<PAGE>   1
 
   
      AS FILED WITH THE SECURITIES AND EXCHANGE COMMISSION ON MAY 6, 1999
    
                                                      REGISTRATION NO. 333-72941
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                       SECURITIES AND EXCHANGE COMMISSION
                              Washington, DC 20549
                      ------------------------------------
 
   
                               Amendment No. 3 to
    
                                    Form S-3
                             REGISTRATION STATEMENT
                                   UNDER THE
                             SECURITIES ACT OF 1933
                      ------------------------------------
                           LASER VISION CENTERS, INC.
                   (Exact name of registrant in its charter)
 
<TABLE>
<S>                                <C>                                <C>
           DELAWARE                                                             43-1530063
   (State of jurisdiction of                                                 (I.R.S. Employer
incorporation or organization)                                            identification number)
</TABLE>
 
                     540 MARYVILLE CENTRE DRIVE, SUITE 200
                           ST. LOUIS, MISSOURI 63141
                                 (314) 434-6900
         (Address and telephone number of principal executive offices.)
 
                              ROBERT W. MAY, ESQ.
                     540 MARYVILLE CENTRE DRIVE, SUITE 200
                           ST. LOUIS, MISSOURI 63141
                                 (314) 434-6900
           (Name, address and telephone number of agent for service)
 
                                With copies to:
 
<TABLE>
<S>                                                 <C>
            JAMES R. DANKENBRING, ESQ.                             J. MARK KLAMER, ESQ.
   DANKENBRING GREIMAN OSTERHOLT & HOFFMANN P.C.                      BRYAN CAVE LLP
           120 SOUTH CENTRAL, SUITE 500                     ONE METROPOLITAN SQUARE, SUITE 3600
             ST. LOUIS, MISSOURI 63105                           ST. LOUIS, MISSOURI 63102
                  (314) 863-7733                                      (314) 259-2000
</TABLE>
 
APPROXIMATE DATE OF COMMENCEMENT OF PROPOSED SALE TO THE PUBLIC:
    As soon as possible following the effectiveness of this registration
statement.
    If the only securities being registered on this form are being offered
pursuant to dividend or interest reinvestment plans, please check the following
box.  [ ]
    If any of the securities being registered on this form are to be offered on
a delayed or continuous basis pursuant to Rule 415 under the Securities Act of
1933, other than securities offered only in connection with dividend or interest
reinvestment plan, check the following box.  [ ]
    If this form is filed to register additional securities for an offering
pursuant to Rule 462(b) under the Securities Act, please check the following box
and list the Securities Act registration statement number of the earlier
effective registration statement for the same offering.  [ ]
    If this form is a post-effective amendment filed pursuant to Rule 462(c)
under the Securities Act, check the following box and list the Securities Act
registration statement number of the earlier effective registration statement
for the same offering.  [ ]
    If delivery of the prospectus is expected to be made pursuant to Rule 434,
please check the following box.  [ ]
                      ------------------------------------
                        CALCULATION OF REGISTRATION FEE
 
<TABLE>
<S>                                            <C>                    <C>                      <C>
-----------------------------------------------------------------------------------------------------------------------
                                                                          PROPOSED MAXIMUM
           TITLE OF EACH CLASS OF                   AMOUNT TO BE         AGGREGATE OFFERING           AMOUNT OF
         SECURITIES TO BE REGISTERED               REGISTERED(1)            PRICE(1)(2)            REGISTRATION FEE
-----------------------------------------------------------------------------------------------------------------------
Common stock, par value $0.01 per share......        1,978,000              $54,395,000                $15,122
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</TABLE>
 
(1) Includes 258,000 shares that the underwriters have the option to purchase
    from selling stockholders to cover over-allotments, if any.
(2) Estimated solely for the purposes of computing the registration fee in
    accordance with Rule 457(c) under the Securities Act of 1933, as amended.
 
    THE REGISTRANT HEREBY AMENDS THIS REGISTRATION STATEMENT ON SUCH DATE OR
DATES AS MAY BE NECESSARY TO DELAY ITS EFFECTIVE DATE UNTIL THE REGISTRANT SHALL
FILE A FURTHER AMENDMENT WHICH SPECIFICALLY STATES THAT THIS REGISTRATION
STATEMENT SHALL THEREAFTER BECOME EFFECTIVE IN ACCORDANCE WITH SECTION 8(A) OF
THE SECURITIES ACT OF 1933, AS AMENDED (THE "ACT"), OR UNTIL THE REGISTRATION
STATEMENT SHALL BECOME EFFECTIVE ON SUCH DATE AS THE COMMISSION, ACTING PURSUANT
TO SAID SECTION 8(A), MAY DETERMINE.
    An Index of the Exhibits to this registration statement can be found at page
II-2.
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<PAGE>   2
 
                                    PART II
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                     INFORMATION NOT REQUIRED IN PROSPECTUS
 
ITEM 14. OTHER EXPENSES OF ISSUANCE AND DISTRIBUTION
 
     The following sets forth the costs and expenses, other than underwriting
discounts and commissions, payable by Laser Vision in connection with the sale
of common stock being registered hereunder:
 
<TABLE>
    <S>                                                           <C>
    SEC Registration fees.......................................  $ 15,122
    Blue Sky and Nasdaq National Market fees and expense........  $      *
    Printing cost...............................................  $      *
    Transfer agent fees.........................................  $      *
    Legal fees and expenses.....................................  $      *
    Accounting fees and expenses................................  $      *
    Miscellaneous...............................................  $      *
    NASD filing fee.............................................  $  5,940
    Nasdaq listing fee..........................................  $ 17,500
                                                                  --------
      Total.....................................................  $      *
                                                                  ========
</TABLE>
 
---------------
 
* To be provided by amendment.
 
ITEM 15. INDEMNIFICATION OF DIRECTORS AND OFFICERS
 
     Section 6 of Laser Vision's Certificate of Incorporation provides for
indemnification of the officers and directors of Laser Vision to the fullest
extent permitted by the laws of the State of Delaware.
 
     Section 145 of the General Corporation Law of the State of Delaware
provides generally and in pertinent part that a Delaware corporation may
indemnify its directors and officers against expenses, judgments, fines and
settlements actually and reasonably incurred by them in connection with any
civil suit or action, except actions by or in the right of the corporation, or
in connection with any administrative or investigative proceedings if, in
connection with the matters in issue, they acted in good faith and in a manner
they reasonable believed to be in, or not opposed to, the best interests of the
corporation and in connection with any criminal suit or proceeding, if in
connection with the matters in issue, they had no reasonably cause to believe
their conduct was unlawful. Section 145 further permits a Delaware corporation
to grant its directors and officers additional rights of indemnification through
bylaw provisions and otherwise and to purchase indemnity insurance on behalf of
its directors and officers.
 
     The Registrant maintains a policy of insurance under which the directors
and officers of the Registrant are insured, subject to the limits of the policy,
against certain losses arising from claims made against such directors and
officers by reason of any acts or omissions covered under such policy in their
respective capacities as directors or officers.
 
                                      II-1
<PAGE>   3
 
ITEM 16. EXHIBITS
 
   
<TABLE>
<S>      <C>
1.1**    Form of Underwriting Agreement
4.1*     Specimen Stock Certificate
5.1**    Opinion of Dankenbring Greiman Osterholt & Hoffmann, P.C.
         with respect to the shares being registered
23.1***  Consent of Independent Accountants, PricewaterhouseCoopers
         LLP
23.2**   Consent of Dankenbring Greiman Osterholt & Hoffmann, P.C. to
         use its opinion letter filed herewith (contained in Opinion
         Letter at Exhibit 5.1)
24.1***  Power of Attorney executed by Laser Vision's officers and
         directors appointing John J. Klobnak and Robert W. May as
         attorneys-in-fact
</TABLE>
    
 
---------------
 
*   Incorporated by reference from registration statement No. 33-33843 effective
    on April 3, 1991
 
**  Filed herewith
 
*** Previously filed
 
   
ITEM 17. UNDERTAKINGS
    
 
     Insofar as indemnification for liabilities arising under the Securities Act
of 1933, as amended (the "Securities Act") may be permitted to directors,
officers and controlling persons of the Registrant pursuant to the foregoing
provisions, or otherwise, the Registrant has been advised that in the opinion of
the Securities and Exchange Commission such indemnification is against public
policy as expressed in the Securities Act and is, therefore, unenforceable. In
the event that a claim for indemnification against such liabilities (other than
the payment by the Registrant of expenses incurred or paid by a director,
officer or controlling person of the Registrant in the successful defense of any
action, suit or proceeding) is asserted by such director, officer or controlling
person in connection with the securities being registered, the Registrant will,
unless in the opinion of its counsel the matter has been settled by controlling
precedent, submit to a court of appropriate jurisdiction the question whether
such indemnification by it is against public policy as expressed in the
Securities Act and will be governed by the final adjudication of such issue.
 
Laser Vision hereby undertakes:
 
(1) To file, during any period in which offers or sales are being made, a
Post-Effective Amendment to this registration statement:
 
     (i) To include any prospectus required by section 10(a) of the Securities
     Act;
 
     (ii) To reflect in the prospectus any facts or events arising after the
     Effective Date of the registration statement (or the most recent
     Post-Effective Amendment thereof) which, individually or in the aggregate,
     represent a fundamental change in the information set forth in the
     registration statement;
 
     (iii) To include any material information with respect to the plan of
     distribution not previously disclosed in the registration statement or any
     material change to such information in the registration statement;
 
provided, however, that paragraphs (1)(i) and (1)(ii) do not apply if the
information required to be included in a post-effective amendment by those
paragraphs is contained in periodic reports filed by the registrant pursuant to
Section 13 or Section 15(d) of the Securities Exchange Act of 1934 (the
"Exchange Act") that are incorporated by reference in the registration
statement.
 
(2) That, for the purpose of determining liability under the Securities Act,
each Post-Effective amendment shall be deemed to be a new registration statement
relating to the securities offered therein, and the offering of such securities
at that time shall be deemed to be the initial bona fide offering thereof.
 
                                      II-2
<PAGE>   4
 
(3) To remove from registration by means of a Post-Effective amendment any of
the securities being registered which remain unsold at the termination of the
offering.
 
(4) That, for purposes of determining any liability under the Securities Act,
the information omitted from the form of prospectus filed as part of the
registration statement in reliance upon Rule 430A and contained in a form of
prospectus filed by the Registrant pursuant to Rule 424(b)(1) or (4) or 497(h)
under the Securities Act shall be deemed to be part of this registration
statement as of the time it was declared effective.
 
(5) That for purposes of determining any liability under the Securities Act,
each filing of the Registrant's annual report pursuant to section 13(a) or
section 15(d) of the Exchange Act (and where applicable, each filing of an
employee benefit plan's annual report pursuant to section 15(d) of the Exchange
Act) that is incorporated by reference in the registration statement shall be
deemed to be a new registration statement relating to the securities offered
therein, and the offering of such securities at that time shall be deemed to be
the initial bona fide offering thereof.
 
(6) That for the purposes of determining any liability under the Securities Act,
each post-effective amendment that contains a form of prospectus shall be deemed
to be a new registration statement relating to the securities offered therein
and the offering of such securities at that time shall be deemed to be the
initial bona fide offering thereof.
 
                                      II-3
<PAGE>   5
 
                                   SIGNATURES
 
   
     In accordance with the requirements of the Securities Act of 1933, the
Registrant has duly caused this registration statement to be signed on its
behalf by the undersigned, thereunto duly authorized, in the County of St.
Louis, Missouri on the 6th day of May, 1999.
    
 
                                          LASER VISION CENTERS, INC.
 
                                          By: /s/    JOHN J. KLOBNAK
 
                                            ------------------------------------
 
                                                      John J. Klobnak,
                                                Chief Executive Officer and
                                             Chairman of the Board of Directors
 
     Pursuant to the requirements of the Securities Act of 1933, this
registration statement has been signed by the following persons in the
capacities and on the dates indicated.
 
   
<TABLE>
<CAPTION>
                  SIGNATURE                                    TITLE                         DATE
                  ---------                                    -----                         ----
<C>                                            <S>                                     <C>
 
             /s/ JOHN J. KLOBNAK               Chief Executive Officer and Chairman    May 6, 1999
---------------------------------------------  of the Board of Directors
               JOHN J. KLOBNAK
 
              /s/ ROBERT W. MAY                Vice-Chairman of the Board, General     May 6, 1999
---------------------------------------------  Counsel and Secretary
                ROBERT W. MAY
 
          /s/ B. CHARLES BONO, III             Executive Vice President, Principal     May 6, 1999
---------------------------------------------  Accounting Officer, Chief Financial
            B. CHARLES BONO, III               Officer and Treasurer
 
       /s/ RICHARD L. LINDSTROM, M.D.*         Director                                May 6, 1999
---------------------------------------------
         RICHARD L. LINDSTROM, M.D.
 
            /s/ DR. HENRY SIMON*               Director                                May 6, 1999
---------------------------------------------
               DR. HENRY SIMON
 
            /s/ JAMES M. GARVEY*               Director                                May 6, 1999
---------------------------------------------
               JAMES M. GARVEY
 
            /s/ STEVEN C. STRAUS*              Director                                May 6, 1999
---------------------------------------------
              STEVEN C. STRAUS
 
          *By: /s/ JOHN J. KLOBNAK                                                     May 6, 1999
   ---------------------------------------
        John J. Klobnak, individually
           and as Attorney-in-fact
</TABLE>
    
 
                                      II-4