeddings, that is, several misinterpreted bits.

  An example of a group of symbol values (hereinafter referred to as a mask or sphere B) is shown in FIG. The symbol pattern shown above has the following characteristics.

  1. For example, any group of symbol values in the shape of FIG. 3 is unique within the pattern. That is, when a sphere is viewed in any of the patterns, it is possible to distinguish where the viewed sphere is located in the pattern. In addition, it uses much less storage than doing this much faster than searching for patterns completely and in search of a match, and still using a large lookup table that contains all possible sphere-pair pairs. Is possible.

  2. If at most one of the 21 symbol values (bits) in a sphere seen in any of the patterns is misinterpreted or missing, detect this and calculate the appropriate value quickly Can do. Note that this requires that any two different spheres in the pattern must be at least three different symbol values.

How was the selection of P (x) combined with the wrap length 187 verified to have these characteristics? This sphere (position (X, Y)) of the r _k occupying (virtual) the upper left corner G (r _k) is achieved by associating the bit is seen the spheres. Note that may be written about r _k as bits spheres is shown in the table below.

Ｇ（ｒ_ｋ＋ｌ）が

における単項式の係数ｃ_ｉの線形組み合わせとして表されてよいことを観察することによって、前述の数学的な説明に従って

を表す関係をＢ＝ＴＣと書くことができる。ここでＢはパターンＰ^Ｗの観察された要素に対応し、Ｃは剰余多項式ｒ_ｋに対応する。有効なシーケンスＳにおいて、ＴはシーケンスＳ、ラッピングスキームＷおよびマスクＢの形状に依存するにすぎない。剰余多項式ｒ_ｋ（つまりＰ（ｘ））を法としたｘ^ｋ）、およびそれにより係数Ｃは再発関係を使用する反復二乗によって〜ｌｏｇ（ｋ）乗算を使用して計算できるため、

変換行列Ｔは効率的に計算できる。本例では、主要定理（前記）は、一意の高速反転可能球体を得るために行列がランク１６を有することを必要とすると規定している。ｗ＝１８７の場合、行列Ｔは、事実上Ｆ２を超えるランク１６を有する

のように見える。

G (r _{k + l} ) is

By observing that it can be expressed as a linear combination of the monomial coefficients c _i in

Can be written as B = TC. Where B corresponds to the observed pattern elements P ^W, C corresponds to the remainder polynomial r _k. In a valid sequence S, T only depends on the shape of the sequence S, the wrapping scheme W and the mask B. Remainder polynomial _{r k} (i.e. P ^(x)) x k) modulo, and for thereby coefficient C can be calculated using ~log (k) multiplied by repeated squaring of using the recurrence relation,

The transformation matrix T can be calculated efficiently. In this example, the main theorem (above) stipulates that the matrix needs to have rank 16 in order to obtain a unique fast invertible sphere. If w = 187, the matrix T has a rank 16 that effectively exceeds F2.

looks like.

  In order to form a valid sequence S, the following steps may be performed.

  Select that sequence S is binary, ie field q = 2.

  For example, an appropriate polynomial P (x) is selected when n = 16.

  Select a wrapping scheme W, such as wrapping on a column with a wrap length w = 187. It is also possible to wrap with respect to the line or diagonally. In the case of diagonal wrapping, it may be desirable for the greatest common divisor between the width and height of the pattern to be one. However, in principle, the only requirement for the wrapping scheme is that it maintains the relative geometric order and relationship between the elements in mask B and the corresponding coefficients C of sequence S. .

  Select a mask pattern B having a specific shape and the number of bits m, for example m = 21.

  Calculate the transformation matrix T using the wrapping scheme W, the shape of the mask B and the polynomial P (x).

Check that T rank N = n. If this is the case, the symbol pattern P ^W , ie the sequence S wrapped with the wrapping scheme W, has the desired properties. If not, change one or more of the wrapping scheme W, the shape of the mask B, and the polynomial P (x) until T rank N = n.

  The transformation matrix T is appropriately calculated by iterative squares.

Further, as shown in FIG. 1, it is also possible to form a subdivision of the symbol pattern ^PW , such as a subdivision ^BP . This is effective when it is desired to generate an area covered by a part of the symbol pattern ^PW by, for example, printing on one sheet of paper. The first element of ^BP at position (X, Y) is calculated by calculating r _k ≡x ^k (modulo P (x)), suitably by iterative squares, then k = q (X , Y) is generated by evaluating G (r _k ) to obtain a symbol value. To obtain the next element to the right, q (X + 1, Y ) -q (X, Y) = d better use of the fact that it is constant, that is, the _{r k} in order to obtain _{r k + d} in ^{x d} G (r _{k + d} ) may be calculated to obtain a symbol value. Therefore, it is easy to move to the next symbol on the right when generating part of the pattern. When generally consider the remainder polynomial _{r k} position (X, Y), the position (X + u, Y + v ) generating an in elements, multiplies _{r k} in powers of x corresponding to the vector (u, v) Then, it is executed by applying the function G.

  As mentioned by the introduction, one use of a symbol pattern may be to determine the position of a detection device that is moved over a displayed pattern, such as on paper or a computer screen. For example, Applicant's US Pat. Nos. 6,674,427 and 6,667,695, which are incorporated herein by reference, further describe a pen-like manual operating device for position determination. These pen-like devices can be used for position determination in accordance with the present invention when properly programmed.

  Hereinafter, an embodiment of such a detection apparatus will be described with reference to FIG. The detection device 400 of this embodiment comprises a pen-shaped housing or shell 401 that forms a window or opening 402 that is captured by a capture means 403 that is configured to scan an image with many symbols of the pattern. .

  The capture means 403 may include any type of sensor suitable for imaging the symbol pattern such that the symbol image is acquired in black and white, grayscale, or color. Such sensors can be solid state single chip devices or multichip devices that are sensitive to electromagnetic radiation in any suitable wavelength range. For example, the sensor may include a CCD element, a CMOS element, or a CID element (charge injection device). Alternatively, the sensor may include a magnetic sensor for detecting the magnetic properties of the symbol. Still further, the sensor may be designed to form an image having any chemical, acoustic, capacitive or inductive characteristic of the symbol.

  The detection device 400 of FIG. 4 allows the user to point the detection device 400 to a particular position on the symbol pattern, and in some cases sees what the user is writing or drawing on the symbol pattern. A nib or writing instrument 404 is also provided to deposit a conventional dye-based marking ink on the symbol pattern so that it can. Contact sensor 405 is operably connected to nib 404 to detect when the nib is lowered onto the surface and / or lifted off the surface. Based on the output of the contact sensor 405, the capture means 403 is controlled to capture an image of an area near or around the pen tip 401 between pen down and pen up. The detection device 400 includes a power source 406, such as a battery and / or main power connector, a communication interface 407 with components for wired or wireless short range or remote communication, and a display, indicator for providing feedback to the user. Also provided is an MMI (Man Machine Interface) 408 such as a lamp, vibrator, or speaker, and one or more buttons that allow the user to activate and / or control the detection device 400.

  The detection device 400 also includes a memory 410 for storing pattern data representing symbols scanned by the capture means 403 and a signal processing device 411 for performing various calculations. The signal processing unit 411 is, for example, by a suitably programmed processor, by specially adapted hardware such as an ASIC (Application Specific Integrated Circuit), DSP (“Digital Signal Processor”) or FPGA (Field Programmable Gate Array), It may be realized by discrete digital components or analog components, or any combination thereof. Alternatively, the memory 410 and / or the signal processing device 411 may be disposed in an external receiving device (not shown) that communicates with the detecting device 400.

The calculations performed by the signal processor 411 will now be briefly described with reference to the mask illustrated in FIG. As described above, the symbols scanned by the capturing means 403 are arranged in a known geometric order and relationship with respect to the sequence. Assume that mask B is placed at a position defined by the coordinates (X, Y) of the upper left corner of mask B. The observed symbols in mask B represent symbol values, ie elements in sequence S. These observed elements B _{X, Y} of the mask B correspond to the special coefficients C _{X, Y} of the sequence S. The relationship between the elements B _{X, Y} and C _{X, Y} is represented by the matrix equation B = TC.

Locating the observed position of the mask B in the symbol pattern PW may include the following steps. First, the element B _{X, Y} of the mask B at position (X, Y) is captured and stored in memory. The matrix equation B _{X, Y} = TC _{X, Y} is then solved for C _{X, Y.}

In one embodiment, the transformation matrix T (appropriately as a factorization that allows a quick answer), ie its inverse T-1, is precomputed for the sequence S and stored in the memory of the detector / receiver. It's okay. The mask B may have a predetermined fixed shape. For successive locations at changing positions (X, Y), the corresponding coefficients C _{X, Y} are solved by the matrix equation described above.

が係数Ｃ_Ｘ，Ｙを有する離散値対数ｋを発見する。 The coefficients C _{X, Y} correspond to a unique position k in the sequence S. Once the coefficients C _{X, Y} are found, k is calculated, for example, by a public-key cryptography (Silver-Pohlig-Hellman) algorithm. Public key cryptanalysis method (with P (x) as modulo)

Find the discrete logarithm k with coefficients C _{X, Y.}

The order of P (x) is 2 ¹⁶ −1 = 3 * 5 * 17 * 257, and the public key cryptanalysis algorithm has a sufficiently small maximum prime (in this case, 257), and k is determined quickly. Is always efficient when possible.

  From k, the (X, Y) -coordinate of the upper left corner of the sphere is indicated by the wrap length for the column w = 187 (k divisor w, (k div w) modulo w).

  In other embodiments, the shape of the mask B 'may vary. For example, the mask B 'may incorporate three elements that are indicated by dashed lines in FIG. The number m of elements may be made constant by excluding the other three elements, or may be increased by incorporating more elements. This can be useful if the value of the decoded symbol is indeterminate. Thus, various shapes of the mask B 'may be tried until a valid transformation matrix T is found. In this case, the transformation matrix T, ie its inverse T-1, may be calculated dynamically in the detector / receiver. A valid transformation matrix T may be defined as having rank N = n. Accordingly, the matrix equation B '= TC may be solved and the location may be located as defined above.

  The following decoding methods may be used. Reorder the interpreted symbol values according to certainty. That is, image processing starts with the symbol that is most reliable for its interpretation. Next, the symbol values are added one by one until the linear transformation matrix obtains rank n, and the position is solved. Note that any shape of the mask may be used, not just the rectangles or spheres of adjacent elements.

In a further embodiment, a valid transformation matrix T ′ is defined as having rank N = n−j. In this case, the matrix equation B = T′C will have a maximum of 2 ^j solutions corresponding to different positions (X, Y) and place k in the sequence S. Needless to say, only one solution is a correct solution, and a false solution may be eliminated by an overlying rule of thumb. For example, false solutions may be eliminated by checking continuity conditions (eg, spatial distance, acceleration, etc.) with respect to one or more previous and / or subsequent positions.

  It is also possible to change the mask B ′ and define a valid transformation matrix T ′ as having rank N = n−j. First, various shapes of the mask B 'may be tried until a valid transformation matrix T' is found. Next, the matrix equation B ′ = T′C with various solutions may be solved to eliminate false solutions.

The present invention also provides a tool for performing error correction on sampled observed bits. The null space of T ^t (T transposed) can be evaluated by known techniques for obtaining a binary matrix H with linearly independent rows that achieve HT = 0.

In this example, H is a 5 × 21 matrix, and H = [h ₁ h ₂ h ₃ . . . h ₂₁ ] is as follows.

このような行列Ｈは、Ｔにより生成される線形コードのエラー訂正コードとの関連においってチェックマトリックスとして知られている。我々のＨが、すべての列ｈ_ｉが全ゼロベクトルと異なり、一意であるという特性を有することに留意する。パターンにおけるすべての考えられる観察されたマスクＢは係数ベクトルＣの何らかの選択のために、フォーマットＢ＝ＴＣであるため、ｉで誤りビットのひとつの見られたマスクは、Ｂ＊＝Ｂ＋ｅ_ｉと書き込まれ、ｅ_ｉはビット位置ｉの中で値一（１）を、および他のすべての位置で値ゼロ（０）を有する列ベクトルである。チェックマトリックスによる乗算は以下を生じさせる。

Such a matrix H is known as a check matrix in connection with an error correction code of a linear code generated by T. Note that our H has the property that every column h _i is unique, unlike all zero vectors. Since all possible observed masks B in the pattern are of format B = TC due to some choice of coefficient vector C, one observed mask of error bits with i writes B * = B + e _{i Ei} is a column vector with the value 1 (1) in bit position i and the value zero (0) in all other positions. Multiplication with a check matrix produces:

つまり、Ｈで見られたマスクを乗算し、エラーの場所を突き止めるために取得された文字列を調べることによって単一のエラーを突き止め、訂正することができる。誤りビットを反転すると正しい値が与えられ、ガウス消去法および例えば前述のように公開鍵暗号解読法アルゴリズムを用いて等、Ｔを介した後退代入を使用してＣについて解くことができる。

That is, a single error can be located and corrected by multiplying the mask found in H and examining the acquired string to locate the error. Inverting the error bit gives the correct value and can be solved for C using backward substitution via T, such as using Gaussian elimination and public key cryptography algorithms as described above.

  The error correction is equally adaptable with a check matrix H ′ associated with a transformation matrix T ′ having a rank N = n−j (ie H′T ′ = 0).

  If we want to find a pattern that would allow to allow v bits to be wrong, check matrix H with the property that any 2v column is linearly independent. I need to find it. This is well known from the theory of linear codes.

  When the detection device is moved over a surface with a symbol pattern, for example to form characters and images, a series of decoding or finding operations are performed. There, each position may be decoded using a transformation matrix T, T 'having a rank N = n or N = n-j, using a fixed or variable mask B, B' as described above. The decoding scheme may also change between positions.

  The present invention may be implemented by various combinations of software and hardware, as will be understood by those skilled in the art. The scope of the invention is limited only by the following claims.

FIG. 4 is an example of a wrapped sequence embodied as a symbol pattern. FIG. FIG. 6 is a schematic diagram of a linear feedback shift register. FIG. 3 is a schematic diagram of an example mask that defines an observed subset of symbol patterns. 1 is a schematic side view of a partial cross-section of a pen-shaped detection device according to an embodiment of the present invention.

Claims (41)

A method for creating a two-dimensional symbol pattern P ^W having the property that an arbitrary subset of symbol values having a size m observed in a symbol pattern is unique,
Define a non-repeating sequence S of symbol values S _k corresponding to a fixed linear combination of monomial coefficients C at x ^k modulo each P (x), where P (x) is the degree n of field F _q And any polynomial
Defining a mask pattern of defined shape and producing a mask vector B comprising the observed m symbol values;
Defining a wrapping scheme W to fold the sequence into the two-dimensional symbol pattern P ^W ;
With
The method wherein the polynomial P (x), the mask pattern, and the wrapping scheme W are defined such that the transformation matrix T that implements the matrix equation B = TC has a rank N = n that exceeds Fq.   The method for creating a symbol pattern according to claim 1, wherein the wrapping scheme is defined to maintain a relative geometric order and a relationship between symbol values in the mask pattern and the coefficients. . S _k = G (f (x)), and G (f (x)) for an arbitrary polynomial f (x) is a coefficient of the monomial x ⁿ⁻¹ in f (x) modulo P (x) The method for creating a symbol pattern according to claim 1 or 2.   The method for creating a symbol pattern according to any one of claims 1 to 3, wherein the transformation matrix T is calculated by iterative squares.   5. A method in creating a symbol pattern according to any one of claims 1 to 4, wherein the wrapping scheme W comprises wrapping a sequence S in a row (or column) with a wrap length w.   5. A method according to claim 1, wherein the wrapping scheme W comprises wrapping the sequence S diagonally. The symbol C according to any one of claims 1 to 6, wherein the coefficient C has a size n and represents a state of a linear feedback shift register LFSR with bit holders of ^xn-1 to 1. the method of. In the wrapping scheme W, [q (X + 1, Y) -q (X, Y)] modulo L and [q (X, Y + 1) -q (X, Y)] modulo L are the symbol patterns P Defined to be constant for an arbitrary position (X, Y) in ^W , and q (X, Y) = k is a position (X, Y) in the symbol pattern P ^W and a place k in the sequence S The method for creating a symbol pattern according to claim 1, wherein L is a length of the sequence S. A method for locating a position (X, Y) of a mask B observed in a two-dimensional symbol pattern P ^W having a characteristic that an arbitrary mask B having a defined shape and a size of at least m symbol values is unique. The symbol pattern is based on a non-repeating sequence S of symbol values S _k corresponding to a fixed linear combination of the unary coefficients C in x ^k modulo each P (x), where P ( x) is an arbitrary polynomial of degree n in the field Fq, the symbol pattern P ^W is formed by folding the sequence S according to a wrapping scheme W;
Extracting information about the relationship between the symbol value in the mask B and the corresponding coefficient C;
Extracting the symbol value of the mask B at the position (X, Y);
And said B by relationships _X, coefficient the corresponding from _Y C _X, calculates the _Y, which is where B _X, the symbol value issued extract of B in _Y is the position (X, Y),
Calculating the location k in the sequence S, where the coefficient C is equal to C _{X, Y} ;
Calculating the position (X, Y) in the symbol pattern P ^W based on the location k and the wrapping scheme W;
A method comprising:   The method according to claim 9, wherein the relationship is a transformation matrix T that implements the matrix equation B = TC and has a rank N = n that exceeds Fq. The relationship is a transformation matrix that implements the matrix equation B = T′C and has a rank N = n−j that exceeds Fq;
Calculating a plurality of solutions of corresponding coefficients C _{X, Y} of B _{X, Y} = T′C _{X, Y} ;
Calculating a plurality of candidate locations k in the sequence where the coefficients of C are equal to C _{X, Y} ;
Calculating a plurality of candidate positions (X, Y) in the symbol pattern P ^W based on the location k and the wrapping scheme W;
Eliminating the false candidate position of the sought position;
The method of locating a position according to claim 9, further comprising:   The method of locating a position according to claim 11, wherein the false candidate positions are eliminated by checking a continuity condition. For error correction, and forming a '(check matrix H or H) by solving (= 0 the equation HT = 0 or _{H'T)', HB X, Y} = h i ( or H'B _{X, Y} = h _i ), and if h _i = 0, maintain B _{X, Y} , but if h _i ≠ 0, the symbol value at position i of B _{X, Y} 13. The method of locating a position according to any one of claims 10 to 12, further comprising changing. Compute the candidate transformation matrices T, T ′ for each set of shapes of the mask B until the candidate transformation matrices T, T ′ computed in this way have a rank N = n or n−j that exceeds Fq. And thus calculated for use in calculating the corresponding coefficients CX, Y with B _{X, Y} = TCX, Y (or B _{X, Y} = T'C _{X, Y} ) The method of locating a position according to any one of claims 10 to 13, further comprising selecting candidate transformation matrices T, T '.   The method according to claim 14, wherein the number m of symbol values in the mask B increases continuously in the set of shapes.   The wrapping scheme W includes folding the sequence S in a sequence of wrap lengths w and the position (X, Y) is calculated as ((k divisor w (k div w) modulo w) Item 16. A method for locating the position according to any one of Items 9 to 15. The location k in the sequence S where the coefficient C equals C _{X, Y} is calculated with an algorithm to find the discrete logarithm of k with rk≡xk having the coefficients CX, Y (modulo P (x)) A method for locating a position according to any one of claims 9 to 16.   18. A method according to any one of claims 9 to 17, repeated for many different positions of the mask B.   The method according to claim 18, wherein the shape of the mask and the relationship are maintained and fixed. Each is a method of calculating a symbol value S _k in a non-repeating sequence S of symbol values corresponding to a fixed linear combination G of monomial coefficients C in x ^k modulo P (x), where P ( x) is an arbitrary polynomial of degree n of the field Fq,
By iterative squares

Calculating
Deriving a symbol value S _k from G (r _k );
A method comprising: How the squared to calculate a symbol value according to claim 20 the use of retro-relationship ^x 2k ^{= (x k) 2} and ^{x2 k + 1 = x · x} 2k. A defined shape and at least a method of the m arbitrary mask B of size of the symbol value to calculate the subdivision B ^P symbol pattern P ^W having the property of being unique, the symbol pattern, each P ( based on a non-repeating sequence S of symbol values S _k corresponding to a fixed linear combination of monomial coefficients in x ^k modulo x), where P (x) is an arbitrary polynomial of degrees in the field Fq; A symbol pattern P ^W is formed by folding the sequence S according to a wrapping scheme W, and the subdivision ^BP represents a set of positions in the symbol pattern P ^W ;
Retrieving said set of positions;
Converting at least one of the positions into a location k in the sequence S based on the wrapping scheme W;
Calculating the symbol value S _k of the location k with the method of claim 20 or 21;
Said method comprising. In the wrapping scheme W, [q (X + 1, Y) -q (X, Y)] modulo L = d1 and [q (X, Y + 1) -q (X, Y)] modulo L = d2 any position in the symbol pattern P ^W (X, Y) is defined to be a constant for, q (X, Y) = k is in relationship between the location k in the symbol pattern PW and the sequence S And L is the length of the sequence;
For at least one other position displaced from the at least one position by a displacement vector (u, v), calculate x ^p · r _k , where d ₁ represents the displacement vector (u, v) and d _{2 is} a linear combination;
Deriving at least one other symbol value from G (x ^p · r _k );
The method further comprising: How Said sub B ^P of the pattern P ^W calculates the granularity according to claim 22 or 23 is adapted to cover an area to be printed. A two-dimensional symbol pattern P ^W having the property that the defined shape and size of at least m symbol values are unique,
Non-repeating sequence of symbol values S _k , each corresponding to a fixed linear combination of monomial coefficients C in x ^k modulo P (x), where P (x) is an arbitrary polynomial of degree n of the field Fq S and
With
The sequence S is folded into the two-dimensional symbol pattern P ^W according to a wrapping scheme W;
The polynomial (Px), the mask B, and the wrapping scheme W are defined such that the transformation matrix that implements the matrix equation B = TC has a rank N = n that exceeds Fq.   26. The symbol pattern of claim 25, wherein the wrapping scheme W is defined to maintain a relative geometric order and relationship between the mask B and the symbol values in the coefficient C. S _k = G (f (x)), and G (f (x)) for an arbitrary polynomial f (x) is a coefficient of the monomial x ⁿ⁻¹ in f (x) modulo P (x) The symbol pattern according to claim 25 or 26, wherein:   28. A symbol pattern according to any one of claims 25 to 27, wherein the wrapping scheme W comprises wrapping in rows (in columns) with a wrap length w.   28. A symbol pattern according to any one of claims 25 to 27, wherein the wrapping scheme W comprises wrapping the sequence S diagonally.   In the wrapping scheme W, [q (X + 1, Y) -q (X, Y)] modulo L and [q (X, Y + 1) -q (X, Y)] modulo L are arbitrary positions ( X, Y) is defined to be constant, and q (X, Y) k is the relationship between the position (X, Y) in the symbol pattern PW and the location k in the sequence S, and L 30. A symbol pattern according to any of claims 25 to 29, wherein is the length of the sequence S. System for determining the position (X, Y) of a mask B observed in a two-dimensional symbol pattern P ^W having the characteristic that an arbitrary mask B of defined shape and size of at least m symbol values is unique The symbol pattern is based on a non-repeating sequence S of symbol values S _k corresponding to a fixed linear combination of the coefficients C of the monomial at x ^k modulo P (x), respectively Where P (x) is an arbitrary polynomial of degree n of the field Fq, and the symbol pattern PW is formed by folding the sequence S according to a wrapping scheme W;
Memory means for storing information about the relationship between the symbol value in B and the corresponding coefficient C;
Extracting the symbol value of the mask B at the position (X, Y);
B _{X, Y} is the extracted symbol value B at the position (X, Y). The corresponding coefficient C _{X, Y} is calculated from B _{X, Y according} to the relationship. The coefficient C is changed to C _{X, Y.} Calculate a place k in an equal sequence S;
Calculating means adapted to calculate the position (X, Y) in the symbol pattern P ^W based on the location k and the wrapping scheme W;
The system comprising:   32. The system for locating a position according to claim 31, wherein the relationship is a transformation matrix T that implements the matrix equation B = TC and has a rank N = n greater than Fq. The relationship is a transition matrix T ′ that implements the matrix equation B = T′C and has a rank N = n−j that exceeds Fq;
Compute multiple solutions for the corresponding coefficients C _{X, Y} with B _{X, Y} = T′C _{X, Y} ,
Calculating a plurality of locations k in the sequence S with a coefficient C equal to C _{X, Y} ;
The system adapted to calculate a candidate position (X, Y) in the symbol pattern P ^W based on the location k and the wrapping scheme W, and to eliminate false candidate positions of the sought position.   34. A system for locating positions according to claim 33, wherein the computing means is adapted to eliminate false candidate positions by checking continuity conditions. Check matrix H (by solving equation HT = 0 (or H′T ′ = 0)
Or H ') is _{formed, HB X, Y = h i} ( or _{HB X,} Y = _{h i)} is _formed, in the case of _h i = _{0, B X,} but maintains the _Y,

35. The system for locating a position according to any one of claims 32 to 34, further comprising error correction means adapted to change the symbol value at position i of B _{X, Y.} The calculating means calculates a candidate transformation matrix for each set of shapes of the mask B until the candidate transformation matrix T, T ′ thus calculated has a rank N = n or n−j that exceeds Fq. Then, the transformation matrix T, T "calculated in this way is converted into the corresponding coefficient C _{X, Y} by B _{X, Y} = TC _{X, Y} (that is, BX, Y = T′C _{X, Y} ). 36. A system for locating a position according to any one of claims 32 to 35 adapted to be selected for use in calculating.   37. The system for locating a position according to claim 36, wherein the calculating means is adapted to successively increase the number m of symbol values of the mask B in the set of shapes.   38. A system for locating a position according to any one of claims 31 to 37, which is operated repeatedly for a number of different positions of the mask B.   39. The system for locating a position according to claim 38, wherein the calculating means is adapted to maintain the shape and relationship of the mask B. The computing means (modulo P (x))

There algorithm for detecting discrete logarithm of k with coefficient C _{X, Y,} is adapted to calculate a該場plants k in the sequence S, the coefficient C is C _X, equal to _Y, claim 40. A system for locating a position according to any one of 31 to 39.   Computer program product comprising program instructions for causing a computer to perform the method according to any one of claims 1 to 24.

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